Multi-type electric hydrogen production optimization control method giving consideration to new energy consumption

Abstract

The invention discloses a multi-type electric hydrogen production optimization control method giving consideration to new energy consumption, and relates to the technical field of control strategies. According to the dynamic response speed difference of different electrolysis technologies, the different electrolysis technologies are matched with new energy power generation loads with different fluctuation characteristics, so that differential utilization is achieved, the working efficiency is improved, and cooperative operation is optimized. The capacity configuration of the multi-type electric hydrogen production system is optimized, so that the operation flexibility of the hydrogen production device is enhanced, and the hydrogen production device adapts to the fluctuation characteristic of new energy power generation. The dynamic coupling effect between the new energy power generation process and the electrolytic hydrogen production process is improved, a new thought and a practical basis are provided for development of an efficient renewable energy hydrogen production technology, and a more sustainable energy utilization mode is assisted to be achieved.

Description

Technical Field

[0001] The present invention belongs to the technical field of control strategies, and in particular relates to a multi-type electric hydrogen production optimization control method that takes into account new energy consumption. Background Art

[0002] Exploring new, efficient and environmentally friendly energy sources has become an important way to solve the current energy crisis.

[0003] Hydrogen is a clean and sustainable energy source. Traditional hydrogen production methods mainly rely on fossil fuels, such as natural gas reforming and coal gasification, which produce a large amount of carbon dioxide emissions. The electrohydrogen technology uses renewable energy (such as wind power, solar energy) or clean energy such as nuclear energy to drive the electrolysis of water to produce hydrogen, which does not produce carbon dioxide emissions. Therefore, it is of great significance to reduce greenhouse gas emissions and respond to climate change. Secondly, electrohydrogen technology can realize energy storage and conversion. Due to the volatility and intermittency of renewable energy, the power system needs an efficient energy storage method to balance the difference between supply and demand. Electrolysis of water can convert excess electricity into hydrogen, and hydrogen can be used as an energy storage medium, and then hydrogen can be converted into electricity through combustion or hydrogen fuel cells. This energy storage and conversion method can help solve the reliability and availability problems of renewable energy. In addition, electrohydrogen technology can also promote energy diversification and energy system integration. As an efficient and clean energy medium, hydrogen can be used in many fields, including transportation, industry, and housing. Through electrohydrogen technology, renewable energy can be directly converted into hydrogen, thereby realizing energy diversification and decentralization and reducing dependence on traditional energy. In addition, hydrogen can be integrated with other forms of energy (such as electricity and natural gas) to form a comprehensive energy system and improve energy utilization efficiency.

[0004] As a clean energy source, power input control in the hydrogen production process is crucial. At present, the power control methods for hydrogen production mainly include traditional PID control, neural network control and multi-level control strategies. Traditional PID control maintains the stability of the electrolyzer by setting target voltage and current, but it is not adaptable enough to the power fluctuations of renewable energy generation, which can easily lead to decreased electrolysis efficiency or damage to the electrolyzer. Neural network control can optimize the input power by learning historical data, providing a certain degree of flexibility, but due to the high requirements for real-time data and computing resources, these methods often face complexity and cost issues in practical applications. In addition, although the multi-level control strategy can combine multiple control methods to improve the system response speed, its implementation difficulty and system complexity cannot be ignored. Summary of the invention

[0005] In view of the shortcomings of the prior art, the present invention provides an optimization control method for multi-type hydrogen production by electricity that takes into account the consumption of new energy, thereby solving the problem that the prior art cannot effectively deal with the volatility of renewable energy power generation, making it difficult for traditional and existing intelligent control methods to maintain the optimal operating state of the electrolyzer, thereby affecting the production efficiency of hydrogen.

[0006] The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy includes the following steps:

[0007] Step 1: Modeling the power characteristics of different types of electrolyzers in a multi-type hydrogen production system to obtain a power model of the multi-type hydrogen production system; the multi-type hydrogen production system includes an alkaline electrolyzer, a proton exchange membrane electrolyzer, and a high-temperature solid oxide electrolyzer;

[0008] The power model for an alkaline electrolyser is:

[0009]

[0010] Where P AEM is the input power of the alkaline electrolyzer, I A With T A are the current and temperature of the alkaline electrolytic cell respectively; r is the ohmic resistance parameter of the electrolyte; A A is the effective area of ​​the electrolytic cell membrane; s is the electrode overvoltage coefficient; U 01 is the reversible voltage;

[0011] The power model of the proton exchange membrane electrolyzer is:

[0012] P PEM =I P ×U P (2)

[0013] Where P PEM is the input power of the proton exchange membrane electrolyzer, I P is the input current of the proton exchange membrane electrolyzer, U P is the input voltage of the proton exchange membrane electrolyzer;

[0014] The input voltage of the proton exchange membrane electrolyzer is:

[0015] U P =U oc,P +U a,P +U diff +U ohm,P (3)

[0016] Among them, U oc,P is the open circuit voltage of the proton exchange membrane electrolyzer, U a,P is the activation overvoltage of the proton exchange membrane electrolyzer, U diffis the diffusion overvoltage of the proton exchange membrane electrolyzer, U ohm,P is the ohmic overvoltage of the proton exchange membrane electrolyzer;

[0017] The open circuit voltage of the proton exchange membrane electrolyzer is:

[0018]

[0019] Among them, U 02 is the standard electromotive force of the proton exchange membrane electrolyzer, R is the gas constant, T P is the temperature of the proton exchange membrane electrolyzer, and are the pressures of hydrogen and oxygen, respectively, is the water activity between electrolytes, and F is the Faraday constant;

[0020] The activation overvoltage of the proton exchange membrane electrolyzer is:

[0021] U a,P =RT P sinh -1 (J P / 2J 0,ap ) / α ap F+RT P sinh -1 (J P / 2J 0,cp ) / α cp F (5)

[0022] Among them, J P is the current density of the proton exchange membrane electrolyzer, J 0,ap and J 0,cp are the exchange current density of the anode and cathode of the proton exchange membrane electrolyzer, α ap and α cp are the charge transfer coefficients of the anode and cathode of the proton exchange membrane electrolyzer, respectively;

[0023] The diffusion overvoltage of the proton exchange membrane electrolyzer is:

[0024]

[0025] Where, T a and T c are the temperatures of the cathode and anode of the proton exchange membrane electrolyzer, and are the oxygen and hydrogen concentrations, and are the standard reference values ​​for oxygen and hydrogen, respectively;

[0026] The ohmic overvoltage of a proton exchange membrane electrolyzer is:

[0027] U ohm =J P ×R P (7)

[0028] Among them, R P is the equivalent resistance of the proton exchange membrane electrolyzer;

[0029] The power model of the high temperature solid oxide electrolyzer is:

[0030] P SOEC =I S ×U S (8)

[0031] Where P SOEC is the input power of the high temperature solid oxide electrolyzer, I S is the input current of the high temperature solid oxide electrolyzer, U S is the input voltage of the high temperature solid oxide electrolyzer;

[0032] The input voltage of the high temperature solid oxide electrolyzer is:

[0033] U S =U oc,s +U a,S +U ohm,S +U conc (9)

[0034] Among them, U oc,s is the equilibrium voltage of the high temperature solid oxide electrolyzer, U a,S is the activation overvoltage of the high-temperature solid oxide electrolyzer, U ohm,S is the ohmic overvoltage of the high-temperature solid oxide electrolyzer, U conc is the concentration difference voltage of the high temperature solid oxide electrolyzer;

[0035] The equilibrium voltage of the high temperature solid oxide electrolyzer is:

[0036]

[0037] Where, T S is the temperature of the high temperature solid oxide electrolyzer, U 03 is the standard electromotive force of a high-temperature solid oxide electrolyzer, and are the pressures of hydrogen and oxygen respectively;

[0038] The activation overvoltage of the high temperature solid oxide electrolyzer is:

[0039] U a,S =RT S sinh -1 (J S / 2J 0,aS ) / α aS F+RT S sinh -1 (J S / 2J 0,cS ) / α cS F (11)

[0040] In the formula, J S is the current density of the high temperature solid oxide electrolyzer, J 0,aS and J 0,cS are the exchange current density of the anode and cathode of the high-temperature solid oxide electrolyzer, α aS and α cS are the charge transfer coefficients of the anode and cathode of the high-temperature solid oxide electrolyzer, respectively;

[0041] Step 2: Analyze the power characteristics of various types of hydrogen production systems, and establish power characteristic constraints and safety characteristic constraints of various types of hydrogen production systems;

[0042] The power characteristic constraint of the alkaline electrolyzer is:

[0043]

[0044] The safety characteristics of alkaline electrolyzers are constrained by:

[0045]

[0046] Among them, δ AEM is the working state of the alkaline electrolytic cell, a value of 1 indicates that the alkaline electrolytic cell is operating, and a value of 0 indicates that the alkaline electrolytic cell is not operating; is the maximum input power of the alkaline electrolyzer, that is, the maximum capacity of the alkaline electrolyzer;

[0047] The power characteristic constraint of the proton exchange membrane electrolyzer is:

[0048]

[0049] The safety characteristics of the proton exchange membrane electrolyzer are constrained as follows:

[0050]

[0051] Among them, δ PEM It is the working state of the proton exchange membrane electrolyzer. Its value is 1, which means the proton exchange membrane electrolyzer is running, and its value is 0, which means the proton exchange membrane electrolyzer is not running. is the maximum input power of the proton exchange membrane electrolyzer, that is, the maximum capacity of the proton exchange membrane electrolyzer;

[0052] The power characteristic constraints of the high temperature solid oxide electrolyzer are:

[0053]

[0054] The safety characteristics of high temperature solid oxide electrolyzers are constrained as follows:

[0055]

[0056] Among them, δ SOEC is the working state of the high-temperature solid oxide electrolyzer, a value of 1 indicates that the high-temperature solid oxide electrolyzer is operating, and a value of 0 indicates that the high-temperature solid oxide electrolyzer is not operating; is the maximum input power of the high-temperature solid oxide electrolyzer, that is, the maximum capacity of the high-temperature solid oxide electrolyzer;

[0057] Step 3: According to the hydrogen production characteristics of various types of electric hydrogen production systems, a hydrogen production rate model of various types of electric hydrogen production systems is established;

[0058] Hydrogen production rate model for alkaline electrolyzer:

[0059]

[0060] In the formula, is the hydrogen production rate of the alkaline electrolyzer, N is the number of alkaline electrolyzers in series, z is the number of transferred electrons, η F,1 is the Faradaic efficiency of the alkaline electrolyzer;

[0061] Hydrogen production rate model of proton exchange membrane electrolyzer:

[0062]

[0063] In the formula, is the hydrogen production rate of the proton exchange membrane electrolyzer, η F,2 is the Faraday efficiency of the proton exchange membrane electrolyzer; the hydrogen production rate model of the high-temperature solid oxide electrolyzer:

[0064]

[0065] In the formula, is the hydrogen production rate of the high-temperature solid oxide electrolyzer, η F,3 is the Faradaic efficiency of the high temperature solid oxide electrolyzer;

[0066] The Faraday efficiency is:

[0067]

[0068] Where η F,i is the Faraday efficiency of different types of electrolyzers, f1 and f2 are the correlation coefficients of Faraday efficiency, i is the type of electrolyzer, A iIndicates the electrolysis area of ​​different types of electrolytic cells, usually a fixed value; I i is the current input to different types of electrolyzers;

[0069] According to equations (18), (19) and (20), the hydrogen production rate model of the entire multi-type electric hydrogen production system is obtained as follows:

[0070]

[0071] In the formula, Indicates the hydrogen production rate of various types of electric hydrogen production systems;

[0072] Step 4: Establish a hydrogen production efficiency model for multiple types of hydrogen production systems based on the hydrogen production rates of the multiple types of hydrogen production systems;

[0073] Defining the hydrogen production efficiency of various types of electric hydrogen production systems Theoretical power of hydrogen production and input power of various types of hydrogen production systems The hydrogen production efficiency model of multi-type electric hydrogen production system is:

[0074]

[0075] In the formula, is the hydrogen production efficiency of various types of hydrogen production systems, is the input power of the multi-type electric hydrogen production system, ΔG is the Gibbs free energy of the electrochemical reaction;

[0076] Hydrogen production efficiency model for alkaline electrolyzer:

[0077]

[0078] Among them, η AEM is the hydrogen production efficiency of the alkaline electrolyzer;

[0079] Hydrogen production efficiency model of proton exchange membrane electrolyzer:

[0080]

[0081] Among them, η PEM is the hydrogen production efficiency of the proton exchange membrane electrolyzer;

[0082] Hydrogen production efficiency model for high temperature solid oxide electrolyzer:

[0083]

[0084] Among them, η SOEC is the hydrogen production efficiency of the high-temperature solid oxide electrolyzer;

[0085] Step 5: Based on the power model of the multi-type hydrogen production system, the power characteristic constraints of the multi-type hydrogen production system, the safety characteristic constraints and the hydrogen production efficiency model of the multi-type hydrogen production system, the objective function of the multi-type hydrogen production system is established with the goal of minimizing the operation control cost and the energy loss rate;

[0086]

[0087] Among them, F1 is the minimum function of energy loss rate, T is the operation cycle, and F2 is the minimum function of operation control cost. represents the initial investment cost function of multiple types of hydrogen production systems, represents the monthly operation and maintenance cost function of multiple types of hydrogen production systems, mincost represents the minimum cost;

[0088] Step 6: According to the input power of the multi-type hydrogen production system, the hydrogen production of the multi-type hydrogen production system is divided into three operating states: high production, moderate production, and low production, and the operating conditions of the electrolyzers in the multi-type hydrogen production system under different operating conditions are set;

[0089] (1) When the multi-type electric hydrogen production system works in the high-yield area;

[0090] (2) When the multi-type electric hydrogen production system works in the moderate production area;

[0091] (3) When the multi-type electric hydrogen production system works in the low-yield area;

[0092] in, is the rated power of the multi-type electric hydrogen production system, y1, y2 and y3 are three set thresholds ranging from 0 to 1;

[0093] It is assumed that when the type of hydrogen production system operates in a high-yield area, alkaline electrolyzers, proton exchange membrane electrolyzers and solid oxide electrolyzers are used to produce hydrogen, and when the type of hydrogen production system operates in a low-yield area and a moderate-yield area, only alkaline electrolyzers and proton exchange membrane electrolyzers are used;

[0094] Step 7: Allocate input power of the multi-type hydrogen production systems under different operating conditions according to the objective functions of the multi-type hydrogen production systems, the power characteristic constraints and the safety characteristic constraints of the multi-type hydrogen production systems;

[0095] Step 7.1: Obtain the input power of the multi-type hydrogen production system, determine the current operating status of the multi-type hydrogen production system, and then determine the operating status of each type of electrolyzer in the multi-type hydrogen production system;

[0096] Step 7.2: According to the operation conditions and power characteristic constraints of each type of electrolyzer, the individual genes are initialized to obtain a number of individuals, and then an initial population with a population size of X is obtained; the individuals represent the input power of different types of electrolyzers, and the genes represent the proportion of the power input to different types of electrolyzers to the total input power;

[0097] Step 7.3: Calculate the objective function value [F1, F2] for each individual;

[0098] Step 7.4: Determine the dominance relationship between individuals, and perform non-inferiority stratification on the entire population based on the dominance relationship between individuals to obtain several non-inferiority frontiers;

[0099] The method to determine the dominance relationship between individuals is: when all the objective function values ​​of individual A are not greater than B, and the objective function values ​​of the two are not completely equal, A is said to dominate B, or B dominates A, which can be expressed as:

[0100]

[0101] in, is the kth objective function value of individual A, The kth objective function value of individual B, k is the number of the objective function, F A ≠F B It means that the objective function values ​​of individual A and individual B are not completely equal;

[0102] The method for performing non-inferiority stratification on the entire population is as follows: when an individual in the population is not dominated by any other individual, it is called a non-dominated state, and the individual is called a non-inferior individual. The non-inferior individuals in the current population form a non-inferior frontier M1. After removing all individuals in M1, the dominance relationship between the remaining individuals is re-determined and the non-inferior individuals in the remaining individuals form a non-inferior frontier M2. In this way, non-inferior frontiers M1, M2, ... M are obtained. n , n is the number of non-inferior frontiers;

[0103] Step 7.5: Assign the crowding degree to each individual in the non-inferior frontier according to the objective function;

[0104] Specifically, first, the individuals in each non-inferior front are sorted according to the value of the first objective function. The crowding degree of the individuals with the largest and smallest values ​​of the first objective function is defined as infinity. The crowding degree of the middle individual under the first objective function is calculated. Then, according to the same method, the crowding degree of each individual under the second objective function is calculated. The crowding degree of each individual under the first and second objective functions is summed to obtain the final crowding degree of the individual.

[0105] The final crowding degree of the lth individual is I[l] distance Defined as:

[0106]

[0107] In the formula, l is the number of the individual, and are the maximum and minimum values ​​of the kth objective function of a population in a non-inferior frontier respectively;

[0108] Step 7.6: According to the non-inferior frontier and the final crowding degree, select, crossover and mutate individuals to obtain a sub-population with a population size of X;

[0109] Step 7.7: Use the parent population and the offspring population with the same population size of X to form an overall population of size 2X, calculate the objective function value of the individuals in the overall population, and perform non-inferiority stratification and final crowding calculation according to the methods in steps 7.4 and 7.5;

[0110] Step 7.8: Select individuals in the non-inferior frontier into the next generation population in order of non-inferior frontier. When adding individuals in the Lth non-inferior frontier to the next generation population will make the population size greater than X, use the final crowding degree to sort, select some individuals with larger final crowding degree values ​​in the Lth layer to enter the next generation population, and obtain a new generation population with a population size of X. The number of iterations increases by 1;

[0111] Step 7.9: Determine whether the current number of iterations has reached the maximum number of iterations. If so, select individuals from the current population according to demand and distribute the input power according to the input powers of different types of electrolytic cells represented by the individuals. Otherwise, return to step 7.6.

[0112] Compared with the prior art, the beneficial effects of the present invention are:

[0113] In order to promote the efficient development of renewable energy hydrogen production technology, the present invention innovatively proposes a hydrogen production method for the coordinated operation of multiple types of electrolyzers based on the fluctuation characteristics of new energy power generation and the dynamic response characteristics of water electrolysis hydrogen production equipment. Specifically, in the coordinated operation of multiple types of electrolysis, the present invention matches different electrolysis technologies, such as alkaline electrolysis (AEM), proton exchange membrane electrolysis (PEM) and high-temperature solid oxide electrolysis (SOEC) technologies, with new energy power generation loads with different fluctuation characteristics according to their dynamic response speed differences, thereby achieving differentiated utilization of AEM, PEM and SOEC. This method not only improves the working efficiency of various types of electrolysis devices, but also optimizes their coordinated operation.

[0114] In addition, the present invention also optimizes the capacity configuration of multi-type hydrogen production systems based on the output characteristics of renewable energy, in order to enhance the operational flexibility of the hydrogen production device and adapt it to the fluctuating characteristics of renewable energy power generation. This optimization process gives full play to the advantages of multi-type hydrogen production systems in power regulation, enabling multi-type hydrogen production systems to more effectively cope with the instability of renewable energy power generation. Through these innovative studies, the dynamic coupling effect between renewable energy power generation and electrolytic hydrogen production processes is improved, providing new ideas and practical basis for the development of efficient renewable energy hydrogen production technology, and helping to achieve a more sustainable energy utilization model. BRIEF DESCRIPTION OF THE DRAWINGS

[0115] Figure 1 This is an operation flow chart of a multi-type electric hydrogen production system in an embodiment of the present invention;

[0116] Figure 2 is a flow chart of a dynamic hydrogen production process in an embodiment of the present invention;

[0117] Figure 3 A flow chart of allocating input power to multiple types of hydrogen production systems under different operating conditions in an embodiment of the present invention;

[0118] Figure 4 Flow chart of the non-inferior stratified genetic algorithm in an embodiment of the present invention. DETAILED DESCRIPTION

[0119] The present invention is described in detail below with reference to the accompanying drawings and embodiments.

[0120] The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy includes the following steps:

[0121] Step 1: Multi-type hydrogen production systems include alkaline electrolyzer (AEM), proton exchange membrane electrolyzer (PEM) and high-temperature solid oxide electrolyzer (SOEC). The main operation flow chart is as follows: Figure 1 As shown, according to the power characteristics of different types of electrolyzers, the power model of multi-type electric hydrogen production system is obtained;

[0122] The power of the alkaline electrolytic cell is mainly affected by its own polarization characteristics (the change of voltage with current intensity or current density) and response speed. According to the polarization characteristics of the alkaline electrolytic cell, its power expression is as follows:

[0123]

[0124] Where P AEM is the input power of the alkaline electrolyzer, I A With T A are the current and temperature of the alkaline electrolytic cell respectively; r is the ohmic resistance parameter of the electrolyte; AA is the effective area of ​​the electrolytic cell membrane; s is the electrode overvoltage coefficient; U 01 is the reversible voltage;

[0125] The polarization characteristics of the proton exchange membrane electrolyzer are affected by open circuit voltage, activation overvoltage, diffusion overvoltage and ohmic overvoltage. Its power expression is as follows:

[0126] P PEM =I P ×U P (2)

[0127] Where P PEM is the input power of the proton exchange membrane electrolyzer, I P is the input current of the proton exchange membrane electrolyzer, U P is the input voltage of the proton exchange membrane electrolyzer, and its expression is as follows:

[0128] U P =U oc,P +U a,P +U diff +U ohm,P (3)

[0129] Among them, U oc,P is the open circuit voltage of the proton exchange membrane electrolyzer, U a,P is the activation overvoltage of the proton exchange membrane electrolyzer, U diff is the diffusion overvoltage of the proton exchange membrane electrolyzer, U ohm,P is the ohmic overvoltage of the proton exchange membrane electrolyzer;

[0130] The open circuit voltage of the proton exchange membrane electrolyzer is:

[0131]

[0132] Among them, U 02 is the standard electromotive force of the proton exchange membrane electrolyzer, R is the gas constant, T P is the temperature of the proton exchange membrane electrolyzer, and are the pressures of hydrogen and oxygen, respectively, is the water activity between electrolytes, and F is the Faraday constant;

[0133] The activation overvoltage of the proton exchange membrane electrolyzer is:

[0134] U a,P =RT P sinh -1 (J P / 2J 0,ap ) / α ap F+RTP sinh -1 (J P / 2J 0,cp ) / α cp F (5)

[0135] Among them, J P is the current density of the proton exchange membrane electrolyzer, J 0,ap and J 0,cp are the exchange current density of the anode and cathode of the proton exchange membrane electrolyzer, α ap and α cp are the charge transfer coefficients of the anode and cathode of the proton exchange membrane electrolyzer, respectively;

[0136] The diffusion overvoltage of the proton exchange membrane electrolyzer is:

[0137]

[0138] Where, T a and T c are the temperatures of the cathode and anode of the proton exchange membrane electrolyzer, and are the oxygen and hydrogen concentrations, and are the standard reference values ​​for oxygen and hydrogen, respectively;

[0139] The ohmic overvoltage of the proton exchange membrane electrolyzer is:

[0140] U ohm =J P ×R P (7)

[0141] Among them, R P is the equivalent resistance of the proton exchange membrane electrolyzer;

[0142] The power model of high-temperature solid oxide electrolyzer is similar to that of AEM and PEM. Its electrolyzer voltage is composed of equilibrium voltage, activation overvoltage, concentration difference voltage and ohmic overvoltage. Its power model expression is as follows:

[0143] P SOEC =I S ×U S (8)

[0144] Where P SOEC is the input power of the high temperature solid oxide electrolyzer, I S is the input current of the high temperature solid oxide electrolyzer, U S is the input voltage of the high temperature solid oxide electrolyzer, and its expression is as follows:

[0145] U S =Uoc,s +U a,S +U ohm,S +U conc (9)

[0146] Among them, U oc,s is the equilibrium voltage of the high temperature solid oxide electrolyzer, U a,S is the activation overvoltage of the high-temperature solid oxide electrolyzer, U ohm,S is the ohmic overvoltage of the high-temperature solid oxide electrolyzer, U conc is the concentration difference voltage of the high temperature solid oxide electrolyzer;

[0147] The equilibrium voltage of the high temperature solid oxide electrolyzer is:

[0148]

[0149] Where, T S is the temperature of the high temperature solid oxide electrolyzer, U 03 is the standard electromotive force of a high-temperature solid oxide electrolyzer, and are the pressures of hydrogen and oxygen respectively;

[0150] The activation overvoltage of the high temperature solid oxide electrolyzer is:

[0151] U a,S =RT S sinh -1 (J S / 2J 0,aS ) / α aS F+RT S sinh -1 (J S / 2J 0,cS ) / α cS F (11)

[0152] In the formula, J S is the current density of the high temperature solid oxide electrolyzer, J 0,aS and J 0,cS are the exchange current density of the anode and cathode of the high-temperature solid oxide electrolyzer, α aS and α cS are the charge transfer coefficients of the anode and cathode of the high-temperature solid oxide electrolyzer, respectively;

[0153] Step 2: Analyze the power characteristics of various types of hydrogen production systems, and establish power characteristic constraints and safety characteristic constraints of various types of hydrogen production systems;

[0154] The power characteristic constraint of the alkaline electrolyzer is:

[0155]

[0156] The safety characteristics of alkaline electrolyzers are constrained by:

[0157]

[0158] Among them, δ AEM is the working state of the alkaline electrolytic cell, a value of 1 indicates that the alkaline electrolytic cell is operating, and a value of 0 indicates that the alkaline electrolytic cell is not operating; is the maximum input power of the alkaline electrolyzer, that is, the maximum capacity of the alkaline electrolyzer;

[0159] The power characteristic constraint of the proton exchange membrane electrolyzer is:

[0160]

[0161] The safety characteristics of the proton exchange membrane electrolyzer are constrained as follows:

[0162]

[0163] Among them, δ PEM It is the working state of the proton exchange membrane electrolyzer. Its value is 1, which means the proton exchange membrane electrolyzer is running, and its value is 0, which means the proton exchange membrane electrolyzer is not running. is the maximum input power of the proton exchange membrane electrolyzer, that is, the maximum capacity of the proton exchange membrane electrolyzer;

[0164] The power characteristic constraints of the high temperature solid oxide electrolyzer are:

[0165]

[0166] The safety characteristics of high temperature solid oxide electrolyzers are constrained as follows:

[0167]

[0168] Among them, δ SOEC is the working state of the high-temperature solid oxide electrolyzer, a value of 1 indicates that the high-temperature solid oxide electrolyzer is operating, and a value of 0 indicates that the high-temperature solid oxide electrolyzer is not operating; is the maximum input power of the high-temperature solid oxide electrolyzer, that is, the maximum capacity of the high-temperature solid oxide electrolyzer;

[0169] Step 3: According to the hydrogen production characteristics of various types of electric hydrogen production systems, a hydrogen production rate model of various types of electric hydrogen production systems is established;

[0170] Since the hydrogen production characteristics of electrolyzers based on different principles are almost the same, it can be obtained that:

[0171] Hydrogen production rate of alkaline electrolyzer:

[0172]

[0173] In the formula, is the hydrogen production rate of the alkaline electrolyzer, N is the number of alkaline electrolyzers in series, z is the number of transferred electrons, η F,1 is the Faradaic efficiency of the alkaline electrolyzer;

[0174] Hydrogen production rate of proton exchange membrane electrolyzer:

[0175]

[0176] In the formula, is the hydrogen production rate of the proton exchange membrane electrolyzer, η F,2 is the Faraday efficiency of the proton exchange membrane electrolyzer; the hydrogen production rate of the high-temperature solid oxide electrolyzer is:

[0177]

[0178] In the formula, is the hydrogen production rate of the high-temperature solid oxide electrolyzer, η F,3 is the Faradaic efficiency of the high temperature solid oxide electrolyzer;

[0179] The Faraday efficiency is:

[0180]

[0181] Where η F,i is the Faraday efficiency of different types of electrolyzers, f1 and f2 are the correlation coefficients of Faraday efficiency, i is the type of electrolyzer, A i Indicates the electrolysis area of ​​different types of electrolytic cells, usually a fixed value; I i is the current input to different types of electrolyzers;

[0182] According to equations (18), (19) and (20), the hydrogen production rate of the entire multi-type electric hydrogen production system is obtained as follows:

[0183]

[0184] In the formula, Indicates the hydrogen production rate of various types of electric hydrogen production systems;

[0185] Step 4: Establish a hydrogen production efficiency model for multiple types of hydrogen production systems based on the hydrogen production rates of the multiple types of hydrogen production systems;

[0186] Defining the hydrogen production efficiency of various types of electric hydrogen production systems Theoretical power of hydrogen production and input power of various types of hydrogen production systems Ratio of:

[0187]

[0188] In the formula, is the hydrogen production efficiency of various types of hydrogen production systems, is the input power of the multi-type electric hydrogen production system, ΔG is the Gibbs free energy of the electrochemical reaction;

[0189] The hydrogen production efficiency models of different types of electrolyzers are as follows:

[0190] The hydrogen production efficiency of alkaline electrolyzer is expressed as:

[0191]

[0192] Among them, η AEM is the hydrogen production efficiency of the alkaline electrolyzer;

[0193] The hydrogen production efficiency of proton exchange membrane electrolyzer is expressed as:

[0194]

[0195] Among them, η PEM is the hydrogen production efficiency of the proton exchange membrane electrolyzer;

[0196] The hydrogen production efficiency expression of high temperature solid oxide electrolyzer is:

[0197]

[0198] Among them, η SOEC is the hydrogen production efficiency of the high-temperature solid oxide electrolyzer;

[0199] According to the dynamic characteristics of different electrolyzers, the dynamic hydrogen production process is as follows: Figure 2 shown.

[0200] Step 5: Based on the power model of the multi-type hydrogen production system, the power characteristic constraints of the multi-type hydrogen production system, the safety characteristic constraints and the hydrogen production efficiency model of the multi-type hydrogen production system, the objective function of the multi-type hydrogen production system is established with the goal of minimizing the operation control cost and the energy loss rate;

[0201] Taking the input power of multi-type hydrogen production systems as input and the hydrogen output as output, considering the safety characteristic constraints and power characteristic constraints of multi-type hydrogen production systems, and minimizing the operation control cost and the energy loss rate as the goal, a multi-objective function is established as follows:

[0202]

[0203] Among them, F1 is the minimum function of energy loss rate, T is the operation cycle, and F2 is the minimum function of operation control cost. represents the initial investment cost function of multiple types of hydrogen production systems, represents the monthly operation and maintenance cost function of multiple types of hydrogen production systems, mincost represents the minimum cost;

[0204] Step 6: According to the input power of the multi-type hydrogen production system, the hydrogen production of the multi-type hydrogen production system is divided into three operating states: high production, moderate production, and low production, and the operating conditions of the electrolyzers in the multi-type hydrogen production system under different operating conditions are set;

[0205] If the rated power of the multi-type hydrogen production system is The safe operating range of various types of electric hydrogen production systems is 55%-100% of the rated power. If the power is lower than this, the purity of the produced hydrogen may be poor, which may easily lead to explosion accidents.

[0206] According to the input power of multi-type electric hydrogen production systems, there are three operating states:

[0207] (1) When the multi-type electric hydrogen production system works in the high-yield area;

[0208] (2) When the multi-type electric hydrogen production system works in the moderate production area;

[0209] (3) When the multi-type electric hydrogen production system works in the low-yield area;

[0210] Since the solid oxide electrolyzer starts up slowly and has a high startup cost, if the working power of the entire multi-type hydrogen production system is not very large and the demand for hydrogen is not very high, frequently starting the solid oxide electrolyzer will greatly increase the regulation cost of the multi-type hydrogen production system. Therefore, it is stipulated that in the low-production area and moderate-production area of ​​the multi-type hydrogen production system, the high-temperature solid oxide electrolyzer will not participate in hydrogen production, and only the alkaline electrolyzer and proton exchange membrane electrolyzer need to be regulated at this time.

[0211] Step 7: Allocate input power of the multi-type hydrogen production systems under different operating conditions according to the objective functions of the multi-type hydrogen production systems, the power characteristic constraints and the safety characteristic constraints of the multi-type hydrogen production systems;

[0212] By classifying the operation of various types of hydrogen production systems under different scenarios, and considering the fluctuation characteristics of power grid, the capacity (power) configuration of AEM electrolyzer, PEM electrolyzer and SOEC electrolyzer is solved by non-inferior hierarchical genetic algorithm (NSGA-Ⅱ). Under the goal of minimizing economic cost and maximizing hydrogen production, the capacity configuration of AEM electrolyzer, PEM electrolyzer and SOEC electrolyzer is obtained, such as Figure 3 As shown;

[0213] The non-inferior hierarchical genetic algorithm equates the capacity configuration optimization process of multi-type hydrogen production systems to the evolution process of the population, which is mainly divided into the following steps: Figure 4 As shown:

[0214] Step 7.1: Obtain the input power of the multi-type hydrogen production system, determine the current operating status of the multi-type hydrogen production system, and then determine the operating status of each type of electrolyzer in the multi-type hydrogen production system;

[0215] Step 7.2: According to the operation conditions and power characteristic constraints of each type of electrolyzer, the individual genes are initialized to obtain a number of individuals, and then an initial population with a population size of X is obtained; the individuals represent the input power of different types of electrolyzers, and the genes represent the proportion of the power input to different types of electrolyzers to the total input power;

[0216] When the multi-type electrolysis hydrogen production system is in the low-production area and the moderate-production area, the proportion of the power of the solid oxide electrolyzer to the total input power during the individual initialization process is 0;

[0217] Step 7.3: Calculate the objective function value [F1, F2] for each individual;

[0218] Step 7.4: Before performing the individual selection operation, first determine the dominance relationship between individuals, and perform non-inferiority stratification on the entire population based on the dominance relationship between individuals to obtain several non-inferiority frontiers;

[0219] The method to determine the dominance relationship between individuals is: when all the objective function values ​​of individual A are not greater than B, and the objective function values ​​of the two are not completely equal, A is said to dominate B, or B dominates A, which can be expressed as:

[0220]

[0221] in, is the kth objective function value of individual A, The kth objective function value of individual B, k is the number of the objective function, F A ≠F B It means that the objective function values ​​of individual A and individual B are not completely equal;

[0222] The method for performing non-inferiority stratification on the entire population is as follows: when an individual in the population is not dominated by any other individual, it is called a non-dominated (non-inferior) state, and the individual is called a non-inferior individual. The non-inferior individuals in the current population form a non-inferior frontier M1. After removing all individuals in M1, the dominance relationship between the remaining individuals is re-determined and the non-inferior individuals in the remaining individuals form a non-inferior frontier M2. In this way, non-inferior frontiers M1, M2, ... M are obtained. n , n is the number of non-inferior frontiers;

[0223] Step 7.5: In order to ensure the diversity of the population during the selection process, the crowding degree of the individuals in each non-inferior frontier is assigned according to the objective function;

[0224] Specifically, first, the individuals in each non-inferior front are sorted according to the value of the first objective function. The crowding degree of the individuals with the largest and smallest values ​​of the first objective function is defined as infinity. The crowding degree of the middle individual under the first objective function is calculated. Then, according to the same method, the crowding degree of each individual under the second objective function is calculated. The crowding degree of each individual under the first and second objective functions is summed to obtain the final crowding degree of the individual.

[0225] The final crowding degree of the lth individual is I[l] distance Defined as:

[0226]

[0227] In the formula, l is the number of the individual, and are the maximum and minimum values ​​of the kth objective function of a population in a non-inferior frontier respectively;

[0228] Step 7.6: According to the non-inferior frontier and the final crowding degree, select, crossover and mutate individuals to obtain a sub-population with a population size of X;

[0229] Step 7.7: Use the parent population and the offspring population with the same population size of X to form an overall population of size 2X, calculate the objective function value of the individuals in the overall population, and perform non-inferiority stratification and final crowding calculation according to the methods in steps 7.4 and 7.5;

[0230] Step 7.8: Select individuals in the non-inferior frontier into the next generation population in order of non-inferior frontier. When adding individuals in the Lth non-inferior frontier to the next generation population will make the population size greater than X, use the final crowding degree to sort, select some individuals with larger final crowding degree values ​​in the Lth layer to enter the next generation population, and obtain a new generation population with a population size of X. The number of iterations increases by 1;

[0231] Step 7.9: Determine whether the current number of iterations reaches the maximum number of iterations. If so, select individuals from the current population according to demand, and distribute the input power according to the input powers of different types of electrolytic cells represented by the individuals. Otherwise, return to step 7.6;

[0232] The solution obtained by the non-inferior hierarchical genetic algorithm is the capacity ratio of the three hydrogen production methods in the multi-type electric hydrogen production system. In different scenarios, according to the different fluctuations of power grid electricity, the capacity ratio of each hydrogen production method is continuously updated to always meet the goals of minimizing regulation cost and maximizing energy utilization.

Claims

1. A multi-type electric hydrogen production optimization control method taking into account the consumption of new energy, characterized in that: The following steps are involved: Step 1: Modeling is performed according to the power characteristics of different types of electrolyzers in the multi-type hydrogen production system to obtain a power model of the multi-type hydrogen production system; Step 2: Analyze the power characteristics of various types of hydrogen production systems, and establish power characteristic constraints and safety characteristic constraints of various types of hydrogen production systems; Step 3: According to the hydrogen production characteristics of various types of electric hydrogen production systems, a hydrogen production rate model of various types of electric hydrogen production systems is established; Step 4: Establish a hydrogen production efficiency model for multiple types of hydrogen production systems based on the hydrogen production rates of the multiple types of hydrogen production systems; Step 5: Based on the power model of the multi-type hydrogen production system, the power characteristic constraints of the multi-type hydrogen production system, the safety characteristic constraints and the hydrogen production efficiency model of the multi-type hydrogen production system, the objective function of the multi-type hydrogen production system is established with the goal of minimizing the operation control cost and the energy loss rate; Step 6: According to the input power of the multi-type hydrogen production system, the hydrogen production of the multi-type hydrogen production system is divided into three operating states: high production, moderate production, and low production, and the operating conditions of the electrolyzers in the multi-type hydrogen production system under different operating conditions are set; Step 7: Allocate input power of the multi-type hydrogen production system under different operating conditions according to the objective function of the multi-type hydrogen production system, the power characteristic constraints and the safety characteristic constraints of the multi-type hydrogen production system.

2. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 1 is characterized in that: The multi-type hydrogen production system described in step 1 includes an alkaline electrolyzer, a proton exchange membrane electrolyzer and a high-temperature solid oxide electrolyzer.

3. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 2 is characterized in that: The power model of the multi-type hydrogen production system in step 1 includes: The power model for an alkaline electrolyser is: Where P AEM is the input power of the alkaline electrolyzer, I A With T A are the current and temperature of the alkaline electrolytic cell respectively; r is the ohmic resistance parameter of the electrolyte; A A is the effective area of ​​the electrolytic cell membrane; s is the electrode overvoltage coefficient; U 01 is the reversible voltage; The power model of the proton exchange membrane electrolyzer is: P PEM =I P ×U P (2) Where P PEM is the input power of the proton exchange membrane electrolyzer, I P is the input current of the proton exchange membrane electrolyzer, U P is the input voltage of the proton exchange membrane electrolyzer; The power model of the high temperature solid oxide electrolyzer is: P SOEC =I S ×U S (8) Where P SOEC is the input power of the high temperature solid oxide electrolyzer, I S is the input current of the high temperature solid oxide electrolyzer, U S is the input voltage of the high temperature solid oxide electrolyzer; The input voltage of the proton exchange membrane electrolyzer is: IN P =U oc,P +U a,P +U diff +U ohm,P (3) Among them, U oc,P is the open circuit voltage of the proton exchange membrane electrolyzer, U a,P is the activation overvoltage of the proton exchange membrane electrolyzer, U diff is the diffusion overvoltage of the proton exchange membrane electrolyzer, U ohm,P is the ohmic overvoltage of the proton exchange membrane electrolyzer; The open circuit voltage of the proton exchange membrane electrolyzer is: Among them, U 02 is the standard electromotive force of the proton exchange membrane electrolyzer, R is the gas constant, T P is the temperature of the proton exchange membrane electrolyzer, and are the pressures of hydrogen and oxygen, respectively, is the water activity between electrolytes, and F is the Faraday constant; The activation overvoltage of the proton exchange membrane electrolyzer is: U a,P =RT P born -1 (J P / 2J 0,ap ) / α ap F+RT P born -1 (J P / 2J 0,cp ) / α cp F (5) Among them, J P is the current density of the proton exchange membrane electrolyzer, J 0,ap and J 0,cp are the exchange current density of the anode and cathode of the proton exchange membrane electrolyzer, α ap and α cp are the charge transfer coefficients of the anode and cathode of the proton exchange membrane electrolyzer, respectively; The diffusion overvoltage of the proton exchange membrane electrolyzer is: Where, T a and T c are the temperatures of the cathode and anode of the proton exchange membrane electrolyzer, and are the oxygen and hydrogen concentrations, and are the standard reference values ​​for oxygen and hydrogen, respectively; The ohmic overvoltage of a proton exchange membrane electrolyzer is: U ohm =J P ×R P (7) Among them, R P is the equivalent resistance of the proton exchange membrane electrolyzer; The input voltage of the high temperature solid oxide electrolyzer is: IN S =U oc,s +U a,S +U ohm,S +U conc (9) Among them, U oc,s is the equilibrium voltage of the high temperature solid oxide electrolyzer, U a,S is the activation overvoltage of the high-temperature solid oxide electrolyzer, U ohm,S is the ohmic overvoltage of the high-temperature solid oxide electrolyzer, U conc is the concentration difference voltage of the high temperature solid oxide electrolyzer; The equilibrium voltage of the high temperature solid oxide electrolyzer is: Where, T S is the temperature of the high temperature solid oxide electrolyzer, U 03 is the standard electromotive force of a high-temperature solid oxide electrolyzer, and are the pressures of hydrogen and oxygen respectively; The activation overvoltage of the high temperature solid oxide electrolyzer is: U a,S =RT S born -1 (J S / 2J 0,aS ) / α aS F+RT S born -1 (J S / 2J 0,cS ) / α cS F (11) In the formula, J S is the current density of the high temperature solid oxide electrolyzer, J 0,aS and J 0,cS are the exchange current density of the anode and cathode of the high-temperature solid oxide electrolyzer, α aS and α cS are the charge transfer coefficients of the anode and cathode of the high-temperature solid oxide electrolyzer, respectively.

4. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 3 is characterized in that: The power characteristic constraints and safety characteristic constraints of the multi-type hydrogen production system in step 2 include: The power characteristic constraint of the alkaline electrolyzer is: The safety characteristics of alkaline electrolyzers are constrained by: Among them, δ AEM is the working state of the alkaline electrolytic cell, a value of 1 indicates that the alkaline electrolytic cell is operating, and a value of 0 indicates that the alkaline electrolytic cell is not operating; is the maximum input power of the alkaline electrolyzer, that is, the maximum capacity of the alkaline electrolyzer; The power characteristic constraint of the proton exchange membrane electrolyzer is: The safety characteristics of the proton exchange membrane electrolyzer are constrained as follows: Among them, δ PEM It is the working state of the proton exchange membrane electrolyzer. Its value is 1, which means the proton exchange membrane electrolyzer is running, and its value is 0, which means the proton exchange membrane electrolyzer is not running. is the maximum input power of the proton exchange membrane electrolyzer, that is, the maximum capacity of the proton exchange membrane electrolyzer; The power characteristic constraints of the high temperature solid oxide electrolyzer are: The safety characteristics of high temperature solid oxide electrolyzers are constrained as follows: Among them, δ SOEC is the working state of the high-temperature solid oxide electrolyzer, a value of 1 indicates that the high-temperature solid oxide electrolyzer is operating, and a value of 0 indicates that the high-temperature solid oxide electrolyzer is not operating; It is the maximum input power of the high temperature solid oxide electrolyzer, that is, the maximum capacity of the high temperature solid oxide electrolyzer.

5. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 4 is characterized in that: The construction process of the hydrogen production rate model of the multi-type electric hydrogen production system in step 3 is: Hydrogen production rate model for alkaline electrolyzer: In the formula, is the hydrogen production rate of the alkaline electrolyzer, N is the number of alkaline electrolyzers in series, z is the number of transferred electrons, η F,1 is the Faradaic efficiency of the alkaline electrolyzer; Hydrogen production rate model of proton exchange membrane electrolyzer: In the formula, is the hydrogen production rate of the proton exchange membrane electrolyzer, η F,2 is the Faradaic efficiency of the proton exchange membrane electrolyzer; Hydrogen production rate model for high temperature solid oxide electrolyzer: In the formula, is the hydrogen production rate of the high-temperature solid oxide electrolyzer, η F,3 is the Faradaic efficiency of the high temperature solid oxide electrolyzer; The Faraday efficiency is: Where η F,i is the Faraday efficiency of different types of electrolyzers, f1 and f2 are the correlation coefficients of Faraday efficiency, i is the type of electrolyzer, A i Indicates the electrolysis area of ​​different types of electrolytic cells, usually a fixed value; I i is the current input to different types of electrolyzers; According to equations (18), (19) and (20), the hydrogen production rate model of the entire multi-type electric hydrogen production system is obtained as follows: In the formula, Represents the hydrogen production rate of multiple types of electric hydrogen production systems.

6. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 5 is characterized in that: The hydrogen production efficiency model of the multi-type electric hydrogen production system in step 4 is: In the formula, is the hydrogen production efficiency of various types of hydrogen production systems, is the input power of the multi-type electric hydrogen production system, ΔG is the Gibbs free energy of the electrochemical reaction; Hydrogen production efficiency model for alkaline electrolyzer: Among them, η AEM is the hydrogen production efficiency of the alkaline electrolyzer; Hydrogen production efficiency model of proton exchange membrane electrolyzer: Among them, η PEM is the hydrogen production efficiency of the proton exchange membrane electrolyzer; Hydrogen production efficiency model for high temperature solid oxide electrolyzer: Among them, η SOEC is the hydrogen production efficiency of the high-temperature solid oxide electrolyzer.

7. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 6 is characterized in that: The objective function in step 5 is: Among them, F1 is the minimum function of energy loss rate, T is the operation cycle, and F2 is the minimum function of operation control cost. represents the initial investment cost function of multiple types of hydrogen production systems, It represents the monthly operation and maintenance cost function of multiple types of hydrogen production systems, and mincost represents the minimum cost.

8. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 6 is characterized in that: The running status described in step 6 is: (1) When the multi-type electric hydrogen production system works in the high-yield area; (2) When the multi-type electric hydrogen production system works in the moderate production area; (3) When the multi-type electric hydrogen production system works in the low-yield area; in, is the rated power of the multi-type electric hydrogen production system, y1, y2 and y3 are three set thresholds ranging from 0 to 1; It is set that when the type of hydrogen production system operates in a high-yield area, alkaline electrolyzers, proton exchange membrane electrolyzers and solid oxide electrolyzers are used to produce hydrogen, and when the type of hydrogen production system operates in a low-yield area and a moderate-yield area, only alkaline electrolyzers and proton exchange membrane electrolyzers are used.

9. The multi-type electric hydrogen production optimization control method taking into account the consumption of new energy according to claim 2 is characterized in that: The step 7 specifically includes: Step 7.1: Obtain the input power of the multi-type hydrogen production system, determine the current operating status of the multi-type hydrogen production system, and then determine the operating status of each type of electrolyzer in the multi-type hydrogen production system; Step 7.2: According to the operation conditions and power characteristic constraints of each type of electrolyzer, the individual genes are initialized to obtain a number of individuals, and then an initial population with a population size of X is obtained; the individuals represent the input power of different types of electrolyzers, and the genes represent the proportion of the power input to different types of electrolyzers to the total input power; Step 7.3: Calculate the objective function value [F1, F2] for each individual; Step 7.4: Determine the dominance relationship between individuals, and perform non-inferiority stratification on the entire population based on the dominance relationship between individuals to obtain several non-inferiority frontiers; The method to determine the dominance relationship between individuals is: when all the objective function values ​​of individual A are not greater than B, and the objective function values ​​of the two are not completely equal, A is said to dominate B, or B dominates A, which can be expressed as: in, is the kth objective function value of individual A, The kth objective function value of individual B, k is the number of the objective function, F A ≠F B It means that the objective function values ​​of individual A and individual B are not completely equal; The method for non-inferior stratification of the entire population is as follows: when an individual in the population is not dominated by any other individual, it is called a non-dominated state, and the individual is called a non-inferior individual. The non-inferior individuals in the current population form a non-inferior frontier M1. After removing all individuals in M1, the dominance relationship between the remaining individuals is re-determined and the non-inferior individuals in the remaining individuals form a non-inferior frontier M2. In this way, non-inferior frontiers M1, M2, etc. are obtained. n , n is the number of non-inferior frontiers; Step 7.5: Assign the crowding degree to each individual in the non-inferior frontier according to the objective function; Specifically, first, the individuals in each non-inferior front are sorted according to the value of the first objective function. The crowding degree of the individuals with the largest and smallest values ​​of the first objective function is defined as infinity. The crowding degree of the middle individual under the first objective function is calculated. Then, according to the same method, the crowding degree of each individual under the second objective function is calculated. The crowding degree of each individual under the first and second objective functions is summed to obtain the final crowding degree of the individual. The final crowding degree of the lth individual is I[l] distance Defined as: In the formula, l is the number of the individual, and are the maximum and minimum values ​​of the kth objective function of a population in a non-inferior frontier respectively; Step 7.6: According to the non-inferior frontier and the final crowding degree, select, crossover and mutate individuals to obtain a sub-population with a population size of X; Step 7.7: Use the parent population and the offspring population with the same population size of X to form an overall population of size 2X, calculate the objective function value of the individuals in the overall population, and perform non-inferiority stratification and final crowding calculation according to the methods in steps 7.4 and 7.5; Step 7.8: Select individuals in the non-inferior frontier into the next generation population in order of non-inferior frontier. When adding individuals in the Lth non-inferior frontier to the next generation population will make the population size greater than X, use the final crowding degree to sort, select some individuals with larger final crowding degree values ​​in the Lth layer to enter the next generation population, and obtain a new generation population with a population size of X. The number of iterations increases by 1; Step 7.9: Determine whether the current number of iterations has reached the maximum number of iterations. If so, select individuals from the current population according to demand and distribute the input power according to the input powers of different types of electrolytic cells represented by the individuals. Otherwise, return to step 7.6.

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