Mean field control method for large-scale hydrogen production array electrolysis power rapid distribution

Abstract

The invention provides an average field control method for large-scale hydrogen production array electrolysis power rapid distribution. The method comprises the steps that a dynamic super-box model and a hydrogen production efficiency optimization function of a hydrogen production array and a hydrogen production dynamic model and controlled input electrolysis power of each electrolysis stack are constructed according to hydrogen production efficiency; constructing a dynamic partial differential equation of the hydrogen production array according to the hydrogen production dynamic model, the compensation Poisson yoke measurement degree, the controlled input electrolysis power and the hydrogen production efficiency optimization function; constructing an efficiency value function of each electrolytic reactor according to the hydrogen production efficiency optimization function; constructing an average field item of a 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 average field item; based on the dynamic hyperbox model, an HJB equation and an FPK equation are solved to obtain an optimal control strategy, and load balancing can be realized on the premise of fully considering the service life state and hydrogen production performance difference of the electrolytic cell monomer.

Description

Technical Field

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

[0002] In renewable energy hydrogen production systems, regarding the impact of fluctuating power sources on hydrogen production effects, existing research usually adopts an operation regulation method that couples electrical energy storage / supercapacitors with a hydrogen production array to suppress the power fluctuations that the electrolysis device cannot effectively load, reduce the start-stop times, and delay its life degradation, thereby improving the dynamic operation efficiency of electrolytic hydrogen production. For the scheduling strategy of the hydrogen production array, traditional control methods rely on preset rules and manual experience adjustments, lacking flexibility and real-time optimization capabilities, resulting in low efficiency and high energy consumption of the hydrogen production system. AI control methods such as reinforcement learning and supervised learning can effectively reduce the start-stop times of the electrolyzer by dynamically adjusting and adaptively controlling the start-stop process of the electrolyzer and the number of operating units, balance the load between electrolyzers, and control the stable change of temperature, thereby increasing the hydrogen production of the hydrogen production array and the life of the electrolyzer. However, most of the above research on the operation strategies for the impact of renewable energy fluctuations and the hydrogen production array starts from the overall perspective of the electrolytic cell array, suppressing fluctuations during grid-connected operation of new energy or directly consuming it during off-grid operation, and the coordinated control strategy does not consider the adjustment characteristics of each monomer of the electrolytic cell array. Summary of the Invention

[0003] Aiming at the problems existing in the prior art, the present invention provides an average field control method for rapid distribution of electrolysis power for large-scale hydrogen production arrays, which can ensure load balancing on the premise of fully considering the life state and hydrogen production performance differences of each electrolytic cell monomer. To achieve the above object, the technical solution adopted by the present invention is as follows: An average field control method for rapid distribution of electrolysis power for large-scale hydrogen production arrays, comprising the following steps: obtaining the hydrogen production efficiency of each electrolytic stack in the hydrogen production array; obtaining the compensated Poisson martingale measure; Constructing a dynamic hyperbox model of the hydrogen production array according to the hydrogen production efficiency; respectively constructing a hydrogen production dynamic model of each electrolytic stack, a controlled input electrolysis power, and a hydrogen production efficiency optimization function of the hydrogen production array according to the hydrogen production efficiency, and the variables of the hydrogen production dynamic model and the variables of the hydrogen production efficiency function are respectively the controlled input electrolysis power; 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 electrolytic stack according to the hydrogen production efficiency optimization function; constructing an average field term of the hydrogen production array according to the hydrogen production dynamic model; Construct the HJB equation based on the dynamic partial differential equation and the efficiency value function; construct the FPK equation based on the dynamic partial differential equation and the mean field term; based on the dynamic hyperbox model, solve the HJB equation and the FPK equation to obtain the optimal control strategy, and the optimal control strategy is the optimal value set of the controlled input electrolysis power.

[0004] In some embodiments, 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.

[0005] 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 as follows: Step S1: Solve the dynamic hyperbox model to obtain a dynamic hyperbox set, and the dynamic hyperbox set includes dynamic hyperboxes, is the total number of the dynamic hyperboxes in the dynamic hyperbox set; initialize to obtain an initial mean field term value set, a final penalty function, and the initial hydrogen production state of each electrolyzer stack; obtain an iteration step size; preset 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; Step S2: Obtain a current hydrogen supply amount set according to the dynamic hyperbox set and the initial hydrogen production state of each electrolyzer stack, and the current hydrogen supply amount set is a set of the current hydrogen supply amounts of each dynamic hyperbox; Step S3: Based on the initial mean field term value set, the current hydrogen supply amount set, and the iteration step size, obtain a 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, calculate and obtain a current efficiency value set and a current control strategy according to the HJB equation; Step S5: Obtain a first convergence judgment according to the current efficiency value set and the first convergence value, and obtain a second convergence judgment according to the current mean field term value set and the second convergence threshold; Step S6: Judge whether the first convergence judgment and the second convergence judgment are established respectively: If at least one of the first convergence judgment and the second convergence judgment is not established, then update the initial mean field term value set according to the current mean field term value set, and update the current hydrogen supply amount set according to the current mean field term value set and the current control strategy, and repeat steps S3 to S6; If both the first convergence judgment and the second convergence judgment are established, then obtain the optimal control strategy according to the current control strategy.

[0006] In some of these embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation also obtains an optimal value set of the efficiency value function.

[0007] In some of these embodiments, the method for obtaining an optimal value set of the efficiency value function by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then the optimal value set of the efficiency value function is obtained according to the current efficiency value set.

[0008] In some of these embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation also obtains a system probability distribution, and the system probability distribution is an optimal value set of the mean field term.

[0009] In some of these embodiments, the method for obtaining a system probability distribution, which is an optimal value set of the mean field term, by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then the system probability distribution is obtained according to the current efficiency value set.

[0010] In some of these embodiments, based on the dynamic hyperbox model, solving the HJB equation and the FPK equation also obtains an optimal hydrogen supply amount set, and the optimal hydrogen supply amount set is a set of optimal hydrogen supply amounts of each of the dynamic hyperboxes.

[0011] In some of these embodiments, the method for obtaining the optimal hydrogen supply amount set by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then the optimal hydrogen supply amount set is obtained according to the current efficiency value set and the current control strategy.

[0012] In some of these embodiments, a finite difference approximation method is used to solve the HJB equation and the FPK equation.

[0013] Compared with the prior art, the present invention has the following beneficial effects: 1. The present invention constructs a dynamic hyperbox model of a hydrogen production array considering the flexible combination of electrolytic cell monomers. In this dynamic hyperbox model, by analyzing the dynamic safety fluctuation tolerance range and hydrogen production efficiency of electrolytic cell monomers, electrolytic stacks with the characteristic of similar hydrogen production efficiency are divided into the same dynamic hyperbox to reduce the dimension of the controlled object. At the same time, the hydrogen production array dynamically adjusts the hyperbox center of the dynamic hyperbox according to the overall hydrogen production efficiency state to ensure load balancing on the premise of fully considering the life state and hydrogen production performance differences of electrolytic cell monomers; 2. The present invention considers the uncertainty problems caused by random power fluctuations and electrolyzer stack failures, constructs a partial differential equation of a linear quadratic HJB-FPK system of equations with Poisson jumps, and breaks through the curse of dimensionality problem caused by the increase in the number of electrolyzer stacks. According to the Hamilton canonical equation, the existence of the mean-field control equilibrium is proved; 3. The present invention adopts a hybrid finite difference scheme that takes into account high-order accuracy and numerical stability, uses derivative approximation to solve the equilibrium field equilibrium value, and proves the stability, compatibility, and convergence of the proposed hybrid finite difference scheme according to the energy method, truncation error analysis, and Lax equivalence theorem respectively, ensuring the solution of the HJB-FPK system of equations and obtaining the optimal control strategy. Description of the Drawings

[0014] Figure 1 is a flowchart of the mean-field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to the present invention; Figure 2 is the framework of the renewable energy hydrogen production system according to the present invention; Figure 3 is the technical framework diagram of the mean-field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to the present invention; Figure 4 is a flowchart of obtaining the optimal control strategy by solving the HJB equation and the FPK equation based on the dynamic hyperbox model in the embodiment of the present invention.

[0015] Among them, the reference numerals are: 1, renewable energy power generation equipment; 2, power distributor; 3, hydrogen production array; 31, dynamic hyperbox; 311, electrolyzer stack; 4, high-pressure hydrogen storage tank; 5, transmission line; 6, hydrogen transmission line. Detailed Embodiment

[0016] How to realize the rapid and reasonable distribution of the electrolysis hydrogen production power in the new energy power station within the large-scale electrolyzer array directly affects the operation life, hydrogen production efficiency of the electrolyzer array, and the electro-hydrogen fusion characteristics of the renewable energy system. To address the above problems, the current multi-mechanism hydrogen production power distribution strategies mainly include equal distribution, chain distribution, and rotation coordination control. The equal distribution strategy evenly distributes the total hydrogen production power of the array to each electrolyzer monomer, which is likely to cause multiple electrolyzers to operate simultaneously under fluctuating power and frequent start-stop conditions, especially with poor operating economy and low safety under low-power conditions; the core idea of the chain distribution strategy is to distribute according to the load rate of the electrolyzers step by step, and there are problems of uneven fluctuation bearing and operation time of the electrolyzer monomers; the rotation coordination control strategy rotates the electrolyzer groups to operate at regular intervals, which can achieve load balance to a certain extent, but insufficient consideration is given to the life state and hydrogen production performance differences of the electrolyzer monomers.

[0017] Mean-field control originally originated from the mean-field theory in statistical physics and was mainly applied in fields such as economics and sociology. Subsequently, it was introduced into the fields of communication and power, including energy management of a large number of plug-in hybrid electric vehicles, joint channel access and power control optimization in unmanned aerial vehicle networks, and real-time peak regulation of virtual power plants. Mean-field control can model and optimize the overall behavior of a large-scale system by simplifying the complex interactions between controlled objects, and has advantages such as reducing the system's computational complexity, enhancing system stability, and improving the efficiency of resource allocation. Therefore, mean-field control provides an effective method to optimize the coordination between multiple hydrogen production units while considering the hydrogen production performance of the array as a whole. The operating state of each hydrogen production unit is not only affected by its own control strategy but is also closely related to the distribution state of the hydrogen production performance of the overall mean-field. There is little research on the mean-field control strategy for large-scale hydrogen production arrays under the operating conditions of fluctuating electrolysis power of renewable energy.

[0018] To clearly illustrate the technical features of this solution, the following will combine the accompanying drawings and embodiments to detail the implementation manner of this application, so as to fully understand and implement the process of how this application uses technical means to solve technical problems and achieve corresponding technical effects. The embodiments of this application and each feature in the embodiments can be combined with each other on the premise of not conflicting, and the formed technical solutions are all within the protection scope of this application.

[0019] See Figure 1 , the embodiment of the present invention provides a mean-field control method for rapid power distribution of electrolysis in a large-scale hydrogen production array, including the following steps: obtaining the hydrogen production efficiency of each electrolyzer in the hydrogen production array; obtaining the compensated Poisson martingale measure; Figure 2Shows the framework of an RHPS (Renewable-Dominated Hydrogen Production System) with a large-scale electrolyzer stack array (hydrogen production array) for green hydrogen production. Generally, the RHPS equipped with various renewable energy sources (RES), the renewable energy power generation device 1 includes photovoltaic panels (PV) and wind turbines (WT), etc., which can generate electricity to power the hydrogen production array 3 to produce green hydrogen, meet the hydrogen supply demand of the RHPS, and store the excess hydrogen in the high-pressure hydrogen storage tank 4 at the same time. Here, the PEM (proton exchange membrane) electrolyzer stack is used as the hydrogen production unit, and a large number of electrolyzer stacks, that is, stacks, are connected in parallel to form a complete electrolyzer array. The electrolysis power command of the hydrogen production array 3 is distributed to each electrolyzer stack through the power distributor 3 to meet the hydrogen production demand. Electric energy is transmitted between the renewable energy power generation device 1 and the power distributor 3, and between the power distributor 3 and the hydrogen production array 3 through the power transmission line 5 respectively, 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 command through the power distributor 3, first perform homogeneous particle division on the hydrogen production array 3 to obtain a dynamic superbox set, the dynamic superbox set includes at least one dynamic superbox 31, and each dynamic superbox 31 includes at least one electrolyzer stack 311, and the electrolysis power command is distributed through the power distributor 3 based on the dynamic superbox set.

[0020] According to Faraday's law and the fitting relationship, the generation efficiency of H2, that is, the hydrogen production efficiency can be expressed as the Faraday efficiency and the voltage efficiency of the joint function, as shown in Equation (1): (1) In the formula, is the first temperature characteristic parameter, is the second temperature characteristic parameter, is t the electrolysis current of the electrolyzer array at time t is the time, is the cross-sectional area, is the electrolysis temperature, is t the electrolysis voltage of the electrolyzer array at time is the temperature change parameter, is the standard reference temperature, is the initial reverse voltage, is the first function; Referring to Equation (2), the electrolysis power is: (2) In the formula, is tThe generated power at time H2, that is, t the electrolysis power at that time, is the calorific value of H2, is the molar mass of H2, is the number of electrolytic cells in the stack, i.e., the electrolyzer stack. The electrolyzer stack includes at least one electrolytic cell. Usually, the electrolyzer stack includes at least two electrolytic cells connected in series, is the second function; Theoretically, according to the fitting relationship among hydrogen production efficiency, electrolysis power, and electrolysis current, it can be found that the hydrogen production efficiency increases with the increase of electrolysis power and gradually decreases after reaching a certain extreme value; Construct a dynamic hyperbox model of the hydrogen production array based on the hydrogen production efficiency; Using the average field control to allocate the electrolysis power regulation command for hydrogen production can achieve fast and large-scale decomposition. Its core idea is to simplify a large number of interacting participant systems into the interaction between a representative participant and the average field (the average effect of all participant behaviors). However, a large number of electrolyzer stack monomers in the electrolyzer stack array are not exactly the same, making it difficult to uniformly schedule. Therefore, construct a dynamic hyperbox granulation model, that is, the dynamic hyperbox model of the hydrogen production array, and divide the large-scale electrolyzer stack array into smaller dynamic hyperbox sets. The dynamic hyperbox set includes dynamic hyperboxes, that is, each dynamic hyperbox is a combination of electrolyzer stacks with similar hydrogen production efficiency. Specifically, first construct a quadruple information system containing the hydrogen production capacity information of the electrolyzer stack. The quadruple information system is Equation (3): (3) In the formula, is the electrolyzer stack set, , is the first electrolyzer stack, is the second electrolyzer stack, is the n th electrolyzer stack, n is the total number of electrolyzer stacks, is the hydrogen production efficiency attribute set, D , is the hydrogen production efficiency of the first electrolytic cell, is the hydrogen production efficiency of the second electrolytic cell, is the n th electrolyzer stack's hydrogen production efficiency, is the standard attribute set, , is the standard attribute of the th dynamic hyperbox, is the total number of dynamic hyperboxes, numerically the same as , is the dynamic hyperbox similarity function, which is used to measure the similarity between the condition attributes of each electrolyzer stack, i.e., the hydrogen production efficiency attribute, and the standard attribute; The homogeneous particle division aims to make the hydrogen production efficiency attributes of the electrolyzer stacks within the dynamic hyperbox as similar as possible, while ensuring the differences between the dynamic hyperboxes, as shown in Eqs. (4) and (5): (4) (5) In the equations, is the similarity function of the th dynamic hyperbox, is the serial number of the dynamic hyperbox, is the th hydrogen production efficiency of the electrolyzer stack, is the serial number of the electrolyzer stack, is the th standard attribute of the dynamic hyperbox, is the th radius of the dynamic hyperbox, is the set of electrolyzer stacks belonging to the th dynamic hyperbox, is the maximization function; The large-scale electrolyzer stacks in the electrolyzer stack set are divided into a set of homogeneous particle dynamic hyperboxes with different standard attributes. In each dynamic hyperbox, the individual electrolyzer stacks are similar in terms of power dynamic fluctuations and hydrogen production efficiency characteristics; According to the hydrogen production efficiency, the hydrogen production dynamic model of each electrolyzer stack, the controlled input electrolysis power, and the hydrogen production efficiency optimization function of the hydrogen production array are constructed respectively. The variables of the hydrogen production dynamic model and the variables of the hydrogen production efficiency function are the controlled input electrolysis power respectively; First, an average field control model is constructed: The electrolysis power of the electrolyzer stack array should be quickly decomposed and distributed to reasonable electrolyzer stacks, which is beneficial for these electrolyzer stacks to produce hydrogen with the best hydrogen production efficiency and reduce life degradation. In order to determine the optimal hydrogen production power distribution, i.e., the controlled input electrolysis power, a linear quadratic average field control model with Poisson jumps is proposed :[[]]END]] ; where, is the set of controlled objects, , contains all the main bodies of the hydrogen production array, is the total number of electrolyzer stacks in the hydrogen production array, numerically n the same as , is the state space, represents the feasible region of the hydrogen production amount of each electrolyzer stack in the hydrogen production array, , is the decision space, which represents the feasible region of the controlled input electrolysis power of each electrolyzer stack in the hydrogen production array, , is the efficiency function, which represents the optimal hydrogen production efficiency of the operation of the hydrogen production array; The -th electrolyzer stack's hydrogen production at t time is expressed as , that is, represents the hydrogen production state of the -th electrolyzer stack at t time, is the end time of time. The controlled input electrolysis power of the -th electrolyzer stack at t time is , which is a function of time and hydrogen production.

[0021] If the electrolyzer stack equipment is in the process of electrolytic hydrogen production, then there is >0, and if the electrolyzer stack equipment is not performing electrolysis, then there is =0. Therefore, the hydrogen production dynamic model of the electrolyzer stack equipment is Equation (6): (6) The diffusion term coefficient of the state equation of the electrolyzer stack operation includes the state term and the control term, and the state equation contains a compensated Poisson martingale measure, and the compensated Poisson martingale measure is the Poisson jump term. Due to the volatility of new energy output, the Poisson jump term can be used to simulate the volatility of new energy output and cope with emergencies in the electrolyzer stack, and can more realistically simulate and control the electrolyzer stack array. Use to represent dimensional Euclidean space, is the total number of electrolyzer stacks, is defined as a standard Brownian motion, is the fluctuation of the input power of the -th electrolyzer stack at t time, is the total number of electrolyzer stacks, is used to characterize the continuous existence of input power fluctuations in the electrolyzer stack array. Define a Poisson random measure independent of , denoted as the compensated Poisson martingale measure, which is used to characterize possible emergencies in the electrolyzer stack.

[0022] Assume that the hydrogen production of each electrolyzer stack satisfies the stochastic differential equation with Poisson jumps in Equation (7): (7) In the formula, is the first constant, is the second constant, is the third constant, is at t the influence of the hydrogen production amount of other electrolyzers in the hydrogen production array at the moment on the hydrogen production amount of the th electrolyzer; , is the probability distribution space of the Poisson jump term, is the initial boundary of the hydrogen production state of the th electrolyzer, that is, the initial hydrogen production state of the th electrolyzer; Under this assumption, is proportional to the difference in hydrogen production amount; For the hydrogen production array, the hydrogen production efficiency optimization function is Equation (8): (8) In the formula, the hydrogen production efficiency optimization function is the function to maximize the hydrogen production efficiency, is the hydrogen production amount, is the controlled input electrolysis power, is the mathematical expectation, is t the process penalty function at the moment, represents the function to penalize the electrolyzers with lower hydrogen production efficiency during the hydrogen production process, is the final penalty function, and the final penalty function is used to constrain the final hydrogen production efficiency state of the hydrogen production array; Construct the dynamic partial differential equation of the hydrogen production array according to 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), (10); (9) (10) In the formula, is the Lagrange multiplier corresponding to the adjoint variable for hydrogen production, is t the value of the mean field term when the hydrogen production amount at the moment is ; Construct the efficiency value function of each electrolyzer according to the hydrogen production efficiency optimization function; At the moment t the th electrolyzer's efficiency value function represents that under the optimal control, from the current state at the moment t i.e., the hydrogen production amountS Starting from the hydrogen production efficiency optimization function of the first electrolytic stack, the maximum value of the efficiency value function is as shown in Equation (11): (11) In the formula, represents the power constraint under different hydrogen production rates, is the maximization function, is the current time; Construct the mean field term of the hydrogen production array according to the hydrogen production dynamic model; In the hydrogen production array, the hydrogen production amount of each electrolytic stack is not only affected by its own state, but also related to the overall hydrogen production amount state distribution of other electrolytic stacks in the whole system. This influence is described by the mean field term . The mean field term can handle the states of electrolytic stacks in a large-scale system. By considering the interactions between electrolytic stacks and the overall state distribution of the array, the optimal performance of the hydrogen production efficiency of the hydrogen production array can be achieved. The mean field term is as shown in Equation (12): (12) In the formula, δ is the Dirac coefficient. When the given condition is satisfied, δ returns 1, and when the given condition is not satisfied, δ returns 0. Therefore, the mean field term represents the probability density function that the hydrogen production state of the electrolytic stack is t at the moment S Due to the number of electrolytic stacks N tending to infinity, a large number of electrolytic stacks can be modeled as a continuum. Therefore, can be regarded as a continuous probability density function and satisfies Equation (13): (13) The mean field equilibrium strategy is generated by the coupled HJB-FPK equations. Among them, the HJB equation is related to the efficiency value function, and the FPK equation is related to the mean field term, that is, the probability distribution function.

[0023] For the optimal functional problem, construct the HJB equation according to the dynamic partial differential equation and the efficiency value function. See Equation (14): (14) According to the dynamic programming principle of HJB, the optimal control strategy of the electrolytic stack array can be obtained, as shown in Equation (15): (15) ​In the formula, represents the value of P when the objective function reaches the minimum value. The objective function refers to the dynamic partial differential equation ; The FPK equation describes the evolution of the mean field term under optimal control and affects the mean field distribution in the HJB equation, forming a coupled system. The FPK equation is constructed based on the dynamic partial differential equation and the mean field term as shown in Equation (16): (16) In the formula, is the initial mean field term distribution state, that is, the initial mean field term value; Based on the dynamic hyperbox model, the HJB equation and the FPK equation are solved to obtain the optimal control strategy. The optimal control strategy is the optimal value set of the controlled input electrolysis power.

[0024] The FPK equation describes the change of the mean field term over time, and its change is determined by the system dynamics equation, that is, the dynamic partial differential equation H , and the determining terms include the controlled input electrolysis power and Equations (9) and (12); the HJB equation gives the optimal control strategy . It can be seen from Equations (9), (11), and (14) that the optimal control strategy depends on the current hydrogen supply S ; through the optimal control strategy and the hydrogen supply S changing over time, it affects the state distribution, that is, the mean field term . The mean field term is solved from the FPK and substituted into the HJB equation. The optimal control strategy is obtained by solving the HJB equation, and then the optimal control strategy is fed back to the FPK to update the system probability distribution until each electrolyzer stack makes an optimal decision according to the mean field term and the optimal control strategy , and it is impossible to improve the hydrogen production by unilaterally changing the controlled input electrolysis power, that is, convergence.

[0025] Considering that the heterogeneous electrolyzer stack combination, that is, different dynamic hyperboxes have different hydrogen production efficiencies, and within the homogeneous electrolyzer stack combination, that is, within the same dynamic hyperbox, there is the same hydrogen production efficiency. The total hydrogen supply of the electrolyzer stack array can be calculated by Equation (17): (17) In the formula, is the number of electrolyzer stacks belonging to the th dynamic hyperbox, is the serial 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, is At time the optimal control strategy of the is At time the mean field term of the dynamic hyperbox with hydrogen supply of is the hydrogen supply of the Optimal control strategy Existence proof: When the electrolyzer solves its optimal control strategy , it generates a control equilibrium solution. Let ( , ) be the control strategy composed of the optimal control strategy of the electrolyzer and the optimal control strategies of other individuals . Then, if and only if the condition of Equation (18) is satisfied for each electrolyzer in the hydrogen production array control, the control strategy ( , ) is a control equilibrium: (18) In the formula, means taking any one, is the set of controlled input electrolysis power strategies; A sufficient condition for the existence of a control equilibrium is that the HJB equation has a solution. If the Hamiltonian is smooth, the HJB equation has a solution. According to the one-dimensional diffusion HJB equation with Poisson jumps, the Hamiltonian is defined as Equation (19): (19) In the formula, is the gradient symbol; Due to the continuity of the efficiency value function, all-order derivatives 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 .

[0026] In some of these embodiments, a finite difference approximation method is used to solve the HJB equation and the FPK equation.

[0027] The HJB equation and the FPK equation are called the HJB-FPK equation system. In the mean-field HJB-FPK equation system, the partial differential equations are coupled due to and and thus there is no explicit expression for the optimal control strategy . Therefore, a finite difference method with a mixed format is adopted, taking into account high-order accuracy and numerical stability. The convection term in the HJB-FPK equation system uses an upwind scheme to ensure stability, and the diffusion term in the HJB-FPK equation system uses a central difference scheme to ensure accuracy. The computational domain is meshed, and then the derivatives in the HJB-FPK equation system are fully approximated to obtain a pair of difference schemes for solving the numerical solutions of the HJB-FPK equation system, and the stability, consistency, and convergence of the proposed difference schemes are analyzed and proven.

[0028] First, the feasible domain space to be optimized is divided into grids by the unit time and the unit state respectively. denotes the approximate value of the efficiency value function V at the point . Among them, , , is an arbitrarily taken step size at time t , is an arbitrarily taken step size at state S . Then the forward Euler discretization format of HJB is approximated as in Eqs. (20), (21): (20) In the formula, is the standard sign function, is the mathematical identifier for the function to be monotonically increasing; (21) In the formula, is the first intermediate expression, ; The forward Euler discretization format of FPK is approximated as in Eq. (22): (22) See Figure 3 , stability proof: Only when Eq. (20) is stable, where is the second intermediate expression. The stability of Eq. (20) is a sufficient condition for the stability of the mixed finite difference format, that is, it satisfies the special case . Therefore, the stability analysis of Eq. (11) in the case of is carried out.

[0029] According to the Courant-Friedrichs-Lewy condition, a sufficient condition for Eqs. (20) and (22) to be stable is that the grid spacing and satisfy the condition of Eq. (23): (23) Proof: Let , , , . For Eq. (20), we have: (24) Define the energy norm which can be the two-norm of the solution, as: (25) Combining Eqs. (24) and (25) and canceling out the common factors, we get: (26) where . Taking the square root of both sides of Eq. (26), we have: (27) According to Eq. (23), , so , and thus there exists a non-negative constant K’ = 1 such that Eq. (11) is stable with respect to the two-norm.

[0030] For Eq. (22), we have: (28) Define the energy norm which can be the two-norm of the solution, as: (29) Combining Eqs. (28) and (29) and canceling out the common factors, we get: (30) Taking the square root of both sides of Eq. (30), we have: (31) That is , and according to the inequality Scaling the above inequality, we have (32) Therefore, there exists a non-negative real number K” = such that Eq. (13) is stable with respect to the two-norm.

[0031] Still refer toFigure 3 , Proof of compatibility and convergence: According to the truncation error analysis principle, a sufficient condition for Eqs. (20) and (22) to be compatible is that there exist positive real numbers , , , such that: (33) Proof: To prove the compatibility of Eq. (20) with the HJB equation, the value function V is Taylor-expanded at the point : (34) After canceling terms and separating the original equation and the remainder term, making the left side the original HJB equation and the right side the remainder term, we get: (35) When and , the remainder term tends to 0, and Eq. (20) is compatible with the HJB equation with respect to the 2-norm.

[0032] To prove the compatibility of Eq. (22) with the FPK equation, the probability density function m is Taylor-expanded at the point : (36) After canceling terms and separating the original equation and the remainder term, making the left side the original FPK equation and the right side the remainder term, we get: (37) When and , the remainder term tends to 0, and Eq. (22) is compatible with the FPK equation with respect to norm.

[0033] Proof: In summary, the proposed mixed finite difference scheme is proven to be stable and compatible with respect to the 2-norm. According to the Lax equivalence theorem, if the finite difference method of the adopted mixed scheme satisfies both stability and compatibility, the scheme converges.

[0034] See Figure 4 , in some of the embodiments, based on the dynamic hyperbox model, the steps to solve the HJB equation and the FPK equation to obtain the optimal control strategy are as follows: Step S1: Solve the dynamic hyperbox model to obtain a dynamic hyperbox set, and the dynamic hyperbox set includes dynamic hyperboxes, 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 electrolyzer stack; obtain the iteration step size, where the iteration step size includes the step size randomly selected at time t and the step size randomly selected at state ; S ; 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; Step S2: Obtain the current hydrogen supply amount set according to the dynamic hyperbox set and the initial hydrogen production state of each electrolyzer stack, where the current hydrogen supply amount set is the set of the current hydrogen supply amounts of each dynamic hyperbox; Step S3: Based on the initial mean field term value set, the current hydrogen supply amount set, and the iteration step size, 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, calculate and obtain the current efficiency value set and the current control strategy according to the HJB equation; Step S5: Obtain the first convergence judgment according to the current efficiency value set and the first convergence value, where the formula for the first convergence judgment is , and obtain the second convergence judgment according to the current mean field term value set and the second convergence threshold, where the formula for the second convergence judgment is ; Step S6: Determine whether the first convergence judgment and the second convergence judgment are established respectively: If at least one of the first convergence judgment or the second convergence judgment is not established, then update the initial mean field term value set according to the current mean field term value set, and update the current hydrogen supply amount set according to the current mean field term value set and the current control strategy, and repeat Step S3 to Step S6; If both the first convergence judgment and the second convergence judgment are established, then obtain the optimal control strategy according to the current control strategy.

[0035] In some embodiments, based on the dynamic hyperbox model, when solving the HJB equation and the FPK equation, the optimal value set of the efficiency value function is also obtained: If both the first convergence judgment and the second convergence judgment are established, then obtain the optimal value set of the efficiency value function according to the current efficiency value set.

[0036] In some embodiments, based on the dynamic hyperbox granulation model, when solving the HJB equation and the FPK equation, the system probability distribution is also obtained, where the system probability distribution is the optimal value set of the mean field term: If both the first convergence judgment and the second convergence judgment are established, then obtain the system probability distribution according to the current efficiency value set.

[0037] In some of these embodiments, based on the dynamic hyperbox granulation model, solving the HJB equation and the FPK equation also obtains the hydrogen supply amount of each dynamic hyperbox: If both the first convergence determination and the second convergence determination are established, then the hydrogen supply amount of each dynamic hyperbox is obtained according to the current mean field term value set and the current control strategy.

[0038] Finally, it should be noted that the above content is only used to illustrate the technical solution of the present invention, rather than limiting the protection scope of the present invention. Any simple modification or equivalent replacement made by those of ordinary skill in the art to the technical solution of the present invention shall not depart from the essence and scope of the technical solution of the present invention.

Claims

1. An average field control method for rapid power distribution of electrolysis in large-scale hydrogen production arrays, characterized in that: It includes the following steps: Obtain the hydrogen production efficiency of each electrolyzer stack in the hydrogen production array; Obtain the compensated Poisson martingale measure; Construct a dynamic hyperbox model of the hydrogen production array according to the hydrogen production efficiency; Construct a hydrogen production dynamic model for each electrolyzer stack, the controlled input electrolysis power, and a hydrogen production efficiency optimization function of the hydrogen production array respectively according to the hydrogen production efficiency. The variables of the hydrogen production dynamic model and the variables of the hydrogen production efficiency function are respectively the controlled input electrolysis power; Construct 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; construct an efficiency value function for each electrolyzer stack according to the hydrogen production efficiency optimization function; construct an average field term of the hydrogen production array according to the hydrogen production dynamic model; Construct a HJB equation according to the dynamic partial differential equation and the efficiency value function; construct a FPK equation according to the dynamic partial differential equation and the average field term; based on the dynamic hyperbox model, solve the HJB equation and the FPK equation to obtain an optimal control strategy, and the optimal control strategy is the optimal value set of the controlled input electrolysis power.

2. The mean field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to claim 1, 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 average field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to claim 2, characterized in that: The steps of solving the HJB equation and the FPK equation based on the dynamic hyperbox model to obtain the optimal control strategy are as follows: Step S1: Solve the dynamic hyperbox model to obtain a dynamic hyperbox set, where the dynamic hyperbox set includes dynamic hyperboxes, being the total number of the dynamic hyperboxes in the dynamic hyperbox set; Initialize to obtain an initial average field term value set, a final penalty function, and the initial hydrogen production state of each electrolyzer stack; obtain an iteration step size; preset 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 average field term; Step S2: Obtain a current hydrogen supply amount set according to the dynamic hyperbox set and the initial hydrogen production state of each electrolyzer stack, and the current hydrogen supply amount set is the set of the current hydrogen supply amounts of each dynamic hyperbox; Step S3: Based on the initial average field term value set, the current hydrogen supply amount set, and the iteration step size, obtain a current average field term value set according to the FPK equation; Step S4: Based on the current average field term value set, the iteration step size, the final penalty function, and the current hydrogen supply amount set, calculate and obtain a current efficiency value set and a current control strategy according to the HJB equation; Step S5: Obtain a first convergence judgment according to the current efficiency value set and the first convergence value, and obtain a second convergence judgment according to the current average field term value set and the second convergence threshold; Step S6: Judge whether the first convergence judgment and the second convergence judgment are established respectively: If at least one of the first convergence judgment or the second convergence judgment is not established, update the initial average field term value set according to the current average field term value set, and update the current hydrogen supply amount set according to the current average field term value set and the current control strategy, and repeat steps S3 to S6; If both the first convergence judgment and the second convergence judgment are established, obtain the optimal control strategy according to the current control strategy.

4. The mean field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to claim 3, 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 of a large-scale hydrogen production array according to claim 4, characterized in that: The method for obtaining the optimal value set of the efficiency value function by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then 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 of a large-scale hydrogen production array according to claim 3, characterized in that: Based on the dynamic hyperbox model, solving the HJB equation and the FPK equation also obtains the system probability distribution, and the system probability distribution is the optimal value set of the mean field term.

7. The mean field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to claim 6, characterized in that: The method for obtaining the system probability distribution, which is the optimal value set of the mean field term, by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then the system probability distribution is obtained according to the current efficiency value set.

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

9. The mean field control method for rapid electrolysis power distribution of a large-scale hydrogen production array according to claim 8, characterized in that: The method for obtaining the optimal hydrogen supply amount set by solving the HJB equation and the FPK equation based on the dynamic hyperbox model is as follows: If both the first convergence judgment and the second convergence judgment hold, then 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 of a large-scale hydrogen production array according to any one of claims 3-9, characterized in that: The finite difference approximation method is used to solve the HJB equation and the FPK equation.

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