CN113793649A - Method for constructing digital twin model of operation characteristics of alkaline electrolytic cell - Google Patents
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Abstract
本发明涉及一种碱性电解槽运行特性数字孪生模型构建方法，包括以下步骤：1)根据碱性电解槽相关试验及工作机理，以槽温作为唯一孪生关联变量构建碱性电解槽阻抗特性数字孪生模型；2)基于碱性电解槽阻抗特性数字孪生模型，将数学驱动模型和电化学机理模型融合，以电解槽总电压、总电流、槽体温度、运行功率以及产氢量的特性表征参数作为观测变量，实现碱性电解槽运行特性的数字孪生建模，具体包括温升特性、功率调节特性、产氢效率特性和分离罐特性。与现有技术相比，本发明具有通用性强、流程简单、准确性高、工程可用性强等优点。
The invention relates to a method for constructing a digital twin model of the operating characteristics of an alkaline electrolytic cell, comprising the following steps: 1) according to the relevant tests and working mechanism of the alkaline electrolytic cell, using the cell temperature as the only twin correlated variable to construct the impedance characteristic digital of the alkaline electrolytic cell Twin model; 2) Based on the digital twin model of the impedance characteristics of the alkaline electrolytic cell, the mathematical driving model and the electrochemical mechanism model are integrated, and the parameters are characterized by the characteristics of the total voltage, total current, cell temperature, operating power and hydrogen production of the electrolytic cell. As observation variables, the digital twin modeling of the operating characteristics of alkaline electrolyzers is realized, including temperature rise characteristics, power regulation characteristics, hydrogen production efficiency characteristics and separation tank characteristics. Compared with the prior art, the present invention has the advantages of strong versatility, simple process, high accuracy, strong engineering usability and the like.
Description
Technical Field
The invention relates to the technical field of hydrogen production by water electrolysis, in particular to a method for constructing a digital twin model of the operating characteristics of an alkaline electrolytic cell.
Background
The hydrogen energy has the characteristics of high energy density, cleanness, no pollution, high efficiency, renewability and the like, is the best way for solving the energy resource crisis and the environmental crisis, and is known as the ultimate energy of the 21 st century. The development of the hydrogen energy industry is not open to green, efficient and safe hydrogen preparation, the power generation and hydrogen production by using renewable energy sources such as wind, light and the like have great application prospects at present, and the hydrogen production by using renewable energy sources taking the water electrolysis hydrogen production technology as the core is listed in respective energy strategies by multiple countries. The electrolytic cell is used as a core device of a hydrogen production system by electrolyzing water by renewable energy, and along with the continuous expansion of the application scale of the hydrogen production field, the problems of stability and safe operation of the electrolytic cell are increasingly prominent, and particularly, the negative effects caused by the defect of the dynamic response capability of the electrolytic cell cannot be ignored. When the electrolytic cell is electrically coupled with wind and light, the intermittent and fluctuating property of wind energy and solar energy causes the problems of frequent start and stop of the system, load change and the like due to the non-constant power transmitted to the electrolytic cell and the large fluctuation range, so that the service life of the equipment is shortened, the working efficiency of the equipment is reduced, the hydrogen production is reduced, and the development of large-scale power generation of renewable energy sources is severely restricted. An alkaline electrolytic cell model is constructed and simulated, the real-time monitoring of the system running state is realized, and the working characteristics and the state of the system are mastered, so that the system has important values for guaranteeing the scientificity, the stability and the safety of the operation of the water electrolysis hydrogen production system.
Disclosure of Invention
The invention aims to overcome the defects of the prior art and provide a method for constructing a digital twin model of the operating characteristics of an alkaline electrolytic cell.
The purpose of the invention can be realized by the following technical scheme:
a method for constructing a digital twin model of the running characteristics of an alkaline electrolytic cell comprises the following steps:
1) according to the relevant tests and the working mechanism of the alkaline electrolytic cell, the cell temperature is used as the only twinning related variable to construct an alkaline electrolytic cell impedance characteristic digital twinning model;
2) based on the alkaline electrolytic tank impedance characteristic digital twin model, a mathematical driving model and an electrochemical mechanism model are fused, and characteristic characterization parameters of total voltage, total current, tank body temperature, operating power and hydrogen production are used as observation variables to realize the digital twin modeling of the alkaline electrolytic tank operating characteristic, specifically comprising a temperature rise characteristic, a power regulation characteristic, a hydrogen production efficiency characteristic and a separation tank characteristic.
In the step 1), the digital twin model of the impedance characteristic of the alkaline electrolytic cell is obtained by binomial fitting, and the expression is as follows:
wherein R isi(T) is the equivalent electrical impedance of the electrolytic cell, A is the quadratic coefficient, B is the first order coefficient, C is the constant term coefficient, and the parameters A, B, C are all one order of magnitude, [ T ]min,Tmax]The fitting value range of the bath temperature T is obtained.
In the step 2), the concrete steps of constructing the temperature rise characteristic model of the alkaline electrolytic cell are as follows:
converting a mathematical expression of the equivalent electrical impedance of the electrolytic cell based on a circuit theory into a mathematical characteristic expression only related to temperature;
based on an impedance generalization model, the economic rated power of the electrolytic cell is obtained by taking the cell temperature as a unique variable and is taken as the upper limit of the operating power of the electrolytic cell;
obtaining a mathematical equation of an electric-thermal model based on an electrochemical reaction heat balance equation, and obtaining a model of which the insulation power of the electrolytic cell is only related to the temperature as the lower limit of the operation power of the electrolytic cell;
and integrating the time according to an electric-thermal model mathematical equation to further obtain a temperature rise characteristic model of the alkaline electrolytic cell.
The electrochemical reaction heat balance equation is specifically as follows:
the heat accumulation rate in the reactor is the rate of heat brought in by the material plus the rate of heat generated in the electrochemical reactor plus the rate of heat brought out by the material plus the heat dissipation rate of the reactor plus or minus the heat exchange rate of the heat exchanger in the reactor.
The expression of the temperature rise characteristic model is as follows:
wherein T is the time required for the bath temperature to reach the specified temperature from the initial temperature, TkIs the bath temperature, T0kIs the initial temperature of the electrolytic cell, S is the area of the material participating in the reaction in the electrolytic cell, JwiFor the incoming flow of component w, MwiIntroduced into the molar mass of component w, CP,wiBringing into isobaric specific heat, T, for component wckTo test the ambient temperature, JwoFor the carry-over flow of component w, MwoBringing about a molar mass of component w, CP,woThe component w brings out isobaric specific heat, I is electrolytic current, V is electrolytic voltage, Delta H is enthalpy change of electrochemical reaction, n is number of electrons participating in reaction, F is Faraday constant, kvIs the heat transfer coefficient of component v, SvIs the heat transfer area of the component v, and Δ T is the tank temperature T and the ambient temperature TcDifference of difference, Q4The heat quantity, mC, introduced or withdrawn by the heat exchanger in the electrolytic cell per unit timePThe amount of heat absorbed per 1 ℃ rise of the reactor contents.
For the power regulation characteristic, the heat preservation power of the electrolytic cell is obtained according to a heat balance equation, and the following steps are carried out:
wherein, PTminFor the holding power of the cell, PemaxIs the economic rated power of the corresponding groove with the highest groove temperature, and Pemax＝PTmax(Tmax) And omega represents a proportionality coefficient which is the minimum power ratio for the safe operation of the electrolytic cell engineering.
When the working condition of the electrolytic cell is stable, the heat preservation power of the electrolytic cell is generalized into a unitary linear equation with the cell temperature as the only variable, and when the environment temperature changes, the heat preservation power is in negative correlation with the environment temperature.
For the hydrogen production efficiency characteristic, the hydrogen production V is obtained according to the electrolysis current of the electrolytic cell, the charge conservation in the electrolysis reaction and the Faraday's law of electrolysisHThen, there are:
wherein K is the electrochemical equivalent of hydrogen, rhoHIs the hydrogen density at standard conditions.
Regarding the characteristics of the separation tank, the separation tank is regarded as a communicating vessel system with a closed top, and a relational expression of liquid levels in the two tanks and the amount of gas substances in the two tanks is obtained according to an ideal gas state equation, a pressure balance theorem and a relationship between the simplified gas volume and the liquid level deviation average liquid level height, and then:
wherein, TKIs the thermodynamic temperature of hydrogen and oxygen in the separation tank, R is the universal gas constant, LH2Is the liquid level of the hydrogen separation tank, LO2Is the liquid level of the oxygen separation tank, nH2N is the amount of material in the hydrogen separation tankO2The amount of substances in the oxygen separation tank is shown, rho is the density of the electrolyte, r and h are respectively the radius and the length of the side cylindrical container type separation tank, and g is the gravity acceleration;
and obtaining the pressure in the two gas-liquid separation tanks according to an ideal gas state equation after obtaining the relational expression between the liquid levels in the two tanks and the amount of the gas substances in the two tanks.
The communicating vessel system comprises a hydrogen separating tank and an oxygen separating tank, the separating tank is a horizontal cylindrical container, generated gas is gathered above the container under the action of gravity and then flows into the scrubber through the air outlet pump, alkali liquor at the bottom enters the electrolytic bath again after being treated, and alkali liquor circulation is formed in a closed pipeline loop.
Compared with the prior art, the invention has the following advantages:
the method is used for constructing the alkaline electrolytic cell operation characteristic model based on the digital twinning technology, performs operation characteristic simulation, has important engineering value for guiding optimization of the operation control parameters and state evaluation of the electrolytic cell, can effectively avoid the problems of poor model universality and complex construction process, realizes simplified construction of the digital twinning simulation model of the electrolytic cell operation characteristic, and has higher accuracy and engineering availability compared with the traditional static model.
Drawings
FIG. 1 is a flow chart of a digital twinning system construction.
FIG. 2 is a schematic view of the static voltammetry characteristic of the electrolyzer.
FIG. 3 is an equivalent electrical impedance characteristic curve of the electrolytic cell, wherein FIG. 3a is a comparison of the fitted impedance curve and the test result, and FIG. 3b is an equivalent impedance fitting error.
FIG. 4 is a flow chart of the construction of a digital twin model system of an alkaline electrolytic cell.
FIG. 5 is a schematic diagram of the structure of the separation tank of the electrolytic cell.
FIG. 6 is a graph of liquid volume versus liquid level in a cylindrical container.
FIG. 7 is a graph showing the temperature rise characteristics of an electrolytic cell.
FIG. 8 is a program flow diagram of a power regulation model algorithm.
FIG. 9 is a power regulation characteristic simulation curve, in which FIG. 9a is an economical rated power curve of an electrolytic cell with time change at different ambient temperatures, FIG. 9b is a temperature holding power curve with ambient temperature change, and FIG. 9c is a power regulation speed curve.
FIG. 10 is a simulation curve of hydrogen generation characteristics, in which FIG. 10a is an electric power curve at different environmental temperatures, and FIG. 10b is a curve of hydrogen generation rate of an electrolytic cell at 15 ℃ as a function of electrolytic current.
FIG. 11 is a simulation curve of the liquid level regulation characteristic at 15 ℃ in which FIG. 11a is a pressure curve in the hydrogen separation tank and FIG. 11b is a liquid level deviation curve of the actual liquid level from the average liquid level in the hydrogen separation tank.
Fig. 12 is a block diagram of a valve PI regulation control flow.
Detailed Description
The invention is described in detail below with reference to the figures and specific embodiments.
Examples
A digital twin technology based on a sensing technology, an Internet of things technology and a simulation modeling technology is an advanced and feasible new technology for realizing real state simulation comparison and deduction evaluation of a physical entity through fusion of a physical model and a data driving model. In recent years, models related to digital twinning attract wide attention in the industrial field, the technology gradually becomes an emerging research hotspot in the fields of intelligent manufacturing and complex system performance monitoring, for example, related research introduces the digital twinning technology into the construction of simulation models, and compared with the traditional static model adopting fixed parameters, the digital twinning model is verified to have higher accuracy and engineering availability. The method has the advantages that the digital twinning technology is applied to the construction of the electrolytic cell working characteristic model by referring to the research results of other objects, the electrolytic cell running characteristic simulation and state evaluation related application is realized through the electrolytic cell digital twinning model, and the method obviously has important engineering value and practical significance in promoting the informatization, digitization and intelligent development of the alkaline electrolytic cell and adapting to the digital transformation of the energy industry.
The common water electrolysis hydrogen production tanks comprise three types of alkaline electrolysis tanks, polymer film electrolysis tanks and solid oxide electrolysis tanks, wherein the alkaline electrolysis tank is most widely applied, is the only water electrolysis hydrogen production equipment meeting the large-scale engineering application at present, and has the advantages of mature technology, low cost and the like. The invention takes the alkaline electrolytic water hydrogen production tank as a research object, combines the working mechanism and the historical operating data of the alkaline electrolytic tank hydrogen production system according to the static and dynamic volt-ampere characteristic test results, and realizes the construction and simulation of the digital twin model of the alkaline electrolytic tank operating characteristics on the basis of constructing the tank body impedance characteristic digital twin model.
The invention provides a method for constructing a digital twin model of the operating characteristics of an alkaline electrolytic cell, and the corresponding contents are specifically described below.
1. Digital twin model frame of alkaline electrolytic cell
1.1 digital twinning model infrastructure
The invention adopts a method based on a digital twinning technology to model the external characteristics of an alkaline electrolytic cell, the core concept of the method is a mixed modeling method formed by fusing a mechanism modeling method and a data modeling method, and a conceptual flow chart of the method for establishing the digital twinning system construction of the alkaline electrolytic cell is shown in figure 1 and mainly comprises three parts of operation data acquisition, mechanism model analysis and digital twinning mixed modeling.
The operation data mainly includes two parts, namely, device attribute parameters and external condition parameters, as shown in table 1.
TABLE 1 measured operating data
The static parameters are obtained according to the specific electrolytic cell equipment condition and the working environment condition, and can be used as constant data to be input into the digital twin model of the alkaline electrolytic cell. The data measured in real time are obtained through a series of high-precision sensors such as voltage and current sensors, temperature sensors, hydrogen sensors and the like which are arranged on various structures of the electrolytic cell, and the data are used for constructing and analyzing a digital twin internal model on one hand and verifying the accuracy and optimization of the model on the other hand.
The digital twin model finally outputs a characteristic function reflecting the actual characteristics of the electrolytic cell, the function parameters are determined by specific data measured by each sensor, the characteristic variables are determined by the operation mechanism of the alkaline electrolytic cell, and compared with a simple mechanism model or a data model, the digital twin model has better model accuracy and interpretability and has huge potential in research and application.
1.2 digital twin model of impedance characteristics
The working process of the electrolytic cell is mainly divided into two stages of starting and normal operation: when the DC input voltage U is<estAnd the temperature of the tank is lower than TminThe method is characterized in that the method is a starting stage of the electrolytic cell, electric energy is mainly used for heating a system in the starting stage, ionization conditions are established, and the hydrogen yield is zero; when the DC input voltage U is more than or equal to erevAnd the temperature T of the tank is greater than TminIn the normal operation stage of the electrolyzer, the voltage and the current are approximately in a linear relationship, and the static volt-ampere characteristic curve of the whole operation process is shown in figure 2.
In electrochemical engineering, the working temperature is a key factor for determining the stable operation of an electrochemical reactor, and according to the working mechanism of an electrolytic cell, the working temperature of the electrolytic cell, namely the cell temperature, has important influence on the efficiency of electrolytic water reaction and electrochemical technical and economic indexes such as working voltage, current efficiency and the like, and the corrosivity of an electrolyte and the stability of an electrode material and a diaphragm material are related to the temperature; according to the test result of the working characteristics of the electrolytic cell, the equivalent impedance, the power regulation characteristic and the hydrogen production characteristic of the electrolytic cell are directly related to the cell temperature; in addition, compared with parameters such as equivalent electrical impedance, operation power and the like which can only be indirectly measured, the bath temperature can be directly measured, and the data acquisition is more convenient and accurate. The key to the accuracy and effectiveness of the digital twinning technique for realizing the model is to select observable and sensitive parameters as characteristic parameters. In conclusion, the invention selects the bath temperature as the uniform variable, and utilizes the digital twinning technology to carry out system modeling and simulation research on the running characteristic digital twinning model, thereby providing theoretical and engineering values for the evaluation research of the running state of the electrolytic bath.
The chemical reaction mechanism of hydrogen production by water electrolysis and the static volt-ampere characteristic test result of the alkaline electrolytic cell show that the equivalent electrical impedance of the alkaline electrolytic cell is only related to the cell temperature, when the electrolytic cell is in a normal operation state after the temperature rise starting state is finished, the cell temperature is gradually kept constant, and the equivalent electrical impedance of the electrolytic cell is hardly influenced by the change of input voltage and keeps unchanged. Meanwhile, the higher the temperature of the bath is, the smaller the equivalent electrical impedance is, and when the temperature of the bath is higher to a certain value, the equivalent electrical impedance is kept constant.
According to the impedance characteristics and the constraint conditions of the alkaline electrolytic cell, the impedance expression (1.1) of the mechanism level can be obtained by deduction based on the circuit theory:
wherein, the calculation formula of the tank back electromotive force is shown as the formula (1.2):
because the formula (1.1) is limited in a mechanism level, parameters such as counter potential in the formula are greatly influenced by actual conditions, the universality is poor, and the calculation is complicated. Based on the theoretical analysis, the electric heating characteristic rule of the cell electrical impedance with the cell temperature as the only variable is obtained by measuring signals of the working voltage and the electrolytic current of the electrolytic cell end at different temperatures, and then a digital twin model of the impedance characteristic of the alkaline electrolytic cell is constructed by data fitting. On the basis of mastering the operation mechanism, the digital twin hybrid modeling is carried out by combining the fitting result of the measured data, so that the problems of poor universality and complex construction process of an impedance characteristic theoretical model are solved.
According to the invention, two traditional alkaline water electrolysis hydrogen production tanks are taken as objects, a series of mathematical models are built according to experimental data obtained by the static and dynamic volt-ampere characteristics and the initial power regulation characteristic test of the water electrolysis hydrogen production tanks which are carried out at an early stage, and the specific parameters of the selected electrolysis tanks are shown in table 2.
TABLE 2 specific parameters of the test cells
According to the impedance-temperature data of the test object 1 and the test object 2, fitting the test data in the range of 55-65 ℃ based on a least square method to obtain the change relation between the impedance of the electrolytic cell and the temperature, namely electrolytic cell impedance fitting functions (1.3) and (1.4), using the obtained fitting functions for 65-80 ℃, respectively obtaining corresponding impedance values, and placing the impedance values and the test results in the same coordinate system for comparison to obtain an equivalent impedance curve shown in figure 3 to verify the accuracy of impedance fitting.
R1(T)＝1.1763e-6T2-2.32e-4T+0.0172 (1.3)
R2(T)＝0.977e-6T2-2.73e-4T+0.0275 (1.4)
As can be seen from the graph (3a), the similarity of the fitting result and the test curve is high at the bath temperature of 55-80 ℃, and the fitting result has certain accuracy and feasibility. When the operating temperature was changed from 55 c to 80 c, the impedance change of the test object 1 was changed from about 7.98m Ω to 6.15m Ω, and the impedance change of the test object 2 was changed from about 16.33m Ω to 2.03m Ω. According to the fitting error curve of the graph (3b), the equivalent electrical impedance fitting errors of the test object are distributed within +/-1%, and the fitting result is accurate.
The mathematical characteristic expression with certain generalization significance of the equivalent electrical impedance of the electrolytic cell is obtained by derivation as follows:
in the formula: ri(T) is equivalent electrical impedance of the electrolytic cell, A is quadratic coefficient, B is first order coefficient, C is constant term coefficient, fitting parameters of different test objects are different, but A, B, C are all one order of magnitude, [ T ]min,Tmax]The fitting value range of the bath temperature T is obtained.
Compared with the formula (1.1), the formula (1.5) reduces the data volume to be measured to only one bath temperature, and can more intuitively reflect the influence of the temperature on the impedance; in addition, the formula has better universality, and under the condition that the structure of the device is determined, impedance data of the whole operation stage of the electrolytic cell can be obtained only by extracting discrete current-voltage data to carry out fitting and parameter change. The construction of the impedance digital twin model lays a foundation for the construction of a digital twin model integral system of the subsequent alkaline electrolytic cell operation characteristics.
2. Digital twin model system for operating characteristics of alkaline electrolytic cell
2.1 modeling of operating characteristics digital twin model system
The modeling method based on the mechanism of the characteristic curve is generally adopted in the field of alkaline electrolytic cell modeling, and because the performance parameters of electrolytic cell equipment are more, the nonlinearity degree is high, the coupling relation is complex, and the characteristics of parts are difficult to obtain, the time consumption for establishing an accurate model is longer, and the difficulty is higher. In consideration of various reasons that unknown offset and the like may occur to the component characteristics of the alkaline electrolytic cell along with long-time operation of the alkaline electrolytic cell in the practical application process, certain errors will exist between the calculation of the mechanism model and the practical alkaline electrolytic cell under the fluctuation working condition of the water electrolysis hydrogen production system. In addition, part of the influence factors are not considered in a relatively simplified mechanism model, and if impurities generated by electrolyte in the cell body after the cell body operates for a period of time affect the reaction efficiency and the cell temperature, errors between the calculation results and the mechanism model are caused; the data modeling is based on historical operating data, the operation mechanism of a research object is not required to be mastered, the deep-level characteristics of the data can be better mined, but the physical mechanism of the research object cannot be embodied, the relation between specific parameters is specified by a related mechanism formula, and the model precision excessively depends on the accuracy of data and parameter association.
Aiming at the problems existing in the method, in order to construct a more accurate alkaline electrolytic cell dynamic model, the invention firstly establishes an accurate alkaline electrolytic cell impedance characteristic digital twin model. On the basis, by combining the static and dynamic volt-ampere characteristic tests of the electrolytic cell and the working mechanism of hydrogen production of the alkaline electrolytic cell, a digital twin model of the temperature rise characteristic, the power regulation characteristic, the hydrogen production characteristic and the pressure characteristic of the separation tank of the alkaline electrolytic cell is further constructed around the characteristic variables of the total voltage, the current, the cell temperature, the operation power, the hydrogen production quantity and the like of the cell body of the device during the operation, and the modeling flow is shown in fig. 4. The impedance characteristic digital twin model can verify the reasonability and the accuracy of the impedance characteristic digital twin model from the aspects of effectiveness of a theoretical model and consistency of a simulation result and an experimental result, so that the system digital twin model developed and constructed on the basis of the impedance characteristic digital twin model also has certain accuracy.
Firstly, converting a mathematical expression of equivalent electrical impedance of an electrolytic cell based on a circuit theory into a mathematical characteristic expression only related to temperature; based on an impedance generalization model, the economic rated power of the electrolytic cell is deduced by taking the cell temperature as a unique variable to serve as the upper limit of the operating power of the electrolytic cell; an electricity-thermal model mathematical equation is obtained on the basis of an electrochemical reaction heat balance equation, and a model of which the insulation power of the electrolytic cell is only related to the temperature is further deduced to be used as the lower limit of the operation power of the electrolytic cell; integrating time by using an electric-thermal model mathematical equation to obtain a temperature rise characteristic model; and (3) connecting all digital twin models with temperature as a unique variable with a temperature rise model, and simplifying time segments to obtain a power regulation model in the temperature rise process. Obtaining electrolytic current based on the change of the equivalent electrical impedance along with the temperature, further deducing to obtain a hydrogen production characteristic model, and obtaining a hydrogen production quality formula through the hydrogen production model; and finally, combining a pressure balance equation to obtain a pressure model of the gas-liquid separation tank. The method converts the characteristics of the electrolytic cell from abstract characteristic description into a mathematical expression which has theory and data analysis as supporting basis, and lays a foundation for the establishment of MATLAB-based alkaline electrolytic cell digital twin system simulation.
2.2 construction of digital twin model of electrolytic cell operating characteristics
2.2.1 modeling of temperature rise characteristics of electrolytic cell
The minimum electrolytic current for maintaining the electrolytic reaction of the electrolytic cell in different working environments can be deduced by researching the temperature rise characteristic model of the electrolytic cell, the heat preservation power of the electrolytic cell in different working environments is calculated, and the method has important guiding significance for the engineering design and the engineering practical application of the electrolytic cell. The temperature at which the electrochemical reaction is carried out in the electrolytic cell depends on various factors, the maintenance of the cell temperature depends on the heat transfer and heat balance in the reactor, and the heat balance equation during the operation of the system can be expressed as:
the heat accumulation rate in the reactor is the rate of heat brought in by the material + the rate of heat generated in the electrochemical reactor-the rate of heat brought out by the material-the heat dissipation rate of the reactor +/-the heat exchange rate of the heat exchanger in the reactor
The heat balance equation can be analyzed as follows:
(1) the total change of the heat quantity taken in by the reactants, the heat quantity taken out by the products and the reaction heat quantity in unit time is respectively Q1in、Q1out、Q1Represents:
wherein S is the area (m2) of the material participating in the reaction in the electrolytic cell, JwThe flow rate (mol.s-1. M-2), M, of the component wwIs the molar mass (g. mol-1) of component w, CP,wIs the isobaric specific heat (J.kg-1. DEG) of the component wK-1)，TkThe cell temperature (K).
(2) The amount of heat (J.s-1) generated per unit time by the electrochemical reaction in the electrolytic cell is Q2Represents:
where Δ H is the enthalpy change (J · mol-1) of the electrochemical reaction, n is the number of electrons participating in the reaction (n ═ 2), and is the faraday constant.
(3) Heat dissipation (heat exchange with the environment) per unit time of the cell, using Q3Represents:
wherein k isvIs the heat transfer coefficient (J/(s.K.m 2)) of component v, SvIs the heat transfer area (m2) of component v, Δ T is the cell temperature TkAnd ambient temperature TcThe difference between them.
(4) The heat brought in (or led out) by the heat exchanger in the electrolytic cell per unit time is Q4It represents an environmental control unit for heat exchange between the electrolyzer and the external environment.
Based on an electrochemical reaction heat balance equation, an electrolytic bath temperature rise speed model, namely an electric-thermal model mathematical equation, is obtained by derivation:
wherein, mCpRepresenting the amount of heat that needs to be absorbed per 1c rise of the contents of the reactor. Integrating the formula (2.4) with time, the time required for the bath temperature to reach a certain specified temperature from the initial temperature can be estimated as shown in the formula (2.5), so that a temperature rise mathematical model based on the electro-thermal characteristics of the electrolytic bath, namely a temperature rise characteristic model, is established:
when the electrolysis equipment and the environment control device are determined, only the voltage, the current, the bath temperature and the ambient temperature in the formula (2.5) are variables, so that the target value can be conveniently measured and controlled in real time, and the time required by the bath temperature from the initial temperature to the target temperature can be obtained.
2.2.2 modeling of electrolyzer power regulation characteristics
In the working process of the alkaline electrolytic cell, the situation that the output power needs to be regulated in real time can occur due to the fluctuation of an external load, so that the power regulation characteristic of the electrolytic cell needs to be researched, and the output power of the electrolytic cell is stabilized in a safe range.
In order to ensure the safe and stable operation and the economical efficiency of the electrolytic cell, the maximum current of the working point of the electrolytic cell at a certain temperature is generally controlled not to exceed the rated working current, and the corresponding rated power is called the economic rated power of the electrolytic cell at the corresponding temperature, namely the upper limit of power regulation. According to the equivalent electrical impedance expression (1.5), an economic rated power expression when the tank temperature is T can be obtained:
the voltage can be approximately considered to be constant in the electrolysis process, and the back electromotive force erevAnd corresponding critical current IrevApproximately constant, extracting the constant for equation (2.5) yields:
the holding power of the cell refers to the minimum power that needs to be consumed to maintain the current operating temperature of the cell. When the electrolytic cell operates at the heat preservation power, the electrolytic cell can achieve self energy balance only by the influence of self reaction heating and external environment under the condition of not adding an environment control device. As the safety problem is caused when the power of the electrolytic cell is too low, the heat preservation power is generally considered to be higher than the rated power P in practical engineering application emax20% of the total. Also with electricityBased on a chemical reaction heat balance equation, a heat preservation power expression of the electrolytic bath can be obtained:
in the formula, PTminFor the holding power of the cell, PemaxIs the economic rated power of the corresponding groove with the highest groove temperature, and Pemax＝PTmax(Tmax) And omega represents a proportionality coefficient which is the minimum power ratio of safe operation of the electrolytic cell engineering, and the value is 0.2 in the example.
After the working condition of the electrolytic cell is stable, only the temperature of the electrolytic cell is a variable in the above formula. After the constants are extracted, the above equation can be simplified to X, Y, which is equation (2.9) with the first order coefficient and constant term coefficient, respectively. When the environmental temperature is constant, the heat preservation power of the electrolytic cell can be generalized into a simple linear equation with the cell temperature as the only variable; the environment temperature changes, and the heat preservation power is in negative correlation with the environment temperature.
2.2.3 modeling of hydrogen production characteristics of electrolytic cell
The hydrogen production speed and the hydrogen production quantity of the alkaline electrolytic cell are important for the working efficiency of the whole renewable energy hydrogen production system, and meanwhile, the monitoring of the hydrogen production condition of the system is also important for the state evaluation of the electrolytic cell. The hydrogen production rate of the electrolytic cell during working is related to the electrolytic current, and on the basis of the formula that the equivalent electrical impedance changes with the temperature in the normal operation stage of the electrolytic cell, the electrolytic current expression of the electrolytic cell can be obtained by combining the volt-ampere characteristic in the normal operation stage:
then, according to the charge conservation in the electrolytic reaction and the Faraday's law of electrolysis, the expression of the hydrogen production (L) can be deduced:
wherein K is the electrochemical equivalent of hydrogen, and the reference data shows that K is 0.041g/Ah, rhoHRepresenting a hydrogen density of 0.089kg/m under standard conditions3. According to the formula (2.11), only the electrolytic current I is taken as a variable, the hydrogen production rate at a certain moment can be obtained by only calculating the electrolytic current during modeling and obtaining the hydrogen production rate of the electrolytic cell within a period of time in the normal working stage.
2.2.4 pressure modeling of electrolyzer separation tank
In the working process of the alkaline electrolytic cell, the hydrogen and oxygen separation tank of the electrolytic cell mainly plays a role in gas-liquid separation, and the simplified structural schematic diagram is shown in fig. 5. And the alkali liquor mixture with oxygen and hydrogen generated by the reaction of the alkaline electrolytic cell flows into respective separation tanks after being cooled. In large-scale industrial application, most of the separation tanks are horizontal cylindrical containers, generated gas is gathered above the containers under the action of gravity and then flows into the scrubber through the air outlet pump, and the alkali liquor at the bottom can reenter the electrolytic bath after a series of treatments to form alkali liquor circulation in a closed pipeline loop.
The gas-liquid separation tank can be regarded as a communicating vessel system with a closed top, and an ideal gas state equation (2.12) can be obtained according to the gas volume above the two separation tanks, wherein the hydrogen yield and the oxygen yield of the reaction can be obtained according to a chemical reaction formula and analysis of the hydrogen production characteristics.
Wherein, PH2、PO2The pressure of hydrogen and oxygen respectively; vH2、VO2The gas volumes (m3) above the liquid levels of the hydrogen separation tank and the oxygen separation tank respectively; n isH2、nO2The amounts of hydrogen and oxygen species respectively; r is a universal gas constant, and the value of R is 8.31 J.mol < -1 > K < -1 >;TKthe thermodynamic temperature (K) of the hydrogen and the oxygen in the two tanks is shown.
According to the pressure balance theorem, because the liquid in the tank is also communicated with each other, the pressure difference of the gas in the tank is equal to the liquid level pressure difference, and the pressure equality can be obtained:
where ρ is the density (kg/m) of the electrolyte3) G is the acceleration of gravity and has a value of 9.8m/s2；LH2、LO2Respectively shows the height (m) of the liquid level in the hydrogen tank and the oxygen tank from the average liquid level, the descending is negative, and the ascending is positive.
To simplify the modeling process, the functional relationship between the liquid level and the liquid volume of the side-mounted cylindrical vessel was approximated. An image of the volume of liquid in a side cylinder container with radius r of 0.3m and length h of 1m as a function of the height of the liquid level is shown in FIG. 6. Near the liquid level height of 0.3m, the relation between the liquid level height and the liquid volume is approximately linear, namely the relation between the liquid level drop and the gas volume above the tank is approximately linearly changed in the modeling process.
The height relation between the volume of the gas above the simplified liquid level and the deviation of the liquid level from the average liquid level is as shown in formula (2.14):
combining it with (2.12) and (2.13) to obtain liquid level L in two tanksH2、LO2And the amount n of gas material in the two tanksH2、nO2The relationship of (1):
in the formula, the liquid level height in the two tanks is the only unknown quantity, and the liquid level height in the gas-liquid separation tank in the working process of the electrolytic cell can be obtained by solving the equation. And combining the ideal gas state equation in the formula (2.12) to obtain the pressure in the two gas-liquid separation tanks.
3. Alkaline cell digital twin model simulation
Based on the constructed alkaline electrolytic cell running characteristic model, the invention integrates and simplifies the deduced electrolytic cell characteristic function by taking the characterization parameters related to the electrolytic cell running characteristic as observation variables, and carries out simulation on an MATLAB/Simulink platform.
3.1 simulation model of temperature rise characteristic of electrolytic cell
The time required for the tank temperature to reach a certain specified temperature from the initial temperature can be calculated according to the formula (2.9), but the calculation process is complicated, and for further simplification, the constants in the formula are extracted:
the simplified formula (3.1) represents that the ambient temperature is TckAt the time, the temperature of the tank is from T0The time required to rise to T. In practical engineering applications, V, I is a variable, and even if the voltage at the end of the electrolytic cell is controlled by a voltage stabilizer, certain fluctuation may occur, so V, I needs to obtain an input in a built model through real-time acquisition. And similarly, in order to simplify the complex modeling process of the temperature rise characteristic of the electrolytic cell, selecting a method driven by fused data to carry out temperature rise characteristic digital twin model simulation:
the similar impedance characteristics of 55-65 ℃ temperature rise data of the electrolytic cell under a specific experimental environment are fitted to obtain values a-e, the obtained fitting function is used for 65-80 ℃ to obtain an electrolytic cell temperature rise characteristic fitting curve shown in figure 7, the temperature rise characteristic fitting curve is compared with an actual temperature change curve along with time, it can be observed that the temperature rise time required by 65-80 ℃ calculated according to the fitting function has higher consistency with an actual measurement result, the accuracy of a temperature rise characteristic simulation model can be verified, and the calculation workload of a traditional pure theoretical model is greatly simplified.
3.2 Power Condition characteristic simulation model
The economic rated power and the heat preservation power of the electrolytic cell are both functions taking the temperature of the electrolytic cell as a unique variable. The adjustment of the electrolytic cell from a low-temperature point and a low-power point to a high-temperature point and a high-power point needs minute-level time, so that only the temperature rise condition needs to be analyzed in the modeling of the power adjustment characteristic.
Equation (2.9) shows that T (T, T) is the time required for the initial temperature T to reach the specified temperature T0, regardless of the environmental control0) Splitting into N δ t, i.e. δ t ═ δt1,δt2,…,δtN]Each delta ti corresponds to a starting temperature T0iCorresponding to a target temperature of Ti＝T0(i+1)(i ═ 1,2,3, …, N-1), assuming TiCorresponding to an economic power rating of PTiThe output power of the electrolytic cell is from PTiChange to PT(i+1)The time required is δ Ti (Ti, T0i), and the objective function is as follows (3.2):
because the economic rated power rising speeds of the electrolytic cells at different temperature working points are different, a segmentation method is adopted for approximate calculation in the power regulation characteristic modeling. And (3) abstract representation of the temperature rise regulating process: the cell is initially operated at a steady state at a lower temperature, assuming a power of P. At tdelThe power of the electrolytic cell needs to be adjusted to P + P at any moment due to the addition of power disturbancedel，PdelRepresenting the power of the disturbance. Simplifying the power regulation time, and reducing PdelAnd (4) segmenting according to time, considering that the power is unchanged in each time segment, and suddenly changing the power when the critical moment of the next time segment is reached. The tank temperature corresponding to the power in each time period can be obtained according to the formula (2.9), and the time required from the time period i to the time period i +1, namely the length of the time period i, can be obtained by combining the formula (3.1). Finally, the complete power adjustment feature is obtained by concatenating each time segment, and the simplified program flow of the algorithm is shown in fig. 8.
Based on the fitting of the set test environment and the actual test data of the electrolytic cell equipment, the voltage, the current and the temperature of the electrolytic cell obtained by the sensor are input into the simulation model in real time, and then the power regulation characteristic can be obtained. When the simulation of the electrolytic cell is independently established, in order to make the simulation result more intuitive, the voltage and the current which are input in real time are simplified into constant values, and the change curve shown in the figure 9 can be obtained by changing the environmental temperature.
According to the economic rated power curve of the electrolytic cell in the graph (9a) which changes with time under different environmental temperatures, the rising speed of the economic rated power curve is accelerated along with the rising of the environmental temperature, and finally the economic rated power curve is overlapped at about 19kW, the rising of the environmental temperature reduces the heat dissipation quantity of the electrolytic cell for heat exchange with the external environment, the rising of the cell temperature is accelerated, so that the economic rated power is synchronously raised, and the characteristic that the economic rated power is only positively correlated with the cell temperature is shown; according to the curve of the heat preservation power varying with the environmental temperature in fig. 9 (b), the heat preservation power decreases with the increase of the environmental temperature, which shows that the increase of the environmental temperature is helpful to reduce the heat loss of the electrolytic cell, and the sustainable temperature increases under the condition of consuming the same electric energy, but the heat preservation power will not decrease when reaching 20% of the rated power due to the limit of the safe operation power of the electrolytic cell; according to the power regulation speed curve of fig. 9c, the power acceleration of the electrolytic cell is accelerated along with the rise of the environmental temperature, and the electrolytic cell has better power regulation capability at higher temperature, which indicates that the regulation of the electrolytic cell from a low-temperature and low-power point to a high-temperature and high-power point requires minute-level time and meets the power regulation characteristic. The simulation result verifies that the simulation model of the temperature rise characteristic and the power regulation characteristic has certain accuracy.
3.3 Hydrogen production characteristic simulation model
The hydrogen production quantity of the electrolytic cell changing along with the current can be obtained according to the formula (2.11), the hydrogen production quantity of the electrolytic cell working for a period of time can be deduced only by calculating the electrolytic current, the hydrogen production rate at a certain moment can be obtained by deriving the hydrogen production quantity with time, the building method of the hydrogen production characteristic simulation model is to obtain the electrolytic current based on an equivalent electrical impedance expression (1.5) obtained by fitting, and then the hydrogen production quantity and the hydrogen production rate can be obtained by using an integral, derivation and multiplication module carried in Simulink, and the simulation result is shown in figure 10.
As can be seen from the power curves at different ambient temperatures in FIG. 10a, the power of the electrolytic cell increases with the increase of the ambient temperature, which shows that when the electrolytic voltage is approximately constant, the equivalent impedance decreases due to the increase of the cell temperature, the electrolytic current increases accordingly, and when the electrolytic current and the equivalent impedance reach a steady state, the power is kept constant. According to the curve of the hydrogen production rate of the electrolytic cell at 15 ℃ along with the change of the electrolytic current in the graph (10b), the hydrogen production rate is synchronously increased along with the increase of the electrolytic current in a certain current range, and the hydrogen production characteristic of the alkaline electrolytic cell is met.
3.4 simulation model of liquid level regulation characteristic of electrolytic cell
The equation (2.15) shows the equation of the liquid level in the gas-liquid separation tank, but the amounts of hydrogen and oxygen are not known in the equation. When the electrolytic cell starts to work, the amount of gas generated in the working process can be quantitatively calculated by monitoring the electrolytic current in real time, so that the amount of the gas in the tank when the reaction is carried out to a certain time can be obtained. Equation (2.15) degrades to an equation where the liquid level in both tanks is the only variable. The liquid level L in the two tanks can be obtained by only using MATLAB to solve the equationH2、LO2And the amount n of gas material in the two tanksH2、nO2The simulation results obtained are shown in FIG. 11.
As can be seen from the pressure curve in the hydrogen separation tank shown in fig. 11a, when the outlet valve is closed, the pressure in the hydrogen tank will rise continuously, which means that the pressure in the hydrogen tank will rise continuously, and therefore, the valve of the hydrogen tank needs to be controlled to open to keep the pressures in the two tanks balanced. The valve PI regulation control strategy shown in figure 12 is introduced into the simulation model, so that the pressure curve shown by the red curve in figure 11(a) can be obtained, and the pressure of the hydrogen separation tank is stabilized at about 1.6 MPa.
According to the liquid level deviation curve between the actual liquid level and the average liquid level in the hydrogen separation tank in the figure (11b), the liquid level of the hydrogen tank continuously drops when the valve is closed, which shows that the injected hydrogen amount is twice of the oxygen amount, and the liquid level of the hydrogen tank drops due to the gas pressure difference, so that the hydrogen production characteristics of the electrolytic cell are met. And after the valve PI is introduced for adjustment, the height difference of the liquid level in the tank is controlled within 0.1cm, thereby meeting the basic production requirement of the electrolytic cell.
3.5 application of digital twin model of alkaline electrolytic cell operating characteristics
The digital twin simulation model of the operation characteristics of the alkaline electrolytic cell constructed by the invention has the characteristics of generalization and simpler construction process, can provide a basis for the state evaluation of the alkaline electrolytic cell, can output state change curves reflecting different operation characteristics of the alkaline electrolytic cell by collecting characteristic characterization parameter data of related sensors in real time as the input of the model and utilizing an artificial intelligence method to perform cluster analysis according to the change trend of the state change curves, thereby realizing the related application of the model in the state evaluation process.
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| CN117252032A (en) * | 2023-11-10 | 2023-12-19 | 三峡科技有限责任公司 | Method, device and equipment for constructing digital twin body of alkaline water electrolysis hydrogen production system |
| CN117252032B (en) * | 2023-11-10 | 2024-02-13 | 三峡科技有限责任公司 | Method, device and equipment for constructing digital twin body of alkaline water electrolysis hydrogen production system |
| CN119361000A (en) * | 2024-12-24 | 2025-01-24 | 吉林省隆氢科技有限公司 | A method, system, equipment and medium for controlling a hydrogen production device |
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