Mean-field control method for rapid electrolysis power allocation in large-scale hydrogen production arrays

Abstract

The present invention provides a mean-field control method for rapid distribution of electrolysis power of a large-scale hydrogen production array, the steps of which include: constructing a dynamic hyperbox model and a hydrogen production efficiency optimization function of the hydrogen production array, as well as a hydrogen production dynamic model and a controlled input electrolysis power of each electrolytic stack according to the hydrogen production efficiency; constructing a dynamic partial differential equation of the hydrogen production array according to the hydrogen production dynamic model, a compensated Poisson martingale measure, the controlled input electrolysis power and the hydrogen production efficiency optimization function; constructing an efficiency value function of each electrolytic stack according to the hydrogen production efficiency optimization function; constructing a mean-field term of the hydrogen production array according to the hydrogen production dynamic model; constructing an HJB equation according to the dynamic partial differential equation and the efficiency value function; constructing an FPK equation according to the dynamic partial differential equation and the mean-field term; and solving the HJB equation and the FPK equation based on the dynamic hyperbox model to obtain an optimal control strategy, thereby ensuring load balancing while fully considering the life status of electrolytic cell monomers and differences in hydrogen production performance.

Description

Technical Field

[0001] The present invention relates to the technical field of electrolytic hydrogen production in new energy stations, and in particular to a mean field control method for rapid distribution of electrolytic power for large-scale hydrogen production arrays. Background Art

[0002] In renewable energy hydrogen production systems, existing research addresses the impact of fluctuating power sources on hydrogen production. This research typically utilizes operational control methods that couple electrical energy storage / supercapacitors with hydrogen production arrays to suppress power fluctuations that prevent electrolyzers from effectively handling the load, reduce the number of starts and stops, and slow down the degradation of their lifespan, thereby improving the dynamic operational efficiency of hydrogen electrolysis. Traditional control methods for hydrogen production array scheduling rely on preset rules and manual adjustments based on experience, lacking flexibility and real-time optimization capabilities, resulting in low hydrogen production system efficiency and high energy consumption. AI-powered control methods, such as reinforcement learning and supervised learning, dynamically adjust and adaptively control the start and stop cycles of electrolyzers and the number of operating units, effectively reducing the number of starts and stops, balancing loads between electrolyzers, and controlling temperature fluctuations, thereby improving hydrogen production and electrolyzer lifespan. However, most of these studies addressing the impact of renewable energy fluctuations and operational strategies for hydrogen production arrays focus on the overall electrolyzer array, either smoothing out the fluctuations of renewable energy when connected to the grid or directly absorbing it when off-grid. These coordinated control strategies fail to consider the regulatory characteristics of individual cells in the array. Summary of the Invention

[0003] The present invention addresses the problems existing in the prior art and provides a mean field control method for rapid distribution of electrolytic power for large-scale hydrogen production arrays, which ensures load balancing while fully considering the life status of electrolytic cell monomers and differences in hydrogen production performance.

[0004] To achieve the above objectives, the present invention adopts the following technical solution: a mean-field control method for rapid electrolysis power distribution in a large-scale hydrogen production array, comprising the following steps: obtaining the hydrogen production efficiency of each electrolysis stack in the hydrogen production array; obtaining a compensated Poisson martingale measure;

[0005] Constructing a dynamic superbox model of the hydrogen production array according to the hydrogen production efficiency; constructing a hydrogen production dynamic model and a controlled input electrolysis power of each electrolysis stack, and a hydrogen production efficiency optimization function of the hydrogen production array according to the hydrogen production efficiency, wherein the variables of the hydrogen production dynamic model and the variables of the hydrogen production efficiency function are respectively the controlled input electrolysis power;

[0006] Constructing a dynamic partial differential equation of the hydrogen production array according to the hydrogen production dynamic model, the compensated Poisson martingale measure, the controlled input electrolysis power and the hydrogen production efficiency optimization function; constructing an efficiency value function of each electrolysis stack according to the hydrogen production efficiency optimization function; constructing a mean field term of the hydrogen production array according to the hydrogen production dynamic model;

[0007] An HJB equation is constructed based on the dynamic partial differential equation and the efficiency value function; an FPK equation is constructed based on the dynamic partial differential equation and the mean field term; based on the dynamic hyperbox model, the HJB equation and the FPK equation are solved to obtain an optimal control strategy, which is an optimal value set of the controlled input electrolysis power.

[0008] In some embodiments, the hydrogen production efficiency optimization function includes a final penalty function, and the final penalty function is used to constrain a final hydrogen production efficiency state of the hydrogen production array.

[0009] In some embodiments, based on the dynamic hyperbox model, the steps of solving the HJB equation and the FPK equation to obtain the optimal control strategy are:

[0010] Step S1: Solve the dynamic hyperbox model to obtain a dynamic hyperbox set, which includes A dynamic hyperbox, is the total number of the dynamic hyperboxes in the dynamic hyperbox set; initializing and obtaining an initial mean field term value set, a final penalty function, and an initial hydrogen production state of each electrolytic stack; obtaining an iteration step size; presetting a first convergence threshold and a second convergence threshold; the first convergence threshold is the convergence threshold of the efficiency value function, and the second convergence threshold is the convergence threshold of the mean field term;

[0011] Step S2: obtaining a current hydrogen supply amount set according to the dynamic super box set and the initial hydrogen production state of each electrolytic stack, wherein the current hydrogen supply amount set is a collection of the current hydrogen supply amount of each dynamic super box;

[0012] Step S3: Based on the initial mean field term value set, the current hydrogen supply amount set and the iteration step, obtain the current mean field term value set according to the FPK equation;

[0013] Step S4: Based on the current mean field term value set, the iteration step size, the final penalty function and the current hydrogen supply amount set, a current efficiency value set and a current control strategy are calculated according to the HJB equation;

[0014] Step S5: obtaining a first convergence judgment according to the current efficiency value set and the first convergence threshold, and obtaining a second convergence judgment according to the current mean field item value set and the second convergence threshold;

[0015] Step S6: respectively judging whether the first convergence judgment and the second convergence judgment are established:

[0016] If at least one of the first convergence judgment or the second convergence judgment is not established, updating the initial average field item value set according to the current average field item value set, and updating the current hydrogen supply amount set according to the current average field item value set and the current control strategy, and repeating steps S3 to S6;

[0017] If both the first convergence judgment and the second convergence judgment are established, the optimal control strategy is obtained according to the current control strategy.

[0018] In some embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains an optimal value set of the efficiency value function.

[0019] In some embodiments, based on the dynamic hyperbox model, a method for solving the HJB equation and the FPK equation and obtaining an optimal value set of the efficiency value function is:

[0020] If both the first convergence judgment and the second convergence judgment are established, the optimal value set of the efficiency value function is obtained according to the current efficiency value set.

[0021] In some embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains a system probability distribution, which is an optimal value set of the mean field term.

[0022] In some embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains a system probability distribution, and the system probability distribution is a method for obtaining an optimal value set of the mean field term:

[0023] If both the first convergence judgment and the second convergence judgment are established, the system probability distribution is obtained according to the current efficiency value set.

[0024] In some embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains an optimal hydrogen supply set, which is a collection of optimal hydrogen supply amounts for each dynamic hyperbox.

[0025] In some embodiments, based on the dynamic hyperbox model, the method for solving the HJB equation and the FPK equation to obtain the optimal hydrogen supply amount set is:

[0026] If both the first convergence judgment and the second convergence judgment are established, the optimal hydrogen supply amount set is obtained according to the current efficiency value set and the current control strategy.

[0027] In some embodiments, the HJB equation and the FPK equation are solved using a finite difference approximation method.

[0028] Compared with the prior art, the present invention has the following beneficial effects:

[0029] 1. The present invention constructs a dynamic superbox model for a hydrogen production array that takes into account the flexible combination of electrolytic cell units. In this dynamic superbox model, by analyzing the dynamic safety fluctuation tolerance range of the electrolytic cell power and the hydrogen production efficiency, electrolytic stacks with similar hydrogen production efficiency are divided into the same dynamic superbox to reduce the dimensionality of the controlled object. At the same time, the hydrogen production array dynamically adjusts the superbox particle center of the dynamic superbox according to the overall hydrogen production efficiency status, ensuring load balancing while fully considering the life status of the electrolytic cell units and the differences in hydrogen production performance;

[0030] 2. This paper considers the uncertainty caused by random power fluctuations and electrolytic reactor failures and constructs a linear quadratic HJB-FPK partial differential equation with Poisson jumps, overcoming the dimensionality curse caused by the increase in the number of electrolytic reactors. Furthermore, based on the Hamiltonian canonical equations, the existence of mean-field controlled equilibrium is proved.

[0031] 3. The present invention adopts a hybrid finite difference scheme that takes into account both high-order accuracy and numerical stability, and uses derivative approximation to solve the equilibrium value of the equilibrium field. The stability, compatibility and convergence of the proposed hybrid finite difference scheme are proved according to the energy method, truncation error analysis and Lax equivalence theorem, respectively, to ensure the solution of the HJB-FPK equations and obtain the optimal control strategy. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 This is a flow chart of the mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to the present invention;

[0033] Figure 2 It is the framework of the renewable energy hydrogen production system of the present invention;

[0034] Figure 3 This is a technical framework diagram of the mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to the present invention;

[0035] Figure 4 This is a flow chart of solving the HJB equation and the FPK equation to obtain the optimal control strategy based on the dynamic hyperbox model in an embodiment of the present invention.

[0036] Among them, the accompanying drawings are marked as: 1. Renewable energy power generation equipment; 2. Power distributor; 3. Hydrogen production array; 31. Dynamic super box; 311. Electrolysis stack; 4. High-pressure hydrogen storage tank; 5. Transmission line; 6. Hydrogen transmission line. DETAILED DESCRIPTION

[0037] How to achieve rapid and reasonable distribution of electrolytic hydrogen production power within a large-scale electrolytic cell array at a new energy station directly affects the operating life of the electrolytic cell array, hydrogen production efficiency, and the electric-hydrogen fusion characteristics of the renewable energy system. In response to the above problems, the current multi-mechanism hydrogen power allocation strategies mainly include average allocation, chain allocation, and rotation coordination control. The average allocation strategy evenly distributes the total hydrogen production power of the array to each electrolytic cell, which can easily cause multiple electrolytic cells to operate simultaneously under fluctuating power and frequent start-stop conditions, especially under low-power conditions, with poor operating economy and low safety; the core idea of ​​the chain allocation strategy is to allocate step by step according to the electrolytic cell load rate, which has the problem of uneven fluctuation load and operating time of the electrolytic cell cells; the rotation coordination control strategy rotates the electrolytic cells in groups at a certain time, which can achieve load balancing to a certain extent, but it does not take into account the life status and hydrogen production performance differences of the electrolytic cell cells.

[0038] Mean-field control, originally derived from mean-field theory in statistical physics, was primarily applied in fields such as economics and sociology, and subsequently expanded into the fields of communications and power generation. Applications include energy management for large numbers of plug-in hybrid electric vehicles, joint channel access and power control optimization in unmanned aerial vehicle networks, and real-time peak regulation in virtual power plants. By simplifying the complex interactions between controlled objects, mean-field control enables modeling and optimization of the overall behavior of large-scale systems. This approach offers advantages such as reduced computational complexity, enhanced system stability, and improved resource allocation efficiency. Therefore, mean-field control provides an effective approach for optimizing the coordination between multiple hydrogen production units while considering the overall hydrogen production performance of the array. The operating state of each unit is influenced not only by its own control strategy but also by the overall mean-field distribution of hydrogen production performance. Few studies have explored mean-field control strategies for large-scale hydrogen production arrays operating under fluctuating electrolysis power conditions.

[0039] To clearly illustrate the technical features of this solution, the following detailed description of the implementation methods of this application will be given in conjunction with the accompanying drawings and examples, so that the implementation process of how this application applies technical means to solve technical problems and achieve corresponding technical effects can be fully understood and implemented accordingly. The embodiments of this application and the various features therein can be combined with each other as long as they do not conflict with each other, and the resulting technical solutions are all within the scope of protection of this application.

[0040] See also Figure 1 , an embodiment of the present invention provides a mean-field control method for rapid distribution of electrolysis power in a large-scale hydrogen production array, comprising the following steps: obtaining the hydrogen production efficiency of each electrolysis stack in the hydrogen production array; obtaining a compensated Poisson martingale measure;

[0041] Figure 2The diagram shows the framework of a Renewable-Dominated Hydrogen Production System (RHPS) with a large-scale electrolyzer array (hydrogen production array) for green hydrogen production. Typically, an RHPS is equipped with various renewable energy sources (RES). Renewable energy generation equipment 1, such as photovoltaic panels (PV) and wind turbines (WT), generates electricity to power a hydrogen production array 3, producing green hydrogen to meet the RHPS's hydrogen supply needs. Excess hydrogen is stored in high-pressure hydrogen storage tanks 4. Here, PEM (proton exchange membrane) electrolyzers serve as hydrogen production units, with a large number of electrolyzers, or stacks, connected in parallel to form a complete electrolyzer array. The electrolysis power instructions of the hydrogen production array 3 are distributed to each electrolytic stack through the power distributor 3 to meet the hydrogen production demand. Electric energy is transmitted between the renewable energy power generation equipment 1 and the power distributor 3, and between the power distributor 3 and the hydrogen production array 3 through the transmission line 5, and hydrogen energy is transmitted between the hydrogen production array 3 and the high-pressure hydrogen storage tank 4 through the hydrogen transmission line 6; when distributing the electrolysis power instructions through the power distributor 3, the hydrogen production array 3 is first divided into homogeneous particles to obtain a dynamic super box set, which includes at least one dynamic super box 31, and each dynamic super box 31 includes at least one electrolytic stack 311. The electrolysis power instructions are distributed through the power distributor 3 based on the dynamic super box set.

[0042] According to Faraday's law and fitting relationship, the generation efficiency of H2 is the hydrogen production efficiency It can be expressed as the Faraday efficiency and voltage efficiency The joint function of is shown in formula (1):

[0043] (1)

[0044] Where, is the first temperature characteristic parameter, is the second temperature characteristic parameter, for t The electrolysis current of the electrolysis stack array at the moment, t For time, is the cross-sectional area, is the electrolysis temperature, for t The electrolysis voltage of the electrolysis stack array at the moment, is the temperature change parameter, is the standard reference temperature, is the initial reverse voltage, is the first function;

[0045] Referring to formula (2), the electrolysis power is:

[0046] (2)

[0047] Where, for t The generated power at time H2 is t The electrolysis power at the moment, is the calorific value of H2, is the molar mass of H2, is the number of electrolytic cells in a stack, i.e. an electrolytic stack comprising at least one electrolytic cell, typically an electrolytic stack comprising at least two electrolytic cells connected in series, is the second function;

[0048] Theoretically, based on the fitting relationship between hydrogen production efficiency, electrolysis power, and electrolysis current, it can be found that hydrogen production efficiency increases with the increase of electrolysis power and gradually decreases after reaching a certain extreme value;

[0049] Construct a dynamic hyperbox model of the hydrogen production array based on hydrogen production efficiency;

[0050] Using mean field control to distribute electrolysis power regulation commands for hydrogen production can achieve rapid and large-scale decomposition. The core idea is to simplify a large number of interacting participant systems into the interaction between a representative participant and the mean field (the average effect of all participant behaviors). However, a large number of electrolysis stacks in an electrolysis stack array are not exactly the same, making it difficult to schedule them uniformly. Therefore, a dynamic superbox granulation model, i.e., a dynamic superbox model of a hydrogen production array, is constructed to divide the large-scale electrolysis stack array into smaller dynamic superbox sets, which include Specifically, we first construct a quadruple information system containing information on the hydrogen production capacity of the electrolytic stack. Formula (3):

[0051] (3)

[0052] Where, For electrolytic stack assembly, , For the first electrolytic stack, For the second electrolytic stack, For the n An electrolytic stack, n is the total number of electrolytic stacks, is the hydrogen production efficiency attribute set, D , is the hydrogen production efficiency of the first electrolyzer, is the hydrogen production efficiency of the second electrolyzer, For the n The hydrogen production efficiency of an electrolysis stack is is a standard attribute set, , For the The standard properties of a dynamic hyperbox, is the total number of dynamic hyperboxes, numerically same , is the dynamic hyperbox similarity function, Used to measure the similarity between each electrolysis stack condition attribute, i.e., hydrogen production efficiency attribute, and the standard attribute;

[0053] The homogeneous particle partitioning aims to make the hydrogen production efficiency properties of the electrolysis stacks within the dynamic superbox as similar as possible while ensuring the differences between the dynamic superboxes, as shown in Equations (4) and (5):

[0054] (4)

[0055] (5)

[0056] Where, For the The similarity function of a dynamic hyperbox, is the serial number of the dynamic hyperbox, For the The hydrogen production efficiency of an electrolysis stack is is the serial number of the electrolytic stack, For the The standard properties of a dynamic hyperbox, For the The radius of the dynamic hyperbox, For the A dynamic hyperbox electrolytic stack collection, is the maximization function;

[0057] Assemble the electrolytic stack The large-scale electrolysis stacks in the paper are divided into a set of homogeneous dynamic superboxes with different standard properties. In each dynamic superbox, the single electrolysis stacks have similar characteristics for power dynamic fluctuations and hydrogen production efficiency.

[0058] According to the hydrogen production efficiency, a hydrogen production dynamic model and a controlled input electrolysis power are constructed for each electrolysis stack, as well as a hydrogen production efficiency optimization function of the hydrogen production array. The variables of the hydrogen production dynamic model and the hydrogen production efficiency function are the controlled input electrolysis power.

[0059] First, a mean field control model is constructed: the electrolysis power of the electrolysis stack array should be quickly decomposed and distributed to reasonable electrolysis stacks, which is conducive to these electrolysis stacks producing hydrogen with optimal hydrogen production efficiency and reducing life degradation. In order to determine the optimal hydrogen production power distribution, that is, the controlled input electrolysis power, a linear quadratic mean field control model with Poisson jump is proposed : ;in, is the set of controlled objects, , Contains the entire main body of the hydrogen production array, is the total number of electrolytic stacks in the hydrogen production array, numerically n same , is the state space, represents the feasible domain of hydrogen production of each electrolytic stack in the hydrogen production array, , For decision space, represents the feasible domain of the controlled input electrolysis power of each electrolysis stack in the hydrogen production array, , is the efficiency function, Indicates the optimal hydrogen production efficiency of the hydrogen production array;

[0060] No. Electrolytic stack t The hydrogen production at the time is expressed as ,Right now Indicates the Electrolytic stack t The hydrogen production status at the moment, For the end of time, Electrolytic stack t The controlled input electrolysis power at the moment is , is a function of time and hydrogen production.

[0061] If the electrolysis stack equipment is in the process of producing hydrogen through electrolysis, >0, and if the electrolysis stack equipment does not perform electrolysis, then = 0. Therefore, the hydrogen production dynamic model of the electrolytic stack equipment is formula (6):

[0062] (6)

[0063] The diffusion coefficient of the state equation of the electrolytic reactor operation includes the state term and the control term, and the state equation contains the compensated Poisson martingale measure, which is the Poisson jump term. Due to the volatility of renewable energy output, the Poisson jump term can be used to simulate the volatility of renewable energy output and deal with emergencies in the electrolytic reactor, which can more realistically simulate and control the electrolytic reactor array. express dimensional Euclidean space, is the total number of electrolytic stacks, is defined as the standard Brownian motion, For the Electrolytic stack t The fluctuation of input power at any moment, is the total number of electrolytic stacks, It is used to characterize the fluctuation of input power of electrolytic stack array. Independent Poisson random measures , denoted as the compensated Poisson martingale measure, Used to characterize possible emergencies in electrolytic stacks.

[0064] Assuming that the hydrogen production of each electrolysis stack is The stochastic differential equation with Poisson jumps in equation (7) is satisfied:

[0065] (7)

[0066] Where, is the first constant, is the second constant, is the third constant, For t The hydrogen production of other electrolytic reactors in the hydrogen production array at this moment The impact of the hydrogen production of the electrolysis stack, , is the probability distribution space of Poisson jump terms, For the The initial boundary of the hydrogen production state of the electrolysis stack, that is, The initial hydrogen production state of an electrolysis stack; under this assumption, Proportional to the difference in hydrogen production;

[0067] For the hydrogen production array, the hydrogen production efficiency optimization function Formula (8):

[0068] (8)

[0069] Where, the hydrogen production efficiency optimization function is To maximize the hydrogen production efficiency function, is the hydrogen production, is the controlled input electrolysis power, is the mathematical expectation, for t The penalty function of the process at time t, It represents the function of penalizing the electrolytic stack with low hydrogen production efficiency in the hydrogen production process, is the final penalty function, which is used to constrain the final hydrogen production efficiency state of the hydrogen production array;

[0070] The dynamic partial differential equation of the hydrogen production array is constructed based on the hydrogen production dynamic model, compensated Poisson martingale measure, controlled input electrolysis power and hydrogen production efficiency optimization function. , is the Hamiltonian function, see equations (9) and (10);

[0071] (9)

[0072] (10)

[0073] Where, is the Lagrange multiplier of the adjoint variable corresponding to hydrogen production, for t The hydrogen production at this moment is The average field value at time ;

[0074] Constructing the efficiency value function of each electrolysis stack according to the hydrogen production efficiency optimization function;

[0075] time t No. Efficiency value function of an electrolytic stack Indicates that under optimal control, from the moment t The current state of hydrogen production S Start, Optimization function of hydrogen production efficiency of an electrolysis stack The maximum value of the efficiency value function As shown in formula (11):

[0076] (11)

[0077] Where, represents the power constraint under different hydrogen production rates, To maximize the function, is the current time;

[0078] The mean field term of hydrogen production array is constructed based on the hydrogen production dynamic model;

[0079] In a hydrogen production array, the hydrogen production of each electrolytic stack is not only affected by its own state, but also related to the overall hydrogen production state distribution of other electrolytic stacks in the entire system. This influence is reflected by the mean field term. The mean field term can handle the state of the electrolytic stack in a large-scale system. By considering the interaction between the electrolytic stacks and the state distribution of the array as a whole, the optimal performance of the hydrogen production efficiency of the hydrogen production array can be achieved. As shown in formula (12):

[0080] (12)

[0081] Where, δ is the Dirac coefficient, and when the given conditions are met δ The value returns 1 if the given condition is not met δ The value returns 0. Therefore, the mean field term Indicates t At this moment, the hydrogen production state of the electrolysis stack is S The probability density function of

[0082] Due to the number of electrolytic stacks N tends to infinity, a large number of electrolytic stacks can be modeled as a continuum, so It can be regarded as a continuous probability density function and satisfies formula (13):

[0083] (13)

[0084] The mean-field equilibrium strategy is generated by the coupled HJB-FPK equations, where the HJB equations are related to the efficiency value function, while the FPK equations are related to the mean-field term, i.e., the probability distribution function.

[0085] For the optimization functional problem, the HJB equation is constructed based on the dynamic partial differential equation and the efficiency value function, see formula (14):

[0086] (14)

[0087] According to HJB's dynamic programming principle, the optimal control strategy of the electrolytic stack array can be obtained , as shown in formula (15):

[0088] (15)

[0089] Where, It represents the value of P when the objective function is minimized. The objective function is the dynamic partial differential equation ;

[0090] The FPK equation describes the mean field term under optimal control The evolution of , and affects the mean field distribution in the HJB equation, forming a coupled system. Based on the dynamic partial differential equation and the mean field term, the FPK equation is constructed as shown in Equation (16):

[0091] (16)

[0092] Where, is the initial mean field term distribution state, that is, the initial mean field term value;

[0093] Based on the dynamic hyperbox model, the HJB equation and FPK equation are solved to obtain the optimal control strategy, which is the optimal value set of the controlled input electrolysis power.

[0094] The FPK equation describes the mean-field term The changes over time are determined by the system dynamics equation, i.e. the dynamic partial differential equation H The decision term includes the controlled input electrolysis power and equations (9) and (12); the HJB equation gives the optimal control strategy , from formula (9) (11) (14), we can see that the optimal control strategy Depends on the current hydrogen supply S ; Through the optimal control strategy and hydrogen supply S Changes over time, affecting the state distribution, i.e., the mean field term The mean field term is obtained from FPK And bring it into the HJB equation, and get the optimal control strategy by solving the HJB equation , and then the optimal control strategy Feedback to FPK, update the system probability distribution until each electrolytic stack is based on the mean field term and optimal control strategy The optimal decision is made and the hydrogen production cannot be increased by unilaterally changing the controlled input electrolysis power, i.e., convergence.

[0095] Considering that heterogeneous electrolytic stack combinations, i.e. different dynamic superboxes, have different hydrogen production efficiencies, homogeneous electrolytic stack combinations, i.e. the same dynamic superbox, have the same hydrogen production efficiency. It can be calculated by formula (17):

[0096] (17)

[0097] Where, For the The number of electrolytic stacks in a dynamic hyperbox, is the sequence number of the dynamic hyperbox in the dynamic hyperbox set, , is the total number of dynamic hyperboxes in the dynamic hyperbox set, is the minimum hydrogen production of the electrolysis array, is the maximum hydrogen production of the electrolysis array, for Moment A dynamic super box has a hydrogen supply of The optimal control strategy under for Moment A dynamic super box has a hydrogen supply of The mean field term under For the The hydrogen supply of each dynamic super box;

[0098] Optimal control strategy Proof of existence:

[0099] When Solve the optimal control strategy for an electrolytic stack When , it will produce a control equilibrium solution. Let ( , ) The optimal control strategy of an electrolytic stack and the optimal control strategy of other individuals Then, if and only if the condition of formula (18) is satisfied for each electrolytic stack in the hydrogen production array control, the control strategy ( , ) is a control equilibrium:

[0100] (18)

[0101] Where, Indicates any choice, is a set of controlled input electrolysis power strategies;

[0102] A sufficient condition for the existence of a control equilibrium is that the HJB equation has a solution. If the Hamiltonian is smooth, then the HJB equation has a solution. According to the one-dimensional diffusion HJB equation with Poisson jumps, the Hamiltonian is defined as Equation (19):

[0103] (19)

[0104] Where, is the gradient symbol;

[0105] Due to the continuity of the efficiency value function, the derivatives of all orders of the Hamiltonian exist, so the Hamiltonian is smooth and the HJB equation has at least one solution , that is, there is at least one Nash equilibrium solution, namely the optimal control strategy .

[0106] In some embodiments, the HJB equation and the FPK equation are solved using a finite difference approximation method.

[0107] The HJB equation and the FPK equation are called the HJB-FPK equations. In the mean field HJB-FPK equations, the partial differential equations are and are coupled together, so there is no optimal control strategy Because explicit expressions for the HJB-FPK equations are not available, a hybrid finite difference method is employed, balancing high-order accuracy and numerical stability. The convection term in the HJB-FPK equations uses an inverse-wind scheme to ensure stability, while the diffusion term in the HJB-FPK equations uses a central difference scheme to ensure accuracy. By meshing the computational domain and performing a complete approximation of the derivatives in the HJB-FPK equations, a pair of difference schemes for the numerical solution of the HJB-FPK equations is derived. The stability, compatibility, and convergence of the proposed difference schemes are demonstrated.

[0108] First, the feasible domain space to be optimized Unit time and unit status Divide into grids, Represents the efficiency value function V At the point The approximate value at , where , , For in time t The step length taken in the previous term, In state S The forward Euler discretization format of HJB is approximately as follows:

[0109] (20)

[0110] Where, is the standard symbolic function, A monotonically increasing mathematical identifier for the function;

[0111] (twenty one)

[0112] Where, is the first intermediate expression, ;

[0113] The forward Euler discretization format of FPK is approximately as follows:

[0114] (twenty two)

[0115] See also Figure 3 , stability proof:

[0116] Only when The formula (20) is stable, where is the second intermediate expression. The stability of Equation (20) is a sufficient condition for the stability of the mixed finite difference scheme, that is, it satisfies the special case Therefore, The stability analysis is performed using Equation (11) under the condition of

[0117] According to the Courant-Friedrichs-Lewy condition, the sufficient condition for (20) and (22) to remain stable is the grid spacing and The conditions satisfying formula (23) are:

[0118] (twenty three)

[0119] Proof: Let , , , For formula (20), we have:

[0120] (twenty four)

[0121] Defining the energy norm can be the two-norm of the solution, which is:

[0122] (25)

[0123] Combining equations (24) and (25), we can get the following equations by reducing the common factors:

[0124] (26)

[0125] in, Taking the square root of both sides of equation (26) yields:

[0126] (27)

[0127] According to formula (23), ,so , so there exists a non-negative constant K’ =1, so that Equation (11) is stable with respect to the 2-norm.

[0128] For formula (22), we have:

[0129] (28)

[0130] Defining the energy norm can be the two-norm of the solution, which is:

[0131] (29)

[0132] Solving the simultaneous equations (28) and (29) and reducing them to common factors, we get:

[0133] (30)

[0134] Taking the square root of both sides of equation (30) yields:

[0135] (31)

[0136] Right now , according to the inequality Scaling the above inequality, we have:

[0137] (32)

[0138] So there are non-negative real numbers K” = , so that Equation (13) is stable with respect to the 2-norm.

[0139] Still see Figure 3 , consistency and convergence proof:

[0140] According to the truncation error analysis principle, the sufficient condition for (20) and (22) to maintain compatibility is the existence of a positive real number 、 、 、 So that:

[0141] (33)

[0142] Proof: Equation (20) is compatible with the HJB equation. V At the point Taylor expansion is performed at:

[0143] (34)

[0144] Reduce the terms and separate the original equation and the remainder, so that the left side is the original HJB equation and the right side is the remainder.

[0145] (35)

[0146] when and When , the remainder tends to 0, and Equation (20) is compatible with the HJB equation with respect to the 2-norm.

[0147] To make Equation (22) compatible with the FPK equation, the probability density function m At the point Taylor expansion is performed at:

[0148] (36)

[0149] Reduce the terms and separate the original equation and the remainder, making the left side the original FPK The equation, with the remainder on the right side, can be obtained:

[0150] (37)

[0151] when and When the remainder tends to 0, Equation (22) and FPK equation are about The norms are consistent.

[0152] Proof: In summary, the proposed hybrid finite difference scheme is proven to be stable and consistent with respect to the 2-norm. According to the Lax equivalence theorem, if the finite difference method of the hybrid scheme satisfies both stability and consistency, then the scheme converges.

[0153] See also Figure 4 In some embodiments, based on the dynamic hyperbox model, the steps of solving the HJB equation and the FPK equation to obtain the optimal control strategy are:

[0154] Step S1: Solve the dynamic hyperbox model to obtain the dynamic hyperbox set, which includes A dynamic hyperbox, is the total number of dynamic hyperboxes in the dynamic hyperbox set; initialize to obtain the initial mean field term value set, the final penalty function and the initial hydrogen production state of each electrolytic stack; obtain the iteration step length, which includes the iteration step length in time t The step length of the previous , and in state S The step length of the previous ; Preset the first convergence threshold and the second convergence threshold ; The first convergence threshold is the convergence threshold of the efficiency value function, and the second convergence threshold is the convergence threshold of the mean field term;

[0155] Step S2: obtaining a current hydrogen supply amount set according to the dynamic super box set and the initial hydrogen production state of each electrolytic stack, where the current hydrogen supply amount set is a collection of the current hydrogen supply amount of each dynamic super box;

[0156] Step S3: Based on the initial mean field term value set, the current hydrogen supply amount set and the iteration step size, the current mean field term value set is obtained according to the FPK equation;

[0157] Step S4: Based on the current mean field term value set, iteration step size, final penalty function and current hydrogen supply amount set, the current efficiency value set and current control strategy are calculated according to the HJB equation;

[0158] Step S5: Obtain a first convergence judgment based on the current efficiency value set and the first convergence threshold. The formula for the first convergence judgment is: , the second convergence judgment is obtained according to the current mean field item value set and the second convergence threshold. The formula for the second convergence judgment is: ;

[0159] Step S6: Determine whether the first convergence judgment and the second convergence judgment are valid.

[0160] If at least one of the first convergence judgment or the second convergence judgment is not established, the initial average field item value set is updated according to the current average field item value set, and the current hydrogen supply amount set is updated according to the current average field item value set and the current control strategy, and steps S3 to S6 are repeated;

[0161] If both the first convergence judgment and the second convergence judgment are established, the optimal control strategy is obtained according to the current control strategy.

[0162] In some embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains the optimal value set of the efficiency value function:

[0163] If both the first convergence judgment and the second convergence judgment are established, the optimal value set of the efficiency value function is obtained according to the current efficiency value set.

[0164] In some embodiments, based on the dynamic hyperbox granular model, solving the HJB equation and the FPK equation further obtains the system probability distribution, which is the optimal value set of the mean field term:

[0165] If both the first convergence judgment and the second convergence judgment are established, the system probability distribution is obtained according to the current efficiency value set.

[0166] In some embodiments, based on the dynamic super-box granulation model, solving the HJB equation and the FPK equation further obtains the hydrogen supply of each dynamic super-box:

[0167] If both the first convergence judgment and the second convergence judgment are established, the hydrogen supply amount of each dynamic hyperbox is obtained according to the current mean field term value set and the current control strategy.

[0168] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than to limit the scope of protection of the present invention. Simple modifications or equivalent substitutions of the technical solution of the present invention by ordinary technicians in this field do not deviate from the essence and scope of the technical solution of the present invention.

Claims

1. A mean-field control method for rapid electrolysis power distribution in a large-scale hydrogen production array, characterized by: The following steps are involved: Obtaining the hydrogen production efficiency of each electrolytic stack in the hydrogen production array; Get the compensated Poisson martingale measure; constructing a dynamic superbox model of the hydrogen production array according to the hydrogen production efficiency; A hydrogen production dynamic model and a controlled input electrolysis power for each electrolysis stack, as well as a hydrogen production efficiency optimization function for the hydrogen production array, are constructed according to the hydrogen production efficiency, wherein the variables of the hydrogen production dynamic model and the variables of the hydrogen production efficiency function are the controlled input electrolysis power respectively; Constructing a dynamic partial differential equation of the hydrogen production array according to the hydrogen production dynamic model, the compensated Poisson martingale measure, the controlled input electrolysis power and the hydrogen production efficiency optimization function; constructing an efficiency value function of each electrolysis stack according to the hydrogen production efficiency optimization function; constructing a mean field term of the hydrogen production array according to the hydrogen production dynamic model; An HJB equation is constructed based on the dynamic partial differential equation and the efficiency value function; an FPK equation is constructed based on the dynamic partial differential equation and the mean field term; based on the dynamic hyperbox model, the HJB equation and the FPK equation are solved to obtain an optimal control strategy, which is an optimal value set of the controlled input electrolysis power.

2. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 1 is characterized in that: The hydrogen production efficiency optimization function includes a final penalty function, and the final penalty function is used to constrain the final hydrogen production efficiency state of the hydrogen production array.

3. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 2, characterized in that: Based on the dynamic hyperbox model, the steps of solving the HJB equation and the FPK equation to obtain the optimal control strategy are: Step S1: Solve the dynamic hyperbox model to obtain a dynamic hyperbox set, which includes A dynamic hyperbox, is the total number of the dynamic superboxes in the dynamic superbox set; Initialization obtains an initial mean field term value set, a final penalty function, and an initial hydrogen production state of each electrolytic stack; obtains an iteration step size; and presets a first convergence threshold and a second convergence threshold; the first convergence threshold is a convergence threshold of the efficiency value function, and the second convergence threshold is a convergence threshold of the mean field term; Step S2: obtaining a current hydrogen supply amount set according to the dynamic super box set and the initial hydrogen production state of each electrolytic stack, wherein the current hydrogen supply amount set is a collection of the current hydrogen supply amount of each dynamic super box; Step S3: Based on the initial mean field term value set, the current hydrogen supply amount set and the iteration step, obtain the current mean field term value set according to the FPK equation; Step S4: Based on the current mean field term value set, the iteration step size, the final penalty function and the current hydrogen supply amount set, a current efficiency value set and a current control strategy are calculated according to the HJB equation; Step S5: obtaining a first convergence judgment according to the current efficiency value set and the first convergence threshold, and obtaining a second convergence judgment according to the current mean field item value set and the second convergence threshold; Step S6: respectively judging whether the first convergence judgment and the second convergence judgment are established: If at least one of the first convergence judgment or the second convergence judgment is not established, updating the initial average field item value set according to the current average field item value set, and updating the current hydrogen supply amount set according to the current average field item value set and the current control strategy, and repeating steps S3 to S6; If both the first convergence judgment and the second convergence judgment are established, the optimal control strategy is obtained according to the current control strategy.

4. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 3 is characterized in that: Based on the dynamic hyperbox model, solving the HJB equation and the FPK equation also obtains the optimal value set of the efficiency value function.

5. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 4 is characterized in that: Based on the dynamic hyperbox model, the method for solving the HJB equation and the FPK equation and obtaining the optimal value set of the efficiency value function is: If both the first convergence judgment and the second convergence judgment are established, the optimal value set of the efficiency value function is obtained according to the current efficiency value set.

6. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 3, characterized in that: Based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains a system probability distribution, which is an optimal value set of the mean field term.

7. The mean field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 6, characterized in that: Based on the dynamic hyperbox model, the HJB equation and the FPK equation are solved to obtain a system probability distribution, and the system probability distribution is the optimal value set of the mean field term as follows: If both the first convergence judgment and the second convergence judgment are established, the system probability distribution is obtained according to the current efficiency value set.

8. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 3 is characterized in that: Based on the dynamic hyperbox model, solving the HJB equation and the FPK equation further obtains an optimal hydrogen supply amount set, which is a collection of the optimal hydrogen supply amount of each dynamic hyperbox.

9. The mean-field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to claim 8, characterized in that: Based on the dynamic hyperbox model, the method for solving the HJB equation and the FPK equation to obtain the optimal hydrogen supply amount set is: If both the first convergence judgment and the second convergence judgment are established, the optimal hydrogen supply amount set is obtained according to the current efficiency value set and the current control strategy.

10. The mean field control method for rapid electrolysis power distribution for large-scale hydrogen production arrays according to any one of claims 3 to 9, characterized in that: The HJB equation and the FPK equation are solved using a finite difference approximation method.

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