Dynamic performance control method for hydrogen production electrolytic cell based on improved particle swarm optimization

Abstract

The invention discloses a hydrogen production electrolytic cell dynamic performance control method based on an improved particle swarm optimization algorithm, which comprises the following steps of: extracting index parameters of an electrolytic cell, constructing a mathematical model which comprises operating voltage, hydrogen production rate and hydrogen production efficiency, and calculating the dynamic performance of the electrolytic cell according to the operating voltage, the hydrogen production rate and the hydrogen production efficiency. The operating voltage, the hydrogen production rate and the hydrogen production efficiency of the mathematical model are calculated to obtain multi-target optimization parameters for constraining the operating temperature of the electrolytic cell, the weight of existing linear quadratic programming control is optimized through a self-adaptive weight multi-target particle swarm algorithm, the dynamic temperature model of the electrolytic cell is constructed, and the optimal temperature of the electrolytic cell is obtained. And controlling the operating temperature of the electrolytic cell to be within a constrained electrolytic cell operating temperature range through the electrolytic cell temperature dynamic model. According to the method, the weight of linear quadratic programming control is optimized through the self-adaptive weight multi-target particle swarm algorithm, and the electrolytic bath temperature dynamic model is constructed, so that stable and rapid feedback control can be performed on the operating temperature of the electrolytic bath.

Description

Technical Field

[0001] The invention relates to the technical field of electrolyzers, and in particular to a method for controlling the dynamic performance of a hydrogen production electrolyzer based on an improved particle swarm algorithm. Background Art

[0002] Photovoltaic water electrolysis hydrogen production technology is beneficial to the consumption of renewable energy on the one hand, and can effectively solve the problem of green hydrogen production on the other hand. As the key equipment of the photovoltaic water electrolysis hydrogen production system, the performance characteristics of the electrolyzer itself play a vital role in the energy utilization rate and hydrogen production efficiency of the photovoltaic water electrolysis hydrogen production system. At present, the cost of alkaline electrolyzers is relatively low (3,000 yuan / kW) and has been widely used in commercial applications. However, the cold start time of AEL under rated load is as long as 60-120 minutes, and the hot start time still takes 60-300 seconds. The startup time is relatively long, and the maximum hydrogen production is 2.09Nm 3 / h·m 2 Moreover, the instability of the output power of the fluctuating power supply will cause the AEL electrolysis efficiency and hydrogen production to decrease, and the AEL equipment to be damaged. In order to improve the compatibility of AEL with fluctuating power supplies, researchers used energy storage systems to assist photovoltaic systems in hydrogen production. Although this method has improved the operating life of AEL to a certain extent, it has greatly increased the cost of hydrogen production, and the limitations of AEL's own performance have not been improved. Compared with AEL, the hot start of the proton exchange membrane electrolyzer is less than 10s, and it has a higher hydrogen production efficiency, and the hydrogen production can reach 12.54Nm 3 / h·m 2 , and has good adaptability with fluctuating power sources. At present, PEMEL application has entered the engineering demonstration stage. However, the cost of PEMEL equipment is relatively high (9,000 yuan / kW). At the same time, in some previous works, previous studies mostly focused on the overall performance of the wind energy, light energy and hydrogen storage coupling system, or only discussed the electrolyzer performance from the perspective of hydrogen production rate, ignoring the importance of hydrogen production efficiency. This limitation makes it difficult for existing electrolyzer control strategies to meet a wider range of engineering needs. At the same time, when constructing the mathematical model of the electrolyzer, in order to simplify the calculation, key factors such as Faraday efficiency and ohmic resistance are often set to fixed values, which to a certain extent affects the accuracy and practicality of the model.

[0003] In combination with the above research results, in order to meet the hydrogen production needs under different working conditions, the present invention conducts more accurate system modeling of PEMEL, including hydrogen production rate, hydrogen production efficiency, and PEMEL electrolyzer temperature control model, and proposes an application of hydrogen production electrolyzer dynamic performance control technology based on improved particle swarm algorithm. According to different working conditions, relying on the improved particle swarm algorithm, namely the adaptive multi-objective particle swarm algorithm, the optimal electrolyzer configuration scheme is finally selected. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a method for controlling the dynamic performance of a hydrogen production electrolyzer based on an improved particle swarm algorithm to solve the problems raised in the above background technology.

[0005] To achieve the above object, the present invention provides the following technical solution: a method for controlling the dynamic performance of a hydrogen production electrolyzer based on an improved particle swarm algorithm, comprising the following steps:

[0006] Step S1: extracting index parameters according to the dynamic characteristics of the electrolytic cell, the index parameters include the electrolytic cell current density and the electrolytic cell operating temperature:

[0007] Step S2: construct a mathematical model, which includes operating voltage, hydrogen production rate and hydrogen production efficiency. The operating dynamic characteristics of the electrolyzer are observed through the mathematical model, and the operating voltage, hydrogen production rate and hydrogen production efficiency of the mathematical model are calculated to obtain the performance parameters of the electrolyzer:

[0008] Step S3: A multi-objective particle swarm algorithm with adaptive weights is used to perform multi-objective optimization on the performance parameters of the electrolyzer obtained in step S2, and the parameters of the multi-objective optimization are obtained. The parameters based on the multi-objective optimization are the optimal solution that takes into account both the hydrogen production efficiency and the maximization of the hydrogen production rate. The electrolyzer current density is constrained based on the optimal solution of the maximization of the hydrogen production efficiency and the hydrogen production rate, and the range of the electrolyzer operating temperature is constrained based on the constrained electrolyzer current density:

[0009] Step S4: Based on the adaptive weighted multi-objective particle swarm algorithm of step S3, the weights of the existing linear quadratic programming control are optimized, and a dynamic model of the electrolytic cell temperature is constructed. The electrolytic cell operating temperature is controlled within the constrained electrolytic cell operating temperature range through the electrolytic cell temperature dynamic model.

[0010] Further, in step S1, the index parameters are extracted according to the dynamic characteristics of the electrolytic cell, and the specific process is as follows:

[0011] According to the dynamic characteristics of the electrolyzer, four index parameters and evaluations of the electrolyzer are extracted, index parameter 1: electrolyzer current density, denoted as I1; index parameter 2: electrolyzer operating temperature, denoted as I2; index parameter 3: electrolyzer anode oxygen partial pressure, denoted as I3; index parameter 4: electrolyzer cathode hydrogen pressure, denoted as I4; the dynamic characteristics of the electrolyzer include operating voltage, hydrogen production rate and hydrogen production efficiency.

[0012] Further, step S2 obtains the performance parameters of the electrolytic cell, and the specific process is as follows:

[0013] The operating voltage, hydrogen production rate and hydrogen production efficiency are taken as target quantities, and a mathematical model is constructed based on the three target quantities, so that the operating dynamic characteristics of the electrolyzer can be observed intuitively so as to perform multi-objective optimization on the target quantities;

[0014] The operating voltage is divided into three parts: the three parts include reversible voltage, activation overvoltage and ohmic overvoltage, expressed as:

[0015] U cell =U rev +U ohm +U act (1);

[0016] Where U cell Indicates the operating voltage of the electrolytic cell; U rev Represents reversible voltage; U ohm Indicates activation overvoltage; U act Indicates ohmic overvoltage;

[0017] The reversible voltage is expressed as:

[0018]

[0019]

[0020]

[0021] In the formula, Indicates the reversible voltage under standard conditions; E rev Indicates the correction value of the reversible voltage; represents Gibbs free energy; F represents Faraday constant; T represents the operating temperature of the electrolytic cell; and Represent the partial pressures of hydrogen and oxygen respectively; α H2 O represents water activity; R represents the ideal gas constant;

[0022] The activation overvoltage is expressed as:

[0023]

[0024] Where U act Represents activation overvoltage; α an and α cat denote the charge transfer coefficients of the anode and cathode respectively; arsinh denotes the inverse hyperbolic sine function; i ce ll represents the current density of the electrolytic cell; i an and i cat represent the cathode exchange current density and the anodic exchange current density, respectively;

[0025] The ohmic overvoltage is expressed as:

[0026]

[0027] Where U ohm Represents ohmic overvoltage; R ele Represents electrode resistance; Rmem Represents the resistance of the proton exchange membrane; A cell Represents the effective activation area of ​​the electrolytic cell; σ mem represents the conductivity of the membrane; d represents the thickness of the electrolyte membrane; λ mem represents the water content of the membrane; exp represents the exponential function;

[0028] The hydrogen production rate is mainly affected by the structure of the electrolyzer and the current density of the electrolyzer, showing a positive correlation, which can be expressed as:

[0029]

[0030] In the formula, Indicates the hydrogen production rate; K 1 represents the conversion coefficient; N represents the number of electrolytic chambers connected in series; η f represents the Faraday efficiency;

[0031] The dynamic change process of Faraday efficiency is expressed as:

[0032]

[0033] Where η f represents the Faraday efficiency; and They represent the hydrogen permeability caused by diffusion phenomenon and the hydrogen permeability caused by pressure difference respectively; and They represent the anode oxygen partial pressure and cathode hydrogen pressure in the catalyst layer of the electrolyzer respectively; represents oxygen permeability; Indicates the hydrogen pressure; Indicates the activation area of ​​hydrogen on the reaction plate; Indicates oxygen pressure; Indicates the activation area of ​​oxygen on the reaction plate;

[0034] The hydrogen production efficiency of the electrolyzer is expressed as:

[0035]

[0036] Where η e It indicates the efficiency of hydrogen production by electrolyzer; Indicates the hydrogen production rate of the electrolyzer; HHV H Indicates the higher heating value of hydrogen under standard conditions; P t Indicates the power consumption of the electrolytic cell PEMEL;

[0037] The power consumption of electrolytic cell is expressed as:

[0038] P t =N·U cell ·A cell ·icell (12);

[0039] In view of the establishment of the reversible voltage and activation overvoltage of the above mathematical model, the existing experimental data are provided for comparison with the reversible voltage and activation overvoltage of the mathematical model to obtain the performance parameters of the electrolytic cell.

[0040] Further, in step S3, the parameters of multi-objective optimization are obtained, and the specific process is as follows:

[0041] The multi-objective particle swarm algorithm with adaptive weights is used to perform multi-objective optimization on the performance parameters of the electrolytic cell and obtain the multi-objective optimization parameters.

[0042] Among them, the weight update strategy of the adaptive weighted multi-objective particle swarm algorithm is expressed as:

[0043]

[0044] Where w represents the adaptive weight coefficient; w min represents the minimum value of the adaptive weight coefficient constraint range; w max represents the maximum value of the adaptive weight coefficient constraint range; f represents the real-time objective function value of the particle; f avg and f min Respectively represent the average value and minimum target value of all current particles;

[0045] When the particle swarm is relatively dispersed, the adaptive weight coefficient w decreases; when the particle swarm target value is relatively consistent, it means that the particle swarm is relatively clustered, and the adaptive weight coefficient w increases the global search capability. The particle swarm position and speed update strategy is expressed as;

[0046]

[0047] In the formula, v k Indicates the speed of the particle; rand() indicates a random number between 0 and 1; P best Indicates the best position found by each particle when it reaches the current position; X k represents the particle position; g best represents the best position that can be obtained in the particle swarm; X k+1 and v k+1 Respectively represent the speed and position of the next generation of particles; c 1 and c2 represent learning factors, respectively;

[0048] The linear reduction strategy of the adaptive weight coefficient w is used to update the learning factor c 1 and c 2 On, it is expressed as:

[0049]

[0050] In the formula, c 1,start and c 2,start represents the initial value of the particle swarm learning factor iteration; k represents the current number of iterations; M represents the total number of iterations; c 1,end and c 2,end They represent the expected values ​​of the learning factors of the particle swarm at the end of the iteration.

[0051] Furthermore, the parameters based on multi-objective optimization are the optimal solution that takes into account both the hydrogen production efficiency and the maximization of the hydrogen production rate, which is expressed as:

[0052]

[0053] Where η e Indicates hydrogen production efficiency; max indicates the maximum value of both hydrogen production efficiency and hydrogen production rate;

[0054] The optimal solution constraining the electrolyzer current density based on maximizing hydrogen production efficiency and hydrogen production rate is expressed as:

[0055] 0.2<i cell <2 (16);

[0056] The range of the electrolyzer operating temperature is constrained based on the constrained electrolyzer current density, expressed as;

[0057] 333.15≤T≤353.15 (17).

[0058] Further, in step S4, the operating temperature of the electrolytic cell is controlled within the constrained operating temperature range of the electrolytic cell through the electrolytic cell temperature dynamic model, and the specific process is as follows:

[0059] The adaptive weighted multi-objective particle swarm algorithm is used to optimize the weights of the existing linear quadratic programming control, and a dynamic model of the electrolytic cell temperature is constructed. The operating temperature of the electrolytic cell is controlled within the constrained operating temperature range through the dynamic model of the electrolytic cell temperature.

[0060] According to the law of conservation of energy in the electrolytic cell, a differential equation is established to describe the law of temperature change in the electrolytic cell, which is expressed as:

[0061]

[0062] In the formula, C stack represents an electrolytic cell; Indicates the rate of change of the operating temperature of the electrolytic cell; Q pemel Represents the heat generated by the electrochemical reaction in the electrolytic cell; q ly Indicates electrolyte flow rate; c ly Represents the specific heat capacity of the electrolyte; T ex.h Indicates heat exchanger; Q dis.stackIndicates the heat lost from the electrolytic cell to the environment; C wt represents the heat capacity of pure water in the water tank; Water tank temperature change rate; T wt Indicates the water tank temperature; Q dis.wt Indicates the heat lost from the water tank to the environment; C ex.h Indicates the heat capacity of the cold outlet of the heat exchanger; Indicates the rate of change of the cold outlet temperature of the heat exchanger; K A represents the empirical constant; ΔT LMTD Expressed as logarithmic mean temperature difference; C ex.c surface

[0063] Indicates the heat capacity of the hot and cold sides; Indicates the rate of change of the cold side inlet temperature of the heat exchanger; c cw represents the specific heat capacity of water; q cw Indicates the liquid flow rate of the chiller; T ex.c Indicates the cold inlet temperature of the heat exchanger; T c.in Indicates the chiller outlet temperature.

[0064] Compared with the existing technology, the present invention has the following beneficial effects:

[0065] (1) The present invention proposes a heat exchange system, which optimizes the weights of linear quadratic programming control (LQR) based on an improved particle swarm algorithm, thereby performing stable and rapid feedback control on the PEMEL operating temperature. Compared with traditional PID control, the control strategy proposed in the present invention can more quickly adjust to the preset temperature under the same external disturbance conditions, greatly reducing the temperature adjustment time, and has obvious advantages.

[0066] (2) The present invention conducts more accurate system modeling of the electrolyzer, including the hydrogen production rate, hydrogen production efficiency, and electrolyzer temperature control model; the dynamic change process of the Faraday efficiency is taken into account when constructing the electrolyzer temperature control model, which has been ignored in previous studies; and an application of a dynamic performance control technology for a hydrogen production electrolyzer based on an improved particle swarm algorithm is proposed. Based on different working conditions, the improved particle swarm algorithm is used to finally select the optimal electrolyzer configuration scheme. The evaluation result is more accurate and objective, and meets the needs of actual operation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the present invention.

[0068] Figure 2 It is a structural diagram of the electrolytic cell temperature dynamic model of the present invention. DETAILED DESCRIPTION

[0069] like Figure 1As shown, the present invention provides a technical solution: a method for controlling the dynamic performance of a hydrogen production electrolyzer based on an improved particle swarm algorithm, comprising the following steps:

[0070] Step S1: extracting index parameters according to the dynamic characteristics of the electrolytic cell, the index parameters including the electrolytic cell current density and the electrolytic cell operating temperature;

[0071] Step S2: constructing a mathematical model, the mathematical model includes operating voltage, hydrogen production rate and hydrogen production efficiency, and calculating the operating voltage, hydrogen production rate and hydrogen production efficiency of the mathematical model by observing the operating dynamic characteristics of the electrolyzer through the mathematical model to obtain the performance parameters of the electrolyzer;

[0072] Step S3: using a multi-objective particle swarm algorithm with adaptive weights to perform multi-objective optimization on the performance parameters of the electrolyzer obtained in step S2, and obtaining parameters for the multi-objective optimization, based on which the parameters for the multi-objective optimization are optimal solutions that take into account both the hydrogen production efficiency and the maximization of the hydrogen production rate, and based on the optimal solution for maximizing the hydrogen production efficiency and the hydrogen production rate, constraining the electrolyzer current density, and based on the constrained electrolyzer current density, constraining the range of the electrolyzer operating temperature;

[0073] Step S4: Based on the adaptive weighted multi-objective particle swarm algorithm of step S3, the weights of the existing linear quadratic programming control are optimized, and a dynamic model of the electrolytic cell temperature is constructed. The electrolytic cell operating temperature is controlled within the constrained electrolytic cell operating temperature range through the electrolytic cell temperature dynamic model.

[0074] Among them, in step S1, the index parameters are extracted according to the dynamic characteristics of the electrolytic cell, and the specific process is:

[0075] The present invention takes into account the dynamic characteristics of the electrolytic cell (PEMEL), and extracts four index parameters and evaluations of the electrolytic cell according to the dynamic characteristics of the electrolytic cell, index parameter 1: electrolytic cell current density, denoted as I1; index parameter 2: electrolytic cell operating temperature, denoted as I2; index parameter 3: electrolytic cell anode oxygen partial pressure, denoted as I3; index parameter 4: electrolytic cell cathode hydrogen pressure, denoted as I4; the dynamic characteristics of the electrolytic cell include operating voltage, hydrogen production rate and hydrogen production efficiency.

[0076] Among them, step S2 obtains the performance parameters of the electrolytic cell, and the specific process is:

[0077] The operating voltage, hydrogen production rate and hydrogen production efficiency are taken as target quantities. A mathematical model is constructed based on the three target quantities to find the control quantity of the electrolyzer, so that the operating dynamic characteristics of the electrolyzer can be observed intuitively so as to perform multi-objective optimization on the target quantities.

[0078] The operating voltage is divided into three parts: the three parts include reversible voltage, activation overvoltage and ohmic overvoltage, expressed as:

[0079] Ucell =U rev +U ohm +U act (1);

[0080] Where U cell Indicates the operating voltage of the electrolytic cell; U rev Represents reversible voltage; U ohm Indicates activation overvoltage; U act Indicates ohmic overvoltage;

[0081] The reversible voltage is expressed as:

[0082]

[0083]

[0084]

[0085] In the formula, Indicates the reversible voltage under standard conditions; E rev Indicates the correction value of the reversible voltage; represents Gibbs free energy, and its value is: 236.48KJ·mol -1 ; F represents the Faraday constant, and its value is: 96485c / mol; T represents the operating temperature of the electrolytic cell; and denote the partial pressures of hydrogen and oxygen respectively; represents water activity; R represents the ideal gas constant, and its value is: 8.31 J / mol·K;

[0086] Since the Gibbs free energy of a chemical reaction is affected by temperature, reactant and electrolyte concentrations, E is required. rev To correct the reversible voltage and obtain the actual value of the reversible voltage under non-standard conditions;

[0087] The activation overvoltage is expressed as:

[0088]

[0089] Where U act Represents activation overvoltage; α an and α cat denote the charge transfer coefficients of the anode and cathode respectively; arsinh denotes the inverse hyperbolic sine function; i cell represents the current density of the electrolytic cell; i an and i cat represent the cathode exchange current density and the anodic exchange current density, respectively;

[0090] The ohmic overvoltage is expressed as:

[0091]

[0092] Where U ohm Represents ohmic overvoltage; R ele Represents electrode resistance; R mem Represents the proton exchange membrane resistance, that is, the ionic resistance; A cell Represents the effective activation area of ​​the electrolytic cell; σ mem represents the conductivity of the membrane; d represents the thickness of the electrolyte membrane; λ mem represents the water content of the membrane; exp represents the exponential function;

[0093] According to the working principle of the electrolyzer PEMEL, the hydrogen production rate is mainly affected by the structure of the electrolyzer and the current density of the electrolyzer, showing a positive correlation, which can be expressed as:

[0094]

[0095] In the formula, Indicates the hydrogen production rate, unit: mol / s; K 1 represents the conversion coefficient; N represents the number of electrolytic chambers connected in series; η f represents the Faraday efficiency;

[0096] In previous studies, the value of Faraday efficiency is usually considered to be a constant of 0.99. However, due to the permeability of the electrolytic cell structure, diffusion and gas doping will occur during the mass transfer process, especially under low load conditions, which reduces the Faraday efficiency. Therefore, it is obviously unreasonable to regard the Faraday efficiency as a constant in actual operation. It is necessary to consider its dynamic change process, which can be expressed as:

[0097]

[0098]

[0099]

[0100] Where η f represents the Faraday efficiency; and They represent the hydrogen permeability caused by diffusion phenomenon and the hydrogen permeability caused by pressure difference respectively; and They represent the anode oxygen partial pressure and cathode hydrogen pressure in the catalyst layer of the electrolyzer respectively; represents oxygen permeability; Indicates the hydrogen pressure; Indicates the activation area of ​​hydrogen on the reaction plate; Indicates oxygen pressure; Indicates the activation area of ​​oxygen on the reaction plate;

[0101] The hydrogen production efficiency of the electrolyzer is expressed as:

[0102]

[0103] Where η e It indicates the efficiency of hydrogen production by electrolyzer; Indicates the hydrogen production rate of the electrolyzer; HHV H Indicates the higher heating value of hydrogen under standard conditions; P t Indicates the power consumption of the electrolytic cell PEMEL;

[0104] The power consumption of electrolytic cell is expressed as:

[0105] P t =N·U cell ·A cell ·i cell (12);

[0106] In view of the establishment of the above reversible voltage and activation overvoltage, experimental data are provided for comparison with the reversible voltage and activation overvoltage to verify the accuracy and authenticity of the mathematical model construction, and the above-mentioned temperature, reactant, electrolyte concentration and electrolytic cell current density, which affect the performance parameters of the electrolytic cell, are experimentally evaluated to obtain the performance parameters of the electrolytic cell;

[0107] The experimental data are shown in Table 1:

[0108]

[0109] Among them, in step S3, the parameters of multi-objective optimization are obtained, and the specific process is:

[0110] When studying multi-objective optimization problems, there are conflicts between different multi-objectives. In the actual solution process, it is usually required that multiple objectives be optimized as much as possible in a restricted area at the same time. Therefore, in order to achieve the overall optimization of multiple objectives, it is necessary to comprehensively consider the conflicting sub-objectives, and the Pareto solution set closest to the sub-objective can be used as the optimal set; the core of the particle swarm algorithm is to compare and select the individual extreme value with the group extreme value, judge the next generation, and finally determine the global optimal value and local optimal value of the particle;

[0111] In order to quickly update the global optimum and find the global optimum quickly, the multi-objective particle swarm algorithm with adaptive weights (IAW-MOPSO) is used to perform multi-objective optimization on the performance parameters of the electrolytic cell PEMEL to obtain the parameters of the multi-objective optimization. The weight update strategy of the multi-objective particle swarm algorithm with adaptive weights is expressed as:

[0112]

[0113] Where w represents the adaptive weight coefficient; wmin represents the minimum value of the adaptive weight coefficient constraint range; w max represents the maximum value of the adaptive weight coefficient constraint range; f represents the real-time objective function value of the particle; f avg and f min Respectively represent the average value and minimum target value of all current particles;

[0114] When the particle swarm is relatively dispersed, the adaptive weight coefficient w decreases; when the particle swarm target value is relatively consistent, it means that the particle swarm is relatively clustered, and the adaptive weight coefficient w increases the global search capability. The particle swarm position and speed update strategy is expressed as;

[0115]

[0116] In the formula, v k represents the speed of the particle, that is, the speed of the particle in the process of pursuing hydrogen production efficiency and hydrogen production rate; rand() represents a random number between 0 and 1; P best Indicates the best position found by each particle when it reaches the current position; X k represents the particle position; g best represents the best position that can be obtained in the particle swarm, that is, the optimal solution set; X k+1 and v k+1 Respectively represent the speed and position of the next generation of particles; c 1 and c2 represent learning factors, respectively;

[0117] For the traditional adaptive weight update particle swarm algorithm, the learning factor often uses a fixed value, which depends largely on the experience value. This is also one of the reasons why the traditional particle swarm algorithm iteration is prone to premature. Therefore, this paper proposes an offline control based on linear quadratic programming control to find a more ideal initial value c of the learning factor. 1,start 、c 2,start On this basis, the linear decreasing strategy that was previously used for the adaptive weight coefficient w is also used to update the learning factor c 1 and c 2 On, it is expressed as:

[0118]

[0119] In the formula, c 1,start and c 2,start It represents the initial value of the learning factor iteration of the particle swarm, that is, the acceleration number; k represents the current number of iterations; M represents the total number of iterations; c 1,end and c 2,end They represent the expected values ​​of the learning factors of the particle swarm at the end of the iteration;

[0120] Compared with the existing multi-objective particle swarm algorithm (MOPSO) with adaptive weights, the improved multi-objective particle swarm algorithm IAW-MOPSO with adaptive weights has obvious advantages, and can dynamically adjust the adaptive weight coefficient w and has a better ability to globally search for the optimal value.

[0121] Among them, the parameters based on multi-objective optimization are the optimal solutions that take into account both the hydrogen production efficiency and the maximization of the hydrogen production rate, expressed as:

[0122]

[0123] Where η e Indicates hydrogen production efficiency; max indicates the maximum value of both hydrogen production efficiency and hydrogen production rate;

[0124] Considering the safety factors of PEMEL under the working conditions of hydrogen production efficiency and hydrogen production rate, if the electrolyzer PEMEL is operated at a lower electrolyzer current density point, it is easy to explode. At a higher electrolyzer current density, the life of the electrolyzer will be accelerated, and this process is irreversible. Therefore, the optimal solution based on maximizing hydrogen production efficiency and hydrogen production rate constrains the electrolyzer current density, which is expressed as:

[0125] 0.2<i cell <2(16);

[0126] In order to increase the hydrogen production rate, the voltage applied to the electrolyzer PEMEL in actual operation is often higher than the reversible voltage. The excess voltage is used to provide activation overvoltage, where the activation overvoltage is the main factor affecting the hydrogen production rate. However, a higher over-activation overvoltage will generate excess heat, resulting in an increase in the electrolyzer temperature. It can be seen from formula (11) that the increase in temperature helps to improve the hydrogen production efficiency of the electrolyzer, but due to the structural and material limitations of the electrolyzer PEMEL, excessively high temperatures will shorten the service life of the membrane in the electrolyzer, and in severe cases may even cause the membrane in the electrolyzer to degrade.

[0127] It can be seen that how to choose a reasonable operating temperature is crucial to the performance of the electrolytic cell. According to previous studies, the electrolytic cell PEMEL generally has better performance when the operating temperature is controlled at 60-80°C, that is, converted to 333.15k-353.15k in Kelvin. Based on this range, the present invention reasonably adjusts the operating temperature according to different working conditions to meet actual needs. Therefore, the range of the electrolytic cell operating temperature is constrained based on the constrained electrolytic cell current density, which is expressed as;

[0128] 333.15≤T≤353.15 (17).

[0129] The following assumptions are made for the electrolyzer PEMEL:

[0130] (1) The temperature inside the electrolytic cell is the same everywhere;

[0131] (2) The water supply of the electrolytic cell is sufficient, so the difference between the electrolyte concentration and the solution concentration near the plate is ignored;

[0132] (3) Ignore the viscosity effect of water and gas in the pipeline;

[0133] (4) The change of the current density of the electrolytic cell has little effect on the electrolytic resistance, so it is assumed that the ohmic resistance of the electrolytic cell and the exchange membrane resistance are constant;

[0134] (5) Assume that the generation rate of oxygen and hydrogen is the same as the transmission rate of the gas storage pump, that is, the rate of gas generation is equal to the rate of gas transmission. Therefore, the gas pressure inside the electrolyzer is the same everywhere and remains unchanged.

[0135] like Figure 2 As shown, the weights of the existing linear quadratic programming control (LQR) are optimized based on the multi-objective particle swarm algorithm with adaptive weights (IAW-MOPSO), and the electrolytic cell temperature dynamic model is constructed. The electrolytic cell temperature module finally realizes the accurate control of the operating temperature of the PEMEL electrolytic cell; the electrolytic cell temperature dynamic model includes a water tank, a water pump, a heat exchanger, a water valve, and a chiller;

[0136] The electrolytic cell water circuit is pure water circulation, and the heat generated by the electrolytic cell is brought to the heat exchanger through the water pump, and the water circuit is cooled by the heat exchanger. For the control of the dynamic model of the electrolytic cell temperature, the duty cycle of the water valve opening can be adjusted to achieve flow regulation on the chiller side, so as to effectively control the electrolytic cell PEMEL operating temperature within the range of the constrained operating temperature.

[0137] The working voltage of the electrolytic cell is usually above the reversible voltage, which means that the electrolytic cell PEMEL will generate excess heat during the electrochemical reaction, thus affecting the operating temperature of the electrolytic cell. According to the law of conservation of energy in the electrolytic cell, a differential equation is established to describe the law of temperature change of the electrolytic cell PEMEL. A dynamic model of the electrolytic cell temperature is constructed, which is expressed as:

[0138]

[0139] In the formula, C stack represents an electrolytic cell; Indicates the rate of change of the operating temperature of the electrolytic cell; Q pemel Represents the heat generated by the electrochemical reaction in the electrolytic cell; q ly Indicates electrolyte flow rate; c ly Represents the specific heat capacity of the electrolyte; T ex.h Indicates heat exchanger; Q dis.stackIndicates the heat lost from the electrolytic cell to the environment; C wt represents the heat capacity of pure water in the water tank; Water tank temperature change rate; T wt Indicates the water tank temperature; Q dis.wt Indicates the heat lost from the water tank to the environment; C ex.h Indicates the heat capacity of the cold outlet of the heat exchanger; Indicates the rate of change of the cold outlet temperature of the heat exchanger; K A represents the empirical constant; ΔT LMTD Expressed as logarithmic mean temperature difference; C ex.c represents the heat capacity of the hot and cold sides; Indicates the rate of change of the cold side inlet temperature of the heat exchanger; c cw represents the specific heat capacity of water; q cw Indicates the liquid flow rate of the chiller; T ex.c Indicates the cold inlet temperature of the heat exchanger; T c.in Indicates the chiller outlet temperature.

[0140] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A method for controlling the dynamic performance of a hydrogen production electrolyzer based on an improved particle swarm algorithm, characterized in that: The following steps are involved: Step S1: extracting index parameters according to the dynamic characteristics of the electrolytic cell, the index parameters include the electrolytic cell current density and the electrolytic cell operating temperature: Step S2: construct a mathematical model, which includes operating voltage, hydrogen production rate and hydrogen production efficiency. The operating dynamic characteristics of the electrolyzer are observed through the mathematical model, and the operating voltage, hydrogen production rate and hydrogen production efficiency of the mathematical model are calculated to obtain the performance parameters of the electrolyzer: Step S3: Use a multi-objective particle swarm algorithm with adaptive weights to perform multi-objective optimization on the performance parameters of the electrolyzer obtained in step S2, and obtain the parameters for the multi-objective optimization. The parameters based on the multi-objective optimization are the optimal solution that takes into account both the hydrogen production efficiency and the maximization of the hydrogen production rate. The electrolyzer current density is constrained based on the optimal solution of the maximization of the hydrogen production efficiency and the hydrogen production rate, and the range of the electrolyzer operating temperature is constrained based on the constrained electrolyzer current density: Step S4: Based on the adaptive weighted multi-objective particle swarm algorithm of step S3, the weights of the existing linear quadratic programming control are optimized, and a dynamic model of the electrolytic cell temperature is constructed. The electrolytic cell operating temperature is controlled within the constrained electrolytic cell operating temperature range through the electrolytic cell temperature dynamic model.

2. The method for dynamic performance control of a hydrogen production electrolyzer based on an improved particle swarm algorithm according to claim 1, characterized in that: In step S1, the index parameters are extracted according to the dynamic characteristics of the electrolytic cell. The specific process is as follows: According to the dynamic characteristics of the electrolyzer, four index parameters and evaluations of the electrolyzer are extracted, index parameter 1: electrolyzer current density, denoted as I1; index parameter 2: electrolyzer operating temperature, denoted as I2; index parameter 3: electrolyzer anode oxygen partial pressure, denoted as I3; index parameter 4: electrolyzer cathode hydrogen pressure, denoted as I4; the dynamic characteristics of the electrolyzer include operating voltage, hydrogen production rate and hydrogen production efficiency.

3. The method for dynamic performance control of a hydrogen production electrolyzer based on an improved particle swarm algorithm according to claim 1, characterized in that: Step S2 obtains the performance parameters of the electrolytic cell, and the specific process is as follows: The operating voltage, hydrogen production rate and hydrogen production efficiency are taken as target quantities, and a mathematical model is constructed based on the three target quantities, so that the operating dynamic characteristics of the electrolyzer can be observed intuitively so as to perform multi-objective optimization on the target quantities; The operating voltage is divided into three parts: the three parts include reversible voltage, activation overvoltage and ohmic overvoltage, expressed as: IN cell =U rev +U ohm +U act (1); Where U cell Indicates the operating voltage of the electrolytic cell; U rev Represents reversible voltage; U ohm Indicates activation overvoltage; U act Indicates ohmic overvoltage; The reversible voltage is expressed as: In the formula, Indicates the reversible voltage under standard conditions; E rev Indicates the correction value of the reversible voltage; represents Gibbs free energy; F represents Faraday constant; T represents the operating temperature of the electrolytic cell; and denote the partial pressures of hydrogen and oxygen respectively; represents water activity; R represents the ideal gas constant; The activation overvoltage is expressed as: Where U act Represents activation overvoltage; α an and α cat denote the charge transfer coefficients of the anode and cathode respectively; arsinh denotes the inverse hyperbolic sine function; i ce ll represents the electrolytic cell current density; i an and i cat represent the cathode exchange current density and the anodic exchange current density, respectively; The ohmic overvoltage is expressed as: Where U ohm Represents ohmic overvoltage; R ele Represents electrode resistance; R mem Represents the resistance of the proton exchange membrane; A cell Represents the effective activation area of ​​the electrolytic cell; σ mem represents the conductivity of the membrane; d represents the thickness of the electrolyte membrane; λ mem represents the water content of the membrane; exp represents the exponential function; The hydrogen production rate is mainly affected by the structure of the electrolyzer and the current density of the electrolyzer, showing a positive correlation, which can be expressed as: In the formula, represents the hydrogen production rate; K1 represents the conversion coefficient; N represents the number of electrolytic chambers connected in series; η f represents the Faraday efficiency; The dynamic change process of Faraday efficiency is expressed as: Where η f represents the Faraday efficiency; and They represent the hydrogen permeability caused by diffusion phenomenon and the hydrogen permeability caused by pressure difference respectively; and They represent the anode oxygen partial pressure and cathode hydrogen pressure in the catalyst layer of the electrolyzer respectively; represents oxygen permeability; Indicates the hydrogen pressure; Indicates the activation area of ​​hydrogen on the reaction plate; Indicates oxygen pressure; Indicates the activation area of ​​oxygen on the reaction plate; The hydrogen production efficiency of the electrolyzer is expressed as: Where η e It represents the efficiency of hydrogen production by electrolyzer; Indicates the hydrogen production rate of the electrolyzer; HHV H Indicates the higher heating value of hydrogen under standard conditions; P t Indicates the power consumption of the electrolytic cell PEMEL; The power consumption of electrolytic cell is expressed as: P t =N·U cell ·A cell ·i cell (12); In view of the establishment of the reversible voltage and activation overvoltage of the above mathematical model, the existing experimental data are provided for comparison with the reversible voltage and activation overvoltage of the mathematical model to obtain the performance parameters of the electrolytic cell.

4. The method for dynamic performance control of a hydrogen production electrolyzer based on an improved particle swarm algorithm according to claim 3 is characterized in that: In step S3, the parameters of multi-objective optimization are obtained. The specific process is as follows: The multi-objective particle swarm algorithm with adaptive weights is used to perform multi-objective optimization on the performance parameters of the electrolytic cell and obtain the multi-objective optimization parameters. Among them, the weight update strategy of the multi-objective particle swarm algorithm with adaptive weights is expressed as: Where w represents the adaptive weight coefficient; w min represents the minimum value of the adaptive weight coefficient constraint range; w max represents the maximum value of the adaptive weight coefficient constraint range; f represents the real-time objective function value of the particle; f avg and f min Respectively represent the average value and minimum target value of all current particles; When the particle swarm is relatively dispersed, the adaptive weight coefficient w decreases; when the particle swarm target value is relatively consistent, it means that the particle swarm is relatively clustered, and the adaptive weight coefficient w increases the global search capability. The particle swarm position and speed update strategy is expressed as; In the formula, v k Indicates the speed of the particle; rand() indicates a random number between 0 and 1; P best Indicates the best position found by each particle when it reaches the current position; X k represents the particle position; g best represents the best position that can be obtained in the particle swarm; X k+1 and v k+1 They represent the speed and position of the next generation of particles respectively; c1 and c2 represent the learning factors respectively; The linear decreasing strategy of the adaptive weight coefficient w is used to update the learning factors c1 and c2, which is expressed as: In the formula, c 1,start and c 2,start represents the initial value of the particle swarm learning factor iteration; k represents the current number of iterations; M represents the total number of iterations; c 1,end and c 2,end They represent the expected values ​​of the learning factors of the particle swarm at the end of the iteration.

5. The method for dynamic performance control of a hydrogen production electrolyzer based on an improved particle swarm algorithm according to claim 4, characterized in that: The parameters based on multi-objective optimization are the optimal solution that takes into account both hydrogen production efficiency and maximization of hydrogen production rate, expressed as: Where η e Indicates hydrogen production efficiency; max indicates the maximum value of both hydrogen production efficiency and hydrogen production rate; The optimal solution constraining the electrolyzer current density based on maximizing hydrogen production efficiency and hydrogen production rate is expressed as: 0.2＜i cell ＜2(16)； The range of the electrolyzer operating temperature is constrained based on the constrained electrolyzer current density, expressed as; 333.15≤T≤353.15(17)。 6. The method for dynamic performance control of a hydrogen production electrolyzer based on an improved particle swarm algorithm according to claim 5, characterized in that: In step S4, the operating temperature of the electrolytic cell is controlled within the constrained operating temperature range of the electrolytic cell through the electrolytic cell temperature dynamic model. The specific process is as follows: The adaptive weighted multi-objective particle swarm algorithm is used to optimize the weights of the existing linear quadratic programming control, and a dynamic model of the electrolytic cell temperature is constructed. The operating temperature of the electrolytic cell is controlled within the constrained operating temperature range through the dynamic model of the electrolytic cell temperature. According to the law of conservation of energy in the electrolytic cell, a differential equation is established to describe the law of temperature change in the electrolytic cell, which is expressed as: In the formula, C stack represents an electrolytic cell; Indicates the rate of change of the operating temperature of the electrolytic cell; Q pemel Represents the heat generated by the electrochemical reaction in the electrolytic cell; q ly Indicates electrolyte flow rate; c ly represents the specific heat capacity of the electrolyte; T ex.h Indicates heat exchanger; Q dis.stack Indicates the heat lost from the electrolytic cell to the environment; C wt represents the heat capacity of pure water in the water tank; Water tank temperature change rate; T wt Indicates the water tank temperature; Q dis.wt Indicates the heat lost from the water tank to the environment; C ex.h Indicates the heat capacity of the cold outlet of the heat exchanger; Indicates the rate of change of the cold outlet temperature of the heat exchanger; K A represents the empirical constant; ΔT LMTD Expressed as logarithmic mean temperature difference; C ex.c represents the heat capacity of the hot and cold sides; Indicates the rate of change of the cold side inlet temperature of the heat exchanger; c cw represents the specific heat capacity of water; q cw Indicates the liquid flow rate of the chiller; T ex.c Indicates the cold inlet temperature of the heat exchanger; T c.in Indicates the chiller outlet temperature.

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