Multi-cell control method for hydrogen production alkaline electrolytic cell based on nonlinear model predictive control

Abstract

The invention relates to a multi-cell control method for hydrogen production alkaline electrolytic cells based on nonlinear model predictive control, which belongs to the technical field of hydrogen production and comprises the following steps of: performing data acquisition on key positions of a hydrogen production alkaline electrolytic cell system in real time; based on the dynamically determined priority of each electrolytic cell, dynamic load distribution of each electrolytic cell is carried out, and a multi-dimensional cooperative regulation strategy is implemented to obtain a hydrogen yield target value of each electrolytic cell; constructing a nonlinear model comprising an electrolytic reaction model, a heat transfer model and an inter-tank coupling model, and performing parameter identification and verification; and designing a nonlinear model predictive control algorithm, performing discretization processing on the nonlinear model, introducing Kalman filtering to process the uncertainty of the model, taking a corresponding hydrogen yield target value reached by each electrolytic cell on the premise of meeting the constraint as a final control target, constructing an optimized target function, and performing solving to obtain an optimal control scheme. Compared with the prior art, the control precision and the system stability can be effectively improved.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of hydrogen production, in particular to a multi-tank control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control. BACKGROUND

[0002] With the growing demand for clean energy worldwide, hydrogen energy has attracted widespread attention as a highly efficient and clean secondary energy source. Water electrolysis is one of the important means to obtain high-purity hydrogen, among which alkaline electrolysis has been widely used in industrial hydrogen production due to its mature technology and relatively low cost. However, the existing multi-tank control technology for alkaline electrolysis still has many problems that need to be solved.

[0003] In traditional alkaline electrolyzer control, simple proportional-integral-derivative (PID) control strategy is often used. Although PID control can maintain the stable operation of the electrolyzer to some extent, its limitations become more apparent when facing complex and variable working conditions. For example, when the input of renewable energy is unstable, the load of the electrolyzer will fluctuate frequently. Due to the strong nonlinearity and time-varying characteristics of the alkaline electrolyzer, the traditional PID control cannot quickly and accurately respond to such changes, resulting in reduced operating efficiency of the electrolyzer and affected hydrogen production and quality.

[0004] Chinese patent CN116536705A discloses a PEM water electrolysis control method and system based on model predictive control, which considers the electrolyzer power tracking, electrolyzer efficiency and system constraints, and uses a model predictive control algorithm to control the heat exchanger and pump based on electrolyzer temperature tracking, which can control the system to quickly and accurately track the electrolyzer heating, ensure the system works in a safe area, and improve the system power. However, this scheme is only for single-tank control and is not suitable for multi-tank control. Chinese patent CN119517203A discloses a multi-tank hybrid hydrogen production optimization method for alkaline electrolysis, which effectively solves the safety and production problems caused by the high number of start-stop times and high or low power of the alkaline electrolysis, and improves the utilization rate of renewable energy and the efficiency of hydrogen production by alkaline electrolysis. However, it does not consider the coupling relationship between multiple electrolyzers.

[0005] From the perspective of multi-tank control, there is a mutual coupling relationship between multiple electrolyzers. When the operating state of one electrolyzer changes, it will affect other electrolyzers through electrolyte, gas pipeline, etc. The existing control technology often cannot effectively consider this inter-tank coupling, resulting in poor stability of the entire multi-tank system. For example, when a certain electrolyzer fails or needs to adjust the load, it may trigger a chain reaction in other electrolyzers, causing the entire system to become unstable, and in severe cases, it may even cause equipment damage.

[0006] In addition, in practical applications, the operation of alkaline electrolyzers is also subject to various factors such as temperature, pressure, electrolyte concentration, etc. These factors interact with each other, further increasing the complexity of control. For example, changes in temperature can affect the rate and efficiency of the electrolysis reaction, and excessively high or low temperatures can lead to a decline in the performance of the electrolyzer. Traditional control methods are difficult to consider the influence of these multiple factors comprehensively, and cannot achieve precise control of the electrolyzer.

[0007] Under the background of energy transformation, there is an increasing demand for large-scale, efficient and stable hydrogen production. The existing multi-tank control technology of alkaline electrolyzers cannot meet this demand, and an innovative control technology is urgently needed to improve the operating performance of the electrolyzer and the stability of the multi-tank system, reduce energy consumption, and improve hydrogen production efficiency and quality. SUMMARY

[0008] The purpose of the present application is to provide a hydrogen production alkaline electrolyzer multi-tank control method based on nonlinear model predictive control, to solve the above problems existing in the prior art, to realize precise, efficient and stable control of the alkaline electrolyzer multi-tank system, to improve hydrogen production efficiency and quality, and to reduce energy consumption.

[0009] The purpose of the present application can be achieved by the following technical solutions:

[0010] A hydrogen production alkaline electrolyzer multi-tank control method based on nonlinear model predictive control, comprising the following steps:

[0011] Real-time data acquisition at key positions of the hydrogen production alkaline electrolyzer system;

[0012] Based on the dynamically determined priority of each electrolyzer, dynamic load distribution of each electrolyzer is carried out, and a multi-dimensional collaborative control strategy is implemented in the load distribution process to obtain the hydrogen production target value of each electrolyzer;

[0013] A nonlinear model containing an electrolysis reaction model, a heat transfer model and an inter-tank coupling model is constructed, and parameter identification and verification are carried out;

[0014] A nonlinear model predictive control algorithm is designed, the nonlinear model is discretized, and model uncertainty is introduced by Kalman filtering. Each electrolyzer reaches the corresponding hydrogen production target value as the final control target under the premise of meeting the constraints, an optimization objective function is constructed, and the optimal control scheme is obtained by solving the optimization objective function. The optimization objective function includes maximizing hydrogen production, maintaining hydrogen purity at a target value, minimizing system energy consumption and enhancing electrolyzer operation stability.

[0015] The priority determination method is:

[0016] The performance index PI of electrolyzer i is calculated i :

[0017]

[0018] where ω1, ω2, ω3 are weight coefficients; η e,i represents energy consumption efficiency, defined as hydrogen production per unit energy consumption: is the hydrogen production of electrolyzer i, E i is the electrical energy consumed by it; represents the hydrogen production rate, calculated by the change in hydrogen production per unit time: is the change in hydrogen production of electrolyzer i, Δt is the time interval; σ s,i represents the operation stability, measured by the fluctuation standard deviation of the key parameters of the electrolyzer within a preset time;

[0019] Based on the performance index, the load distribution priority of each electrolyzer is dynamically determined.

[0020] The dynamic load distribution is specifically:

[0021] According to the total hydrogen production demand of the system and the performance index of each electrolyzer, the dynamic load distribution is carried out, wherein the hydrogen production target value allocated to the i-th electrolyzer is calculated by the formula:

[0022]

[0023] where n is the number of electrolyzers.

[0024] The multi-dimensional collaborative regulation strategy includes:

[0025] Thermal balance collaborative regulation strategy: when the temperature T i of a certain electrolyzer deviates from the set value T set,i , based on the heat balance equation by introducing the heat transfer coefficient, the cooling system or load distribution of the adjacent electrolyzer is adjusted to realize the reasonable transfer of heat;

[0026] Gas pressure collaborative regulation strategy: according to the ideal gas state equation, the relationship between the gas pressure in the pipeline and the gas quantity, temperature and pipeline volume is determined, and by real-time monitoring the gas production of each electrolyzer and the gas pressure in the pipeline, when the gas pressure in the pipeline exceeds the set range, the gas production of each electrolyzer is adjusted for regulation.

[0027] The electrolysis reaction model considers the influence of impurity ions on the reaction, and introduces an impurity influence factor, which is represented as:

[0028] U = U rev + η act + η ohm+ η conc + ΔU imp

[0029] wherein, U rev is the reversible voltage; η act is the activation overpotential; η ohm is the ohmic overpotential; η conc is the concentration overpotential; ΔU imp is the impurity-induced overpotential, i.e. the impurity influence factor, ΔU imp = k c imp , k is a constant related to the impurity species and the electrode material, and c imp is the impurity ion concentration.

[0030] The heat transfer model takes into account the temperature variation inside the electrolytic cell and introduces a temperature variation rate term, which is expressed as:

[0031]

[0032] wherein, m is the electrolyte mass, C p is the specific heat capacity of the electrolyte, T is the electrolyte temperature, t is time, i.e. the temperature variation rate term, Q elec is the heat generated by the electrolysis reaction, Q ohm is the ohmic heat, Q conv is the convective heat dissipation, and Q rad is the radiative heat dissipation.

[0033] The inter-tank coupling model is established by taking into account the influence of temperature on the flow rate and the electrolyte conductivity, and is expressed as:

[0034]

[0035] wherein, Q gas is the gas flow rate, ΔP is the pressure difference between the two ends of the pipeline, R gas is the gas flow resistance, T ref is the reference temperature, T gas is the gas temperature, σ sol is the electrolyte conductivity, σ0 is the pre-exponential factor, E a is the activation energy, R is the gas constant, and T is the absolute temperature.

[0036] The optimization objective function is expressed as:

[0037]

[0038] wherein, is the predicted hydrogen production at time k+i at time k; y purity,k+i|k is the predicted hydrogen purity at time k+i at time k; y is the target value of the hydrogen purity; and Pk+i|k is the system energy consumption at k+i time predicted at k time; Δu k+i|k k+i|k k+i-1|k is the change of control variable, u k+i|k is the control vector at k+i time predicted at k time; R u is the weight matrix of control variable change; α1, α2, α3, α4 are weight coefficients; N is the prediction time domain.

[0039] The constraints include upper and lower constraints of current and voltage, temperature safety range constraints of electrolytic cell and gas pressure range constraints.

[0040] The hydrogen production alkaline electrolytic cell system adopts a hierarchical distributed communication architecture and is divided into a device layer, a regional layer and a central control layer, wherein the device layer is responsible for collecting real-time operation data of each electrolytic cell and transmitting the data to the regional layer; the regional layer uploads the data of the electrolytic cells in the region to the central control layer after summarizing and preliminarily processing the data; the central control layer performs comprehensive analysis and decision-making based on global data, and issues global optimization targets and strategies to the regional layer; the regional layer refines and adjusts the optimization targets and strategies according to the actual situation of the local electrolytic cell, and sends control instructions to the device layer.

[0041] Compared with the prior art, the present application has the following beneficial effects:

[0042] (1) Significantly improve the control accuracy:

[0043] In the model construction stage, the present application greatly improves the description accuracy of the model to the complex operation characteristics of the alkaline electrolytic cell by considering the influence of impurity ions on the electrolysis reaction, introducing a temperature change rate term to improve the heat transfer model, and establishing an inter-tank coupling model coupled with multiple physical fields. Compared with traditional models, the nonlinear model constructed by the present application can more accurately reflect the behavior of the electrolytic cell under various operating conditions. The nonlinear model predictive control algorithm based on this accurate model can realize accurate prediction of the operating state of the electrolytic cell, thereby providing a reliable basis for control decision-making and significantly improving the control accuracy. For example, when dealing with the change of operating conditions caused by unstable renewable energy input, the control parameters can be quickly and accurately adjusted to effectively reduce the fluctuations in hydrogen production and quality.

[0044] (2) Greatly enhance the system stability:

[0045] ​​The multi-tank coordinated control strategy of the present application can reasonably distribute the load and balance the operating parameters between the tanks according to the actual operating state of each electrolysis tank and the overall demand of the system through the dynamic determination of priority based on multi-factor evaluation and the dynamic load distribution algorithm. When a certain electrolysis tank fails or the load suddenly changes, the system can quickly adjust the load distribution and transfer part of the load to other normally operating electrolysis tanks to ensure that the total hydrogen production demand of the system is met and the stable operation of the entire multi-tank system is maintained. For example, when part of the electrolysis tanks need to reduce the load due to failure, through coordinated control, other electrolysis tanks can automatically increase the load to avoid a chain reaction caused by local failure and reduce the risk of equipment damage.

[0046] In addition, the introduction of the heat balance coordinated regulation and gas pressure coordinated regulation mechanism effectively solves the heat transfer and gas pressure coupling problem in the multi-tank system. When the temperature or gas pressure of a certain electrolysis tank is abnormal, through the coordinated regulation strategy, the operating parameters of the adjacent electrolysis tanks can be adjusted in time to realize the reasonable distribution of heat and gas pressure, maintain the heat balance and gas pressure stability of the system, and further enhance the stability of the system.

[0047] (3) Overall optimization of hydrogen production efficiency:

[0048] The precise control of the present application enables the electrolysis tank to always operate under optimal conditions, fully utilizing its hydrogen production potential. Through the optimization of the objective function, maximizing hydrogen production is one of the important goals, and combined with the dynamic load distribution strategy, each electrolysis tank can meet the system demand while maximizing the hydrogen production rate as much as possible. In addition, the heat balance coordinated regulation and gas pressure coordinated regulation help maintain the stable operation of the electrolysis tank, reduce the decline in hydrogen production efficiency caused by temperature and pressure fluctuations, and significantly improve the hydrogen production efficiency of the entire multi-tank system.

[0049] In the optimization objective function, maintaining the hydrogen purity at the target value is one of the important goals. Through the model predictive control algorithm, the operating parameters of the electrolysis tank are monitored and adjusted in real time to ensure that the hydrogen purity always meets the requirements. For example, when the impurity content in the raw material gas changes, the control algorithm can adjust the electrolysis conditions in time to ensure that the purity of the produced hydrogen is not affected and meets higher quality requirements.

[0050] Minimizing system energy consumption is one of the optimization goals. Through reasonable load distribution, optimization of control parameters, and coordinated regulation of heat balance and gas pressure, unnecessary energy consumption is avoided. For example, in the load distribution process, the load is preferentially distributed to electrolysis tanks with high energy consumption efficiency, and at the same time, through heat balance regulation, the heat transfer between electrolysis tanks is fully utilized to reduce the energy consumption of the cooling system and improve energy utilization efficiency.

[0051] (4) Effectively reduce operation and maintenance costs:

[0052] The multi-tank coordinated control strategy and precise model predictive control algorithm of the present application can monitor the operating state of the electrolytic cell in real time and discover potential hidden trouble in time. By adjusting the control parameters in advance or taking corresponding measures, the occurrence of faults can be avoided, and the frequency of equipment maintenance and downtime can be reduced. When a fault occurs, the system can quickly respond and maintain system operation through load transfer and other methods to reduce production losses caused by faults, thereby effectively reducing operation and maintenance costs.

[0053] In addition, stable operating state and precise control help to reduce the wear and tear and aging of internal components of the electrolytic cell. For example, through heat balance coordinated regulation, the temperature of the electrolytic cell is prevented from being too high or too low, and the damage to the electrode and electrolyte is reduced; through gas pressure coordinated regulation, the impact of excessive gas pressure on pipelines and equipment is prevented. These measures help to prolong the service life of the electrolytic cell and related equipment and reduce the cost of equipment replacement. BRIEF DESCRIPTION OF DRAWINGS

[0054] Figure 1 The present application is a method for the whole flow chart;

[0055] Figure 2 The present application is a load intelligent distribution flow chart;

[0056] Figure 3 The present application is a nonlinear model construction and identification, verification flow chart;

[0057] Figure 4 The present application is a nonlinear model predictive control algorithm implementation flow chart. DETAILED DESCRIPTION

[0058] The present application will be described in detail below in conjunction with the drawings and specific embodiments. The present embodiment is implemented on the premise of the technical solution of the present application, and detailed implementation and specific operation process are given, but the protection scope of the present application is not limited to the following examples.

[0059] In view of the problems of poor control accuracy, poor system stability, low hydrogen production efficiency and quality, and high energy consumption of the existing multi-tank control technology of alkaline electrolytic tank in dealing with complex working conditions, the embodiment provides a multi-tank control method for hydrogen production alkaline electrolytic tank based on nonlinear model predictive control. The technical scheme covers three aspects: first, an accurate nonlinear model is established. A variety of sensors are deployed at key positions of the electrolytic tank system to collect data, a model considering electrolytic reaction, heat transfer, and inter-tank coupling is constructed, and a particle swarm optimization algorithm is combined with a least square method to identify and verify parameters; second, a nonlinear model predictive control algorithm is designed. The model is processed by Runge-Kutta fourth-order discretization, Kalman filtering is introduced to deal with uncertainty, an optimization function is constructed by multiple objectives, and an adaptive interior point method is used to solve; third, a multi-tank coordinated control strategy is implemented. Intelligent load distribution, multi-dimensional collaborative regulation and control are performed, and a hierarchical distributed communication architecture is built to realize data interaction and collaborative optimization. The application effectively improves control accuracy and system stability, significantly improves hydrogen production efficiency and quality, reduces energy consumption, reduces operation and maintenance cost, and prolongs equipment service life.

[0060] Specifically, as shown in Figure 1 The method comprises the following steps:

[0061] S1, real-time data acquisition is performed on key positions of the hydrogen production alkaline electrolytic tank system.

[0062] In the embodiment, current, voltage, temperature, pressure, gas concentration, and impurity ion concentration sensors are installed at positions such as the electrolytic tank body, electrolyte pipeline, and gas pipeline, and the collected data is filtered and preprocessed to remove noise and outliers, thereby ensuring the accuracy and reliability of the data.

[0063] In a preferred embodiment, a multi-sensor fusion data acquisition system is designed to obtain high-quality operation data. In addition to conventional current, voltage, temperature, and pressure sensors, a mass spectrometer is introduced to measure the purity of hydrogen and oxygen, and a nuclear magnetic resonance sensor is introduced to measure the concentration of electrolyte. These sensors convert analog signals into digital signals through high-precision A / D converters, and use synchronous acquisition technology to ensure the time synchronization of different types of data.

[0064] S2, based on the priority of each electrolytic tank determined dynamically, dynamic load distribution of each electrolytic tank is performed, and a multi-dimensional collaborative regulation and control strategy is implemented in the load distribution process to obtain the hydrogen production target value of each electrolytic tank.

[0065] Intelligent load distribution calculates the performance index to determine the load distribution priority by real-time acquisition of the operation data of each electrolytic tank, and calculates the hydrogen production target of each electrolytic tank according to the total hydrogen production demand of the system, which is converted into control input.

[0066] Specifically, as shown in Figure 2The method comprises the following steps:

[0067] S21, dynamically determining the priority based on multi-factor evaluation

[0068] In actual hydrogen production process, the running state, health degree and performance of different electrolyzers are different. In order to realize more reasonable load distribution, a multi-factor evaluation system is constructed. The electrolyzer performance index PI i is introduced, which comprehensively considers the key factors such as energy consumption efficiency η e,i , hydrogen production rate , running stability σ s,i and the like. The performance index PI i of electrolyzer i is calculated as follows:

[0069]

[0070] Among them, ω1, ω2, ω3 are weight coefficients, which are adjusted according to actual production requirements; η e,i represents the energy consumption efficiency, which is defined as the hydrogen production under unit energy consumption: is the hydrogen production of electrolyzer i, E i is the consumed electric energy; represents the hydrogen production rate, which is calculated by the hydrogen production change in unit time: is the hydrogen production change of electrolyzer i, and Δt is the time interval; σ s,i represents the running stability, which is measured by the fluctuation standard deviation of key parameters (such as voltage, current, temperature) of electrolyzer within a preset time.

[0071] Based on the performance index, the load distribution priority of each electrolyzer is dynamically determined.

[0072] S22, dynamic load distribution

[0073] According to the total hydrogen production demand of the system and the performance index of each electrolyzer, the dynamic load distribution is carried out, wherein the calculation formula of the hydrogen production target value allocated to the i th electrolyzer is as follows:

[0074]

[0075] Among them, n is the number of electrolyzers.

[0076] In order to ensure that each electrolyzer runs within the safety range, the hydrogen production target is converted into the corresponding control input (such as current I i ) combined with the constraint conditions such as current, voltage and temperature. Through the electrolysis reaction model, the relationship between hydrogen production and current is established:

[0077]

[0078] wherein, is the molar mass of hydrogen, and F is the Faraday constant.

[0079] The current value that meets the hydrogen production target can be obtained as follows:

[0080]

[0081] S23, multi-dimensional coordinated regulation strategy

[0082] The multi-dimensional coordinated regulation includes heat balance coordinated regulation and gas pressure coordinated regulation. The former adjusts the operating parameters of adjacent electrolytic cells to maintain heat balance according to the situation that the electrolytic cell temperature deviates from the set value, and the latter adjusts the gas production of each electrolytic cell to maintain stable pressure according to the situation that the gas pipeline pressure exceeds the set range.

[0083] (1) Heat balance coordinated regulation strategy

[0084] In a multi-cell system, there is heat transfer and thermal coupling between electrolytic cells. In order to maintain the temperature stability of each electrolytic cell and achieve system heat balance, a heat balance coordinated regulation strategy is designed. When the temperature T i of a certain electrolytic cell deviates from the set value T set,i , based on the heat balance equation by introducing the heat transfer coefficient, the heat is reasonably transferred by adjusting the cooling system or load distribution of adjacent electrolytic cells.

[0085] The heat transfer coefficient k ij between electrolytic cells i and j is introduced, and according to the heat conduction law, the heat balance equation of electrolytic cell i is as follows:

[0086]

[0087] wherein, C p,i is the specific heat capacity of the electrolyte, m i is the mass of the electrolyte, Q elec,i is the heat generated by the electrolysis reaction of electrolytic cell i, Q ohm,i is the ohmic heat of electrolytic cell i, Q conv,i is the convective heat dissipation of electrolytic cell i, and Q rad,i is the radiative heat dissipation of electrolytic cell i. When T i >T set,i , the load of the electrolytic cell is appropriately reduced, and the load of the adjacent low-temperature electrolytic cell is increased to promote heat transfer.

[0088] (2) Gas pressure coordinated regulation strategy

[0089] When multiple electrolytic cells share a gas pipeline, fluctuations in gas pressure will affect each other. To maintain stable gas pipeline pressure, a gas pressure coordination control mechanism is established. According to the ideal gas state equation, the relationship between gas pressure P, gas quantity n, temperature T, and pipeline volume V in the pipeline is determined:

[0090]

[0091] By monitoring the gas production of each electrolytic cell and the gas pressure in the pipeline in real time, when the gas pressure P in the pipeline exceeds the set range [P min ,P max ], the gas production of each electrolytic cell is adjusted for control. For example, when P > P max , reduce the current of the electrolytic cell with faster gas production rate to reduce gas production; when P < P min , appropriately increase the load of the electrolytic cell with lower gas production rate.

[0092] S3, construct a nonlinear model including an electrolytic reaction model, a heat transfer model, and an inter-cell coupling model, and perform parameter identification and verification.

[0093] The electrolytic reaction model is constructed based on electrochemical principles and the influence of impurity ions on the reaction, the heat transfer model considers internal heat generation, heat dissipation, and temperature change rate in the electrolytic cell, and the inter-cell coupling model considers the coupling of material transfer in the gas pipeline and the electrolyte pipeline, as well as the coupling of temperature field and electric field.

[0094] Specifically, as shown in Figure 3 , the following steps are included:

[0095] S31, construct an electrolytic reaction model with complex reaction mechanism

[0096] The core reaction of an alkaline electrolytic cell is the electrolysis of water to produce hydrogen and oxygen. Based on the traditional electrolytic reaction model, the influence of impurity ions on the reaction is innovatively considered, especially in the industrial hydrogen production scenario, where various impurity ions inevitably exist in the electrolyte, which will change the reaction activity on the electrode surface. An impurity influence factor is introduced to construct the following electrolytic reaction model:

[0097] U = U rev + η act + η ohm + η conc + ΔU imp

[0098] Where U rev is the reversible voltage; η act is the activation overpotential; η ohm is the ohmic overpotential; η conc is the concentration overpotential; ΔU impoverpotential caused by impurities, i.e. impurity influence factor.

[0099] Reversible voltage U rev Determined by Nernst equation:

[0100]

[0101] where E 0 is the standard electrode potential, R is the gas constant, T is the absolute temperature, z is the number of electrons transferred in the reaction, F is the Faraday constant, are the activities of the reactant water and the products hydrogen and oxygen, respectively.

[0102] Activation overpotential η act Described by Butler-Volmer equation:

[0103]

[0104] where α is the transfer coefficient, j is the current density, and j0 is the exchange current density.

[0105] Ohmic overpotential η ohm is expressed as:

[0106] η ohm = j (R elec + R sol )

[0107] where R elec is the electrode resistance, and R sol is the electrolyte resistance.

[0108] Concentration difference overpotential η conc Considering the influence of diffusion layer thickness δ, it is derived by Nernst-Planck equation:

[0109]

[0110] where D is the diffusion coefficient, and c is the reactant concentration.

[0111] Impurity-induced overpotential ΔU imp is related to the impurity ion concentration c imp , and the empirical formula is obtained by experimental fitting:

[0112] ΔU imp = kc imp

[0113] where k is a constant related to the type of impurity and the electrode material.

[0114] In the actual calculation process, according to the real-time data collected by the sensor, the parameters in the equation are determined, such as temperature, current density, activities of reactants and products, etc.

[0115] S32, constructing a heat transfer model considering dynamic characteristics

[0116] To more accurately describe the temperature change inside the electrolytic cell, the embodiment introduces a temperature change rate term into the heat transfer model, which is represented as:

[0117]

[0118] where m is the mass of the electrolyte, C p is the specific heat capacity of the electrolyte, T is the temperature of the electrolyte, t is time, i.e. the temperature change rate term, Q elec is the heat generated by the electrolysis reaction, Q ohm is the ohmic heat, Q conv is the convective heat dissipation, and Q rad is the radiative heat dissipation.

[0119] The heat generated by the electrolysis reaction Q elec can be calculated from the reaction enthalpy change:

[0120] Q elec = jV cell

[0121] where V cell is the voltage of a single electrolytic cell.

[0122] The ohmic heat Q ohm is:

[0123] Q ohm = j 2 (R elec + R sol )

[0124] The convective heat dissipation Q conv uses Newton's cooling law:

[0125] Q conv = hA(T-T amb )

[0126] where h is the convective heat transfer coefficient, A is the heat dissipation area, T amb is the ambient temperature.

[0127] The radiative heat dissipation Q rad is determined according to the Stefan-Boltzmann law:

[0128]

[0129] where σ is the Stefan-Boltzmann constant and ∈ is the emissivity.

[0130] In the model, the specific heat capacity C is determined according to the structure and material properties of the electrolytic cell.p Parameters such as heat dissipation area A, convective heat transfer coefficient h, and emissivity.

[0131] S33, Construct an inter-slot coupling model considering multi-physics coupling.

[0132] In multi-tank systems, not only is there mass transfer coupling between gas and electrolyte, but also coupling between temperature and electric fields. A multiphysics coupling model is established to comprehensively describe the inter-tank interactions. Taking a hydrogen pipeline as an example, considering the impact of gas temperature changes on flow rate, the following coupling model is established:

[0133]

[0134] Among them, Q gas R is the gas flow rate, ΔP is the pressure difference between the two ends of the pipeline, and R is the pressure difference between the two ends of the pipeline. gas T represents the gas flow resistance. ref For reference temperature, T gas The temperature is the gas temperature.

[0135] For electrolyte piping, the effect of temperature on electrolyte conductivity is considered, which in turn affects the ohmic overpotential, establishing a coupling relationship:

[0136]

[0137] Where, σ sol E is the electrolyte conductivity, σ0 is the pre-exponential factor, and E a This is the activation energy. The ohmic overpotential is related to the conductivity, thus achieving coupling between the temperature field and the electric field.

[0138] The gas flow resistance R is determined by measuring parameters such as the length, diameter, and roughness of the pipeline. gas and electrolyte conductivity σ sol The relevant parameters.

[0139] S34, Parameter Identification

[0140] In this embodiment, parameter identification employs a combination of Particle Swarm Optimization (PSO) and Least Squares (LS) methods. First, PSO is used to perform a global search within a large parameter space to quickly determine the approximate range of the parameters. Then, using this result as initial values, Least Squares is used for local fine-tuning to improve the accuracy of parameter identification. The specific steps are as follows:

[0141] (1) Global Search in PSO Algorithm: Define the particle's position vector x as the set of parameters to be identified, and the velocity vector v determines the particle's search direction and step size. Each particle updates its velocity and position based on its own historical best position pbest and the swarm's global best position gbest.

[0142]

[0143] where i is the particle number, k is the iteration number, ω is the inertia weight, c1, c2 are learning factors, r1, r2 are random numbers between [0, 1], is the position vector of particle i at the kth iteration, is the velocity vector of particle i at the kth iteration.

[0144] (2) LS algorithm local optimization: to minimize the sum of squared errors between the model predicted value and the actual measured value , the LS objective function is constructed:

[0145]

[0146] where n represents the number of samples.

[0147] By optimizing E, the optimal parameter estimation value is obtained.

[0148] S35, model verification

[0149] The model parameters identified are substituted into the model, and another set of actual operation data not involved in parameter identification is used for model prediction.

[0150] First, multi-index comprehensive verification is carried out: multiple indexes such as mean absolute error (MAE), root mean square error (RMSE), determination coefficient (R 2 ) and other indexes are used to comprehensively verify the model. MAE reflects the average error between the model predicted value and the actual value:

[0151]

[0152] RMSE measures the fluctuation degree of the model prediction error:

[0153]

[0154] R 2 is used to evaluate the goodness of fit of the model to the data:

[0155]

[0156] where, is the average value of the actual measured value.

[0157] In addition to model validation under steady-state conditions, dynamic conditions such as rapid changes in renewable energy input, step changes in load, etc. are simulated in actual operation. By comparing the predicted results of the model under dynamic conditions with the actual measured values, the accuracy and reliability of the model are further verified. If the model validation fails, analyze the reasons, adjust the model structure or re-identify the parameters.

[0158] S4, design a nonlinear model predictive control algorithm, discretize the nonlinear model, and introduce Kalman filtering to handle model uncertainty. Each electrolytic cell reaches the corresponding hydrogen production target value as the final control target under the premise of meeting the constraints, constructs an optimization objective function, and solves it to obtain the optimal control scheme.

[0159] Specifically, as shown in Figure 4 the following steps are included:

[0160] S41, high-order discretization

[0161] In order to more accurately capture the dynamic characteristics of the alkaline electrolytic cell, this embodiment discards the traditional simple Euler discretization method, and adopts the Runge-Kutta fourth-order discretization method for discretization processing. The discretized state transition equation is calculated according to the sampling time interval.

[0162] For continuous state space model The Runge-Kutta fourth-order discretization formula is as follows:

[0163] k1=hf(x k ,u k )

[0164]

[0165] k4=hf(x k +k3,u k )

[0166]

[0167] Where x is the state vector, including key operating parameters of the electrolytic cell such as electrolyte temperature T, current density j, hydrogen and oxygen production, etc.; u is the control vector, mainly the input current and voltage; h is the sampling time interval; k1, k2, k3, k4 are intermediate calculation vectors.

[0168] According to the sampling time interval h, the discretized state transition equation is calculated. In the calculation process, numerical solution of the functions in the model is required to ensure the accuracy of discretization.

[0169] S42, prediction correction considering model uncertainty

[0170] In view of the existence of many uncertain factors in the operation of the alkaline electrolyzer, such as fluctuations in impurity content, sensor measurement errors, etc., Kalman filtering is introduced to correct the prediction model. Let the predicted state be Consider the process noise w k and the measurement noise v k , the system state equation and the measurement equation are respectively:

[0171] x k+1 =f(x k ,u k )+w k

[0172] y k =g(x k )+v k

[0173] Kalman filtering estimates and corrects the state through two steps of prediction and update, and its core formula is as follows:

[0174] (1) Prediction step:

[0175]

[0176] (2) Update step:

[0177]

[0178] P k+1 =(I-K k H k )P k+1|k

[0179] where, is the state estimate, P is the estimation error covariance matrix, F k is the state transition matrix, Q k is the process noise covariance matrix, H k is the observation matrix, R k is the measurement noise covariance matrix, K k is the Kalman gain.

[0180] At each time step, the state is estimated and corrected through the prediction and update steps of Kalman filtering, and a more accurate prediction result is obtained.

[0181] The Runge-Kutta fourth-order discretization method and Kalman filtering were used to optimize the prediction model, further improving the prediction accuracy. Compared with traditional Euler discretization, the Runge-Kutta fourth-order discretization method can more accurately approximate the dynamic characteristics of continuous systems and reduce discretization errors. Kalman filtering can effectively handle model uncertainties and measurement noise, and correct prediction results in real time. The application of these techniques enables the control algorithm to more accurately track changes in system state, achieving fine-grained control of the electrolyzer.

[0182] S43, Construct the optimization objective function

[0183] In this embodiment, the objective function is optimized to maximize hydrogen production, maintain hydrogen purity at the target value, minimize system energy consumption, and enhance the operational stability of the electrolyzer, while taking into account constraints such as current, voltage, and temperature.

[0184] For the hydrogen production process in an alkaline electrolyzer, multiple optimization objectives are established and balanced using weighted coefficients. The optimization objective function is constructed with the goals of maximizing hydrogen production, maintaining hydrogen purity at a target value, minimizing system energy consumption, and enhancing the operational stability of the electrolyzer:

[0185]

[0186] in, y represents the predicted hydrogen production at time k+i. purity,k+i|k Let be the hydrogen purity predicted at time k+i, given at time k. The target value for hydrogen purity; P k+i|k Let Δu be the system energy consumption at time k+i predicted at time k. k+i|k =u k+i|k -u k+i-1|k To control the change in quantity, u k+i|k R is the control vector predicted at time k+i at time k; u α1, α2, α3, α4 are weighting matrices for controlling changes in variables; α1, α2, α3, α4 are weighting coefficients that are dynamically adjusted according to actual operational needs and importance; N is the prediction time domain.

[0187] During the optimization process, various system constraints were strictly considered, including upper and lower limits for current and voltage, the safe temperature range of the electrolyzer, and the gas pressure range. The current constraint is expressed as follows:

[0188] I min ≤I k+i|k ≤I max

[0189] Temperature constraints are expressed as:

[0190] T min ≤Tk+i|k ≤T max

[0191] where I min , I max are preset minimum and maximum current values, I k+i|k is the predicted current at time k+i at time k; T min , T max are preset minimum and maximum temperature values, T k+i|k is the predicted temperature at time k+i at time k.

[0192] The temperature safety range constraint and the gas pressure range constraint of the electrolytic cell are achieved through the multidimensional collaborative regulation strategy in the aforementioned step S2, which will not be described here in detail.

[0193] These constraints are achieved by adding inequality constraints in the optimization problem, ensuring that the control input and system state are always within a safe and reasonable range.

[0194] S44, optimization solving

[0195] To efficiently solve complex nonlinear optimization problems, the optimization solving uses an adaptive interior point method, constructs a barrier function to convert the inequality constraint problem into an unconstrained problem, and uses the parallel computing power of a graphics processing unit to improve the solving speed.

[0196] Specifically, by introducing a barrier function, the inequality constraint problem is converted into an unconstrained problem for solving. For an optimization problem with inequality constraints c(x)≤0, a barrier function B(x,μ) is constructed:

[0197]

[0198] where μ is the barrier parameter, which gradually decreases with the iteration process; m is the number of inequality constraints, c j (x) is the jth inequality constraint. The original optimization problem is converted to:

[0199] min x {J(x)+B(x,μ)}

[0200] The adaptive interior point method updates the search direction and step size through iteration, gradually approaching the optimal solution. In each iteration, the search direction is obtained by solving the Newton equation:

[0201]

[0202] where H is the Hessian matrix and Δx is the search direction. According to the search direction and step size selection strategy, the variable x is updated until the convergence condition is met.

[0203] In each iteration, the gradients and Hessian matrix of the objective function and barrier function are calculated, and the search direction is obtained by solving the Newton equation. According to the search direction and step size selection strategy, the variable is updated until the convergence condition is met.

[0204] In addition, considering that model predictive control needs to quickly solve the optimization problem in each sampling period, parallel computing technology is used to speed up the solving process. By using the parallel computing capability of the graphics processing unit (GPU), the matrix operations and function evaluations in the optimization problem are parallelized. By reasonably allocating computing resources, the optimization solving time is significantly shortened, meeting the requirements of real-time control.

[0205] In addition, in order to improve the reliability and real-time performance of the multi-tank system communication, a hierarchical distributed communication architecture is designed. The hierarchical distributed communication architecture includes a device layer, a regional layer, and a central control layer. The device layer collects and transmits data, the regional layer aggregates and preliminarily processes data, and the central control layer comprehensively analyzes and decides and issues control instructions, and the communication process uses a unified data format and communication protocol.

[0206] Specifically, the device layer is responsible for collecting real-time operation data of each electrolytic tank and transmitting the data to the regional layer; the regional layer aggregates and preliminarily processes the data of the electrolytic tanks in the region and uploads it to the central control layer; the central control layer performs comprehensive analysis and decision-making based on global data and issues global optimization targets and strategies to the regional layer; the regional layer refines and adjusts the optimization targets and strategies according to the actual situation of the local electrolytic tank and sends control instructions to the device layer. In the communication process, a unified data format and communication protocol are used between the layers to ensure accurate data transmission. Through this data interaction mechanism, the collaborative optimization and stable operation of the multi-tank system are realized.

[0207] The technical innovation points of the above scheme are:

[0208] A. Model level

[0209] A1. Multi-factor precise modeling: innovatively incorporates the influence of impurity ions on the electrolysis reaction into the electrolysis reaction model, making the model more consistent with the actual situation of electrolyte containing impurities in the industrial hydrogen production scene, breaking through the limitations of traditional models that only consider ideal reaction conditions. In the heat transfer model, the temperature change rate term is introduced to accurately reflect the dynamic thermal response characteristics of the electrolytic tank, which is more timely and accurate than traditional heat transfer models in describing temperature changes. In addition, a multi-physical field coupled inter-tank coupling model is constructed, which comprehensively considers the coupling of gas and electrolyte material transfer, as well as the coupling of temperature field and electric field, achieving a deep description of the complex coupling relationship of the multi-tank system and providing a solid model foundation for multi-tank collaborative control.

[0210] A2. Multi-algorithm fusion parameter identification: A parameter identification method combining particle swarm optimization algorithm and least squares method is adopted to take advantage of the strong global search ability of particle swarm optimization algorithm to quickly lock the approximate range of parameters, and then use the local optimization precision of least squares method to finely adjust the parameters, greatly improving the accuracy and identification efficiency of model parameters. Compared with single algorithm, it has stronger adaptability and reliability.

[0211] B. Control algorithm level

[0212] B1. High-order discretization and uncertainty processing: In the model predictive control algorithm, the traditional Euler discretization method is abandoned, and the Runge-Kutta fourth-order discretization is adopted to significantly reduce the discretization error and more accurately capture the dynamic characteristics of the electrolytic cell. At the same time, Kalman filter is introduced to correct the prediction model, effectively dealing with model uncertainty and measurement noise in the running process, ensuring the accuracy and reliability of the prediction results, and improving the adaptability of the control algorithm to complex working conditions.

[0213] B2. Multi-objective weighting and adaptive solution: A multi-objective weighted optimization function is constructed with the goals of maximizing hydrogen production, meeting hydrogen purity standards, minimizing system energy consumption, and enhancing electrolytic cell operation stability. By dynamically adjusting the weight coefficients, different production stages and needs are met. Adaptive interior point method is used to solve the optimization problem, combined with parallel computing technology of graphics processing unit, which not only improves the solution accuracy, but also greatly shortens the solution time, meeting the real-time requirements of model predictive control.

[0214] C. Multi-cell coordinated control level

[0215] C1. Multi-factor load distribution: A priority dynamic determination method based on multi-factor evaluation is proposed, which considers key factors such as energy efficiency, hydrogen production rate, and operation stability of electrolytic cells to calculate performance index and dynamically determine load distribution priority. Compared with traditional fixed priority or simple proportional distribution method, it can more reasonably distribute the load, fully utilize the advantages of each electrolytic cell, and improve the overall performance of the system.

[0216] C2. Multi-dimensional collaborative regulation: Design of heat balance collaborative regulation and gas pressure collaborative regulation mechanism to effectively solve the coupling problem of heat transfer and gas pressure in multi-cell system. By real-time monitoring and adjusting the operating parameters of each electrolytic cell, the heat balance and gas pressure stability of the system are maintained, ensuring the stable operation of the multi-cell system under various working conditions.

[0217] C3. Hierarchical distributed communication architecture: a hierarchical distributed communication architecture is built, including a device layer, a region layer and a central control layer, each layer has clear division of labor, realizes efficient collection, processing and transmission of data. A unified data format and communication protocol are adopted, a data interaction mechanism is established, collaborative optimization of multi-slot systems is realized, the reliability and real-time performance of communication are improved, and powerful communication guarantee is provided for multi-slot coordinated control.

[0218] The preferred embodiments of the application are described in detail above. It should be understood that those of ordinary skill in the art can make many modifications and changes without requiring creative efforts, based on the concept of the present application. Therefore, any technical solutions obtained by logical analysis, reasoning or limited experiments based on the prior art according to the concept of the present application shall be within the protection scope defined by the claims.

Claims

1. A multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control, characterized in that, The method comprises the following steps: Real-time data acquisition at key positions of the hydrogen production alkaline electrolyzer system; Based on the dynamically determined priority of each electrolyzer, dynamic load distribution of each electrolyzer is performed, and a multi-dimensional collaborative control strategy is implemented in the load distribution process to obtain the hydrogen production target value of each electrolyzer; A nonlinear model including an electrolysis reaction model, a heat transfer model and an inter-tank coupling model is constructed, and parameter identification and verification are performed; A nonlinear model predictive control algorithm is designed, the nonlinear model is discretized, model uncertainty is introduced by Kalman filtering, each electrolyzer reaches the corresponding hydrogen production target value as the final control target under the premise of meeting the constraints, an optimization objective function is constructed and solved to obtain an optimal control scheme, and the optimization objective function includes maximizing hydrogen production, maintaining hydrogen purity at a target value, minimizing system energy consumption and enhancing electrolyzer operation stability.

2. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The priority determination method is: calculating a performance index PI for the electrolysis cell i i : where ω1, ω2, ω3 are weight coefficients; η e,i represents energy efficiency, defined as hydrogen production per unit energy consumption: is the hydrogen production of electrolyzer i, E i is the electrical energy consumed by it; represents hydrogen production rate, calculated by the change of hydrogen production per unit time: is the change of hydrogen production of electrolyzer i, Δt is the time interval; σ s,i represents operation stability, measured by the fluctuation standard deviation of key parameters of electrolyzer within a preset time; The load distribution priority of each electrolyzer is dynamically determined based on a performance index.

3. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 2, characterized in that, The dynamic load distribution is specifically: According to the total hydrogen production demand of the system and the performance index of each electrolytic cell, dynamic load distribution is performed, wherein the hydrogen production target value allocated to the i th electrolytic cell The calculation formula is: Wherein, n is the number of electrolyzers.

4. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The multi-dimensional collaborative control strategy includes: Thermal balance coordinated regulation strategy: when the temperature T of a certain electrolytic cell deviates from the set value T i , based on the heat balance equation of the introduced heat transfer coefficient, the reasonable transfer of heat is realized by adjusting the cooling system or load distribution of the adjacent electrolytic cell; set,i ​ Gas pressure collaborative control strategy: according to the ideal gas state equation, the relationship between gas pressure, gas quantity, temperature and pipeline volume in the pipeline is determined, the gas production of each electrolyzer and the gas pressure in the pipeline are monitored in real time, and when the gas pressure in the pipeline exceeds the set range, the gas production of each electrolyzer is adjusted for regulation and control.

5. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The electrolysis reaction model considers the influence of impurity ions on the reaction, introduces an impurity influence factor, and is expressed as: U = U rev + η act + η ohm + η conc + ΔU imp where U rev is the reversible voltage; η act is the activation overpotential; η ohm is the ohmic overpotential; η conc is the concentration overpotential; ΔU imp is the overpotential due to impurities, i.e. the impurity influence factor, ΔU imp = kc imp , where k is a constant related to the impurity species and the electrode material, and c imp is the impurity ion concentration.

6. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The heat transfer model considers the temperature change inside the electrolyzer, introduces a temperature change rate term, and is expressed as: where m is the mass of electrolyte, C p is the specific heat of electrolyte, T is the temperature of electrolyte, t is time, is the temperature change rate term, Q elec is the heat generated by electrolysis reaction, Q ohm is the ohmic heat, Q conv is the convective heat dissipation, Q rad is the radiative heat dissipation.

7. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The inter-tank coupling model considers the influence of temperature on flow and electrolyte conductivity, and is expressed as: Among them, Q gas R is the gas flow rate, ΔP is the pressure difference between the two ends of the pipeline, and R is the pressure difference between the two ends of the pipeline. gas T represents the gas flow resistance. ref For reference temperature, T gas For gas temperature, σ sol E is the electrolyte conductivity, σ0 is the pre-exponential factor, and E a R is the activation energy, R is the gas constant, and T is the absolute temperature.

8. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The optimization objective function is expressed as: wherein, is the hydrogen production at time k+i predicted at time k; y purity,k+i|k is the hydrogen purity at time k+i predicted at time k; y is the target value of the hydrogen purity; P k+i|k is the system energy consumption at time k+i predicted at time k; Au k+i|k = u k+i|k - u k+i-1|k is the change of the control variable, u k+i|k is the control vector at time k+i predicted at time k; R u is the weight matrix of the control variable change; a1, a2, a3, a4 are weight coefficients; N is the prediction time domain.

9. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The constraints include upper and lower constraints of current and voltage, temperature safety range constraints of electrolyzer and gas pressure range constraints.

10. The multi-cell control method for hydrogen production alkaline electrolyzer based on nonlinear model predictive control according to claim 1, characterized in that, The hydrogen production alkaline electrolyzer system adopts a hierarchical distributed communication architecture, which is divided into a device layer, a regional layer and a central control layer. The device layer is responsible for collecting real-time operation data of each electrolyzer and transmitting the data to the regional layer. The regional layer aggregates and preliminarily processes the data of electrolyzers in the region and uploads it to the central control layer. The central control layer performs comprehensive analysis and decision-making based on global data, and issues global optimization objectives and strategies to the regional layer. The regional layer refines and adjusts the optimization objectives and strategies according to the actual situation of local electrolyzers and sends control instructions to the device layer.

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