Alkaline electrolytic cell global sensitivity analysis method and system based on dynamic model

Abstract

The invention discloses an alkaline electrolytic cell global sensitivity analysis method and system based on a dynamic model, and belongs to the field of power system operation regulation and control. The global sensitivity analysis method comprises the following steps: randomly sampling the control variables in a preset distribution interval of alkali liquor flow, cooling liquid flow, system pressure, input power, initial temperature and hydrogen concentration in initial oxygen; based on the dynamic simulation model of the alkaline electrolytic cell, performing dynamic simulation on the alkaline electrolytic cell according to a sampling result, and performing numerical integration calculation on the alkaline electrolytic cell through a fixed time step to obtain simulation time sequence data of temperature, efficiency and hydrogen concentration in oxygen under each group of samples; respectively constructing a time sequence polynomial fitting model between each control variable and the temperature, efficiency and hydrogen concentration in oxygen of the electrolytic cell by utilizing simulation time sequence data; and based on the time sequence polynomial fitting model, a global sensitivity analysis method is adopted to quantify the influence degree of each control variable on the temperature and efficiency of the electrolytic cell and the concentration of hydrogen in oxygen.

Description

TECHNICAL FIELD

[0001] The application belongs to the field of power system operation and regulation, and particularly relates to a dynamic model-based global sensitivity analysis method and system for an alkaline electrolytic cell. BACKGROUND

[0002] Alkaline water electrolysis has become an important technical route for large-scale hydrogen production and renewable energy storage due to its mature process, low energy consumption, high equipment reliability, and other advantages. In actual operation, multiple parameters such as alkaline solution flow rate, cooling liquid flow rate, system pressure, input power, operating temperature, and hydrogen concentration in oxygen continuously change in the time domain, which jointly determine key performance indicators such as temperature field distribution, energy efficiency level, and gas quality of the electrolytic cell. How to systematically and quantitatively evaluate the influence of each operating parameter on the operating state of the electrolytic cell under dynamic conditions is a prerequisite for precise control and energy saving.

[0003] However, the existing method has the following difficulties when applied to dynamic simulation of the alkaline electrolytic cell: 1) it is difficult to depict the non-equilibrium and strongly coupled dynamic process of the electrolytic cell evolving over time under actual operating conditions; 2) it is unable to accurately capture the dominant role of different input parameters on state quantities such as temperature, efficiency, and hydrogen concentration in oxygen at different time scales in the short, medium, and long term; and 3) the control strategy optimization guidance value for the multi-stage operating process is limited.

[0004] Therefore, a dynamic model-based global sensitivity analysis method for an alkaline electrolytic cell is proposed. SUMMARY

[0005] In view of the deficiencies of the prior art, the purpose of the present application is to provide a dynamic model-based global sensitivity analysis method and system for an alkaline electrolytic cell, which solves the problems in the prior art.

[0006] The purpose of the present application can be achieved by the following technical solutions:

[0007] The dynamic model-based global sensitivity analysis method for an alkaline electrolytic cell comprises the following steps:

[0008] Within the preset distribution intervals of the alkaline solution flow rate, cooling liquid flow rate, system pressure, input power, initial temperature, and initial hydrogen concentration in oxygen, random sampling is performed on the above control variables;

[0009] Based on the dynamic simulation model of the alkaline electrolytic cell, dynamic simulation of the alkaline electrolytic cell is performed according to the sampling results, numerical integral calculation of the alkaline electrolytic cell is performed through a fixed time step, and simulation time series data of the temperature, efficiency, and hydrogen concentration in oxygen under each sample are obtained;

[0010] Using the simulation time series data, time series polynomial fitting models between each control variable and the temperature, efficiency, and hydrogen concentration in oxygen of the electrolytic cell are constructed;

[0011] Based on the timing polynomial fitting model, a global sensitivity analysis method is used to quantify the influence degree of each control variable on the temperature, efficiency and hydrogen concentration in oxygen of the electrolytic cell.

[0012] Further, the random sampling is Latin hypercube sampling.

[0013] Further, the dynamic simulation model of the alkaline electrolytic cell comprises an electrochemical model, a thermal dynamic model and an oxygen hydrogen dynamic model.

[0014] The electrochemical model is:

[0015] U = U rev + U act + U Ω

[0016]

[0017] In the formula, U rev , U act , U Ω are the inverse voltage, the activation voltage and the ohmic voltage respectively; U rev0 is the inverse voltage fixed value, U is the electrolysis voltage, R0 is the gas constant, T is the temperature, F is the Faraday constant, P is the gas pressure, P0 is the standard atmospheric pressure, s, t1, t2, t3, r1 and r2 are all empirical fitting parameters, A is the electrode plate area, and I is the current.

[0018] The thermal dynamic model is:

[0019]

[0020] Q loss = (T-T amb ) / R

[0021] Q lye = c lye ρ lye v lye (T t -T ch,t-τ )

[0022]

[0023] In the formula, C cell , C ch and C cool are the heat capacities of the electrolytic cell, the heat exchanger and the cooling liquid respectively; Q ele , Q loss , Q lye are the heat generated by electrolysis, the natural heat dissipation and the heat taken away by the alkali respectively; p ele is the total power of electrolysis, H is the hydrogen production rate, H is the hydrogen heat value, T amb T is the ambient temperature, R is the thermal resistance, c lye , p lye , v lye are the specific heat capacity, density and flow rate of the caustic solution respectively; c cool , p cool , v cool are the specific heat capacity, density and flow rate of the cooling liquid respectively; T ch is the heat exchanger temperature, ΔT is the logarithmic mean temperature difference of the heat exchanger, kA is the heat transfer coefficient of the heat exchanger; T cool is the cooling liquid temperature, T t is the temperature of the electrolyzer at time t, T ch,t-τ is the temperature of the exchanger at time t-τ, T cell,t is the temperature of the electrolyzer at time t, T ch,t is the temperature of the exchanger at time t, T cool,in,t is the temperature of the cooling liquid flowing in at time t, T cool,t is the temperature of the cooling liquid at time t;

[0024] The hydrogen dynamic model in the oxygen is:

[0025]

[0026] τ an = 2V an / v lye

[0027]

[0028] In the formula, n in represents the hydrogen flow rate at the anode; represents the hydrogen flow rate entering through gas diffusion; represents the hydrogen flow rate entering through pressure difference; represents the hydrogen flow rate entering through caustic solution mixing; ξ diff is the diffusion coefficient; ξ conv is the convection coefficient; S in is the solubility of hydrogen in the caustic solution; γ lye is the time constant related to the caustic solution; P ele is the electrolyzer pressure; P0 is the reference pressure; a1 is the quadratic fitting parameter between solubility and temperature; a2 is the linear fitting parameter between solubility and temperature; a3 is the constant fitting parameter between solubility and temperature; T is the temperature; HTO(s) is the hydrogen transfer function; is the oxygen generation flow rate; τ an is the anode time constant; τ sep is the gas-liquid separation time constant; τ out is the hydrogen discharge time constant; Van is the anode volume; v lye is the caustic fluid parameter; P is pressure; V sep,g is the separator gas volume; R g is the gas constant; s is the Laplace transform variable.

[0029] Further, the form of the time series polynomial fitting model is:

[0030]

[0031] wherein X = [X1, X2, …, X6] respectively correspond to caustic flow rate, coolant flow rate, system pressure, input power, initial temperature and initial oxygen hydrogen concentration; represents X i a i th Legendre polynomial, c α is a coefficient to be solved; Y is an output parameter of the system, g(·) is a polynomial function, Ψ α (X) is a polynomial composed of each input variable at the αth degree, α is a degree vector of the input variable, Θ is a set composed of the degree vector of the input variable; is a tensor product of the polynomial.

[0032] Further, the coefficient c α to be solved satisfies:

[0033]

[0034] wherein, represents the simulation result under X l , N ED represents the number of simulation samples, λ is a sparsity index, and Θ n,P are both sets of polynomial coefficients; ‖α‖ q is the q-norm of α, is the ith element in the α vector raised to the qth power, n is the number of input variables, is a sparsity coefficient threshold, Ψ(X l ) is a polynomial under the lth set of experimental input data, c T is the transpose of the c α composing vector.

[0035] Further, the process of the global sensitivity analysis method comprises: based on the Sobol sensitivity index, decomposing the time series polynomial fitting model, and calculating the first order sensitivity and global sensitivity of each control variable:

[0036]

[0037] wherein, 0n denotes all-zero vector, S i denotes the first-order sensitivity of the i-th state variable, denotes the global sensitivity of the i-th state variable; A i denotes the set of composed of α whose i-th element is not 0 and j-th element is 0, α i denotes the i-th element in the α vector, α j denotes the j-th element in the α vector, B i denotes the set of composed of α whose i-th element is not 0.

[0038] The global sensitivity analysis system of the alkaline electrolytic cell based on a dynamic model comprises:

[0039] The sampling module randomly samples the control variables within the preset distribution intervals of the lye flow, the cooling liquid flow, the system pressure, the input power, the initial temperature and the initial oxygen-hydrogen concentration;

[0040] The dynamic simulation module performs dynamic simulation on the alkaline electrolytic cell based on a dynamic simulation model of the alkaline electrolytic cell according to the sampling results, performs numerical integral calculation on the alkaline electrolytic cell through a fixed time step, and obtains simulation time series data of the temperature, the efficiency and the oxygen-hydrogen concentration under each group of samples;

[0041] The fitting model construction module constructs time series polynomial fitting models between each control variable and the temperature, the efficiency and the oxygen-hydrogen concentration of the electrolytic cell by using the simulation time series data;

[0042] The analysis module quantifies the influence degree of each control variable on the temperature, the efficiency and the oxygen-hydrogen concentration of the electrolytic cell by using a global sensitivity analysis method based on the time series polynomial fitting models.

[0043] A computer storage medium stores a readable program, and when the program runs, the program can instruct a computing device to execute the global sensitivity analysis method of the alkaline electrolytic cell based on a dynamic model as described above.

[0044] An electronic device comprises a processor, a memory, a communication interface and a communication bus, and the processor, the memory and the communication interface complete communication with each other through the communication bus;

[0045] The memory is used to store at least one executable instruction, and the executable instruction makes the processor execute the operation corresponding to the global sensitivity analysis method of the alkaline electrolytic cell based on a dynamic model as described above.

[0046] A computer program product comprises computer instructions, and the computer instructions instruct a computing device to execute the operation corresponding to the global sensitivity analysis method of the alkaline electrolytic cell based on a dynamic model as described above.

[0047] Advantages of the present application:

[0048] 1、The present application comprehensively considers the alkali flow, the cooling liquid flow, the system pressure, the input power and other key control variables, can system reveal the dominant influence of each variable on the electrolytic cell running state (temperature, efficiency and oxygen hydrogen concentration) in different short time (0-1 minute), medium time (1-5 minutes) and long time (5-30 minutes) time scale. This achievement not only helps to understand the dynamics characteristics of electrolytic cell, but also is an important basis for more accurate regulation.

[0049] 2、The present application overcomes the limitations of static analysis method by establishing a dynamic model based on electrochemistry-thermodynamics-mass transfer coupling, can consider the evolution process of the system with time comprehensively, so as to simulate the reaction behavior of the electrolytic cell under the condition of renewable energy fluctuation. The introduction of dynamic model makes the prediction of system behavior more accurate, can capture the dynamic characteristics of electrolytic cell in different time periods, provides scientific basis for the operation optimization of electrolytic cell, ensures that the system can quickly adjust and keep stable operation when facing instantaneous fluctuation. This emphasis on time evolution ability, lays a solid foundation for efficient and flexible energy management and control.

[0050] 3、The sensitivity analysis results of the alkaline electrolytic cell will help to identify the most influential operating variables, through the timely adjustment of the dominant variables, can significantly improve the operation efficiency and hydrogen production of the electrolytic cell, at the same time, reduce the system instability caused by power fluctuation. In practical application, this will help to realize the rapid response of electrolytic cell operation, ensure that the stable hydrogen production capacity can be maintained when facing power grid fluctuation.

[0051] 4、The sensitivity analysis of the present application combined with dynamic model, provides specific guidance suggestions for multi-stage optimization of electrolytic cell, can flexibly adjust the parameters according to the real-time operation conditions. This optimization control strategy helps to improve the consumption capacity of renewable energy, reduces the economic loss caused by supply fluctuation, improves the overall operation stability and security of power grid. BRIEF DESCRIPTION OF DRAWINGS

[0052] In order to more clearly illustrate the technical solutions of the embodiments of the present application or the prior art, the following will briefly introduce the drawings needed to be used in the embodiment or prior art description of the present application. Obviously, for those skilled in the art, other drawings can also be obtained without creative labor on the basis of these drawings.

[0053] Figure 1 It is the sensitivity analysis method flowchart of the present application;

[0054] Figure 2 It is the schematic diagram of alkaline electrolytic cell;

[0055] Figure 3 is a schematic diagram of the first-order and total sensitivity of each input parameter to temperature in Example 2;

[0056] Figure 4 is a schematic diagram of the first-order and total sensitivity of each input parameter to the hydrogen concentration in oxygen in Example 2. DETAILED DESCRIPTION

[0057] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments of the present application. Based on the embodiments in the present application, all other embodiments obtained by a person of ordinary skill in the art without creative work fall within the protection scope of the present application.

[0058] Example 1

[0059] As shown in the following table, the global sensitivity analysis method of the alkaline electrolyzer based on the dynamic model includes the following steps: Figure 1

[0060] S1, randomly sampling the control variables within the preset distribution intervals of the lye flow rate, the cooling liquid flow rate, the system pressure, the input power, the initial temperature and the initial hydrogen concentration in oxygen;

[0061] In this embodiment, the random sampling of the control variables is Latin hypercube sampling. Figure 2 A schematic diagram of the AWE system is shown, which includes five main components: electrolyzer stack, gas-liquid separator, heat exchanger, water tank and compressor. The electrolyzer stack is the core component where the electrolysis reaction occurs, the separator is used to separate the generated gas from the lye, the heat exchanger is used to reheat the lye to maintain the reaction temperature, the water tank is used to ensure a stable water level in the electrolyzer stack, and the compressor is used to adjust the system pressure.

[0062] S2, based on the dynamic simulation model of the alkaline electrolyzer, performing dynamic simulation of the alkaline electrolyzer according to the sampling results of S1, performing numerical integral calculation of the alkaline electrolyzer through fixed time steps to obtain simulation time series data of the temperature, efficiency and hydrogen concentration in oxygen under each sample;

[0063] The dynamic simulation model of the alkaline electrolyzer includes an electrochemical model, a thermal dynamic model and a hydrogen-in-oxygen dynamic model.

[0064] The electrochemical model is:

[0065] U = U rev + U act + U Ω

[0066] ​

[0067] wherein U rev , U act , and U Ω are the reverse voltage, the activation voltage and the ohmic voltage, respectively; U rev0 is the reverse voltage fixed value, U is the electrolysis voltage, R0 is the gas constant, T is the temperature, F is the Faraday constant, P is the gas pressure, P0 is the standard atmospheric pressure, s, t1, t2, t3, r1 and r2 are all empirical fitting parameters, A is the electrode plate area, and I is the current;

[0068] The thermal dynamic model is:

[0069]

[0070] Q loss = (T - T amb ) / R

[0071] Q lye = c lye ρ lye v lye (T t - T ch,t-τ )

[0072]

[0073] wherein C cell , C ch and C cool are the heat capacity of the electrolytic cell, the heat exchanger and the cooling liquid, respectively; Q ele , Q loss and Q lye are the heat generated by electrolysis, the natural heat dissipation and the heat taken away by the alkali solution, respectively; P ele is the total power of electrolysis, is the hydrogen production rate, H is the hydrogen heat value, T amb is the external temperature, R is the thermal resistance, c lye , ρ lye , v lye are the specific heat capacity, the density and the flow rate of the alkali solution, respectively; c cool , ρ cool , v cool are the specific heat capacity, the density and the flow rate of the cooling liquid, respectively; T ch is the temperature of the heat exchanger, ΔT is the logarithmic mean temperature difference of the heat exchanger, and kA is the heat exchange coefficient of the heat exchanger; T cool is the temperature of the cooling liquid, T t is the temperature of the electrolytic cell at time t, T ch,t-τ is the temperature of the heat exchanger at time t-τ, T cell,t is the temperature of the electrolytic cell at time t, and T ch,tT is the temperature of the exchanger at time t cool,in,t T is the temperature of the incoming coolant at time t cool,t T is the temperature of the coolant at time t

[0074] The hydrogen dynamic model is:

[0075]

[0076] τ an = 2V an / v lye

[0077]

[0078] where n in represents the hydrogen flow at the anode; represents the hydrogen flow entering through gas diffusion; represents the hydrogen flow entering through pressure differential; represents the hydrogen flow entering through lye mixing; ξ diff is the diffusion coefficient; ξ conv is the convection coefficient; S in is the solubility of hydrogen in lye; γ lye is the lye related time constant; P ele is the cell pressure; P0 is the reference pressure; a1 is a quadratic fit parameter between solubility and temperature; a2 is a linear fit parameter between solubility and temperature; a3 is a constant fit parameter between solubility and temperature; T is the temperature; HTO(s) is the hydrogen transfer function; is the oxygen generation flow; τ an is the anode time constant; τ sep is the gas-liquid separation time constant; τ out is the hydrogen exhaust time constant; V an is the anode volume; v lye is the lye fluid parameter; P is the pressure; V sep,g is the separator gas volume; R g is the gas constant; s is the Laplace transform variable.

[0079] Numerical integration calculations were performed on the alkaline electrolyzer using a fixed time step to obtain simulated time-series data on temperature, efficiency, and hydrogen concentration in oxygen for each sample group. Specifically, numerical integration calculations involve converting a system of differential equations in the continuous time domain into a system of difference equations using discretization methods (such as Euler schemes or trapezoidal schemes), and then progressively solving for the numerical solutions of the system state variables within a preset fixed time interval. The fixed time step refers to the fact that during the simulation calculation, the time domain is uniformly divided into several equal time intervals (0.2 seconds in this embodiment), and the length of each time interval remains constant.

[0080] Simulation time-series data refers to time-series data reflecting the dynamic response characteristics of a system, obtained through numerical integration. This data contains the values ​​of various state variables of the system at different times, and can completely describe the dynamic behavior of the system. Through the above calculation process, complete time-series variation data of hydrogen concentration and temperature in the oxygen of the alkaline electrolyzer under different operating conditions are finally obtained, providing data support for subsequent system analysis, control strategy design, and operation optimization.

[0081] S3. Using the simulation time series data obtained in S2, construct time series polynomial fitting models between each control variable and the electrolyzer temperature, efficiency and hydrogen concentration in oxygen, respectively.

[0082] The time-series polynomial fitting model employs Adaptive Sparse Polynomial Chaotic Expansion (Adaptive SparsePCE), with Legendre polynomials as the basis functions. The form of the time-series polynomial fitting model is as follows:

[0083]

[0084] Where X = [X1,,X2,,…,,X6], corresponding to alkaline solution flow rate, coolant flow rate, system pressure, input power, initial temperature, and initial hydrogen concentration in oxygen, respectively; X represents i a i Legendre polynomial, c α Ψ represents the coefficients to be determined; Y represents the output parameters of the system; g(·) is a polynomial function; Ψ α (X) is a polynomial composed of each input variable at degree α, where α is the degree vector of the input variables and Θ is the set of degree vectors of the input variables; It is the tensor product of a polynomial.

[0085] To ensure the sparsity of the time-series polynomial fitting model, the coefficients c to be determined... α satisfy:

[0086]

[0087] In the formula, represent the simulation results under X l ED N represents the simulation sampling number, and λ is a sparsity index, Θ n,P are sets of polynomial coefficients; ‖α‖ q is the q-norm of α, is the ith element in the α vector, and n is the number of input variables, is a sparsity coefficient threshold, Ψ(X l ) is a polynomial under the lth set of experimental input data, c T is the transpose of the c α composing vector.

[0088] S4, based on the time series polynomial fitting model, a global sensitivity analysis method is used to quantify the influence degree of each control variable on the electrolytic cell state variable (temperature, efficiency and hydrogen concentration in oxygen);

[0089] The specific process of the global sensitivity analysis method is as follows:

[0090] Based on Sobol sensitivity index, the time series polynomial fitting model is decomposed, and the first-order sensitivity and global sensitivity of each control variable are calculated. The calculation formula is as follows:

[0091]

[0092] In the formula, 0 n represents a zero vector, S i represents the first-order sensitivity of the ith state variable, represents the global sensitivity of the ith state variable; A i is a set composed of α whose ith element is not 0 and whose jth element is 0, α i is the ith element in the α vector, α j is the jth element in the α vector, and B i is a set composed of α whose ith element is not 0.

[0093] Then, according to the change law of the sensitivity of each variable with time, the dominant influence variable under each time scale is identified, and the recommended parameters for control strategy optimization are output.

[0094] Based on the similar inventive concept, the embodiment of the present application also provides a computer storage medium storing a readable program, which can execute the above-mentioned global sensitivity analysis method of the alkaline electrolytic cell based on a dynamic model when the program is run by a processor.

[0095] ​Based on similar inventive concepts, the embodiment of the present application provides an electronic device, comprising a processor, a memory, a communication interface and a communication bus, the processor, the memory and the communication interface complete communication with each other through the communication bus;

[0096] The memory is used to store at least one executable instruction, and the executable instruction makes the processor execute the operation corresponding to the above-mentioned dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell.

[0097] Based on similar inventive concepts, the embodiment of the present application also provides a computer program product comprising computer instructions instructing a computing device to execute the operation corresponding to the above-mentioned dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell.

[0098] Embodiment 2

[0099] This embodiment analyzes and optimizes a certain alkaline water electrolytic cell system by applying the dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell, and the specific steps are as follows:

[0100] Step 1: Random sampling - under the experimental conditions of gas-liquid flow, the following distribution intervals of control variables are set:

[0101] Alkaline solution flow (Q lye ): 5-20L / h

[0102] Cooling liquid flow (Q cool ): 0-70L / h

[0103] System pressure (P): 1-2MPa

[0104] Input power (p): 0.5-6MW

[0105] Initial temperature (T0): 70-90℃

[0106] Initial hydrogen concentration in oxygen (HTO0): 0-0.018

[0107] The Latin hypercube sampling method is used to randomly select 1000 groups of samples from the above distribution intervals.

[0108] Step 2: Dynamic simulation - based on the following electrochemical, thermodynamic and mass transfer models, the selected samples are dynamically simulated:

[0109] Electrochemical model:

[0110] U=U rev +U act +U Ω

[0111]

[0112] Thermal model:

[0113]

[0114] Q loss = (T - T amb ) / R

[0115] Q lye = c lye p lye v lye (T t - T ch,t-τ )

[0116]

[0117] Hydrogen-in-oxygen model:

[0118]

[0119] τ an = 2V an / v lye

[0120]

[0121] Wherein, the parameters of the electrolytic cell are shown in Table 1 as follows:

[0122] Table 1 Electrolytic cell parameter table

[0123] Parameter Value Parameter Value Parameter Value A 0.3325 [ t3 ] 247.3 f1 25000 s 0.12 [r1] 8.05*1e-5 f2 0.9564 ​ 1.002 [r2] -0.00000025 d e ]]> 500*1e-6 [t2] 8.424 <![CDATA[N ele ]]> 300 K 50.2 m 0.1 γ 1.4 P sto ]]> 3000000 κ 108 com ]]> ​ 0.8 [P0] 101325 J 99750 [CAT amb ]]> 10 [C awe ]]> 55*1e06 U rev,0 ]]> 1.219 [R sta ]]> 0.001 [C ch ]]> 0.5*1e06 [C c ]]> 0.1*1e06 kA 11000 V an ]]> 0.005 [CAT c,in ]]> 10 V sep,g ]]> 1 sep ]]> ​ 5

[0124] The temperature, efficiency and oxygen hydrogen concentration time series response data under each group of samples are obtained by numerical integration calculation of the system with fixed time step (0.2 seconds).

[0125] Step 3: adaptive sparse chaotic expansion polynomial fitting - time series data processing is performed on the simulation results to construct a polynomial model between the response variables (temperature, efficiency, oxygen hydrogen concentration) and the control variables. Adopting Legendre polynomial as the base function, the adaptive sparse algorithm is used for parameter optimization, and finally the fitting model in the following form is established:

[0126]

[0127] Step 4: Sobol global sensitivity analysis - based on the above PCE proxy model, the first order and total effect Sobol sensitivity index of each control variable and state variable at each time point is calculated. The specific formula is as follows:

[0128] The first order and total sensitivity index of power to temperature at t time:

[0129]

[0130] The results of sensitivity analysis of each parameter to temperature and HTO are shown in FIGS. 5 and 6, respectively. Figure 3 and Figure 4 The results show that, in 0-14 minutes, the first-order sensitivity of initial temperature to temperature is the highest, in 14-60 minutes, the first-order sensitivity of power to temperature is the highest, in 14-25 minutes, the first-order sensitivity of initial temperature is higher than that of cooling flow, and then the first-order sensitivity of cooling flow is the second highest. On average, the first-order sensitivity and total sensitivity of power to temperature are 0.54 and 0.56, respectively, the first-order sensitivity and total sensitivity of initial temperature to temperature are 0.25 and 0.27, respectively, and the first-order sensitivity and total sensitivity of cooling flow to temperature are 0.14 and 0.19, respectively. In order to improve the operation efficiency of the electrolytic cell, it is recommended to monitor the input power in real time and adjust the cooling flow and system pressure in a timely manner. As for the hydrogen concentration in oxygen, in 0-4 minutes, the first-order sensitivity of initial hydrogen concentration in oxygen is the highest, and then the power is the first-order sensitivity of the highest variable. The first-order sensitivity of pressure exceeds that of initial hydrogen concentration in oxygen at the sixth minute, and then it is always the second highest variable. On average, the first-order sensitivity and total sensitivity of power are 0.59 and 0.69, respectively, the first-order sensitivity and total sensitivity of pressure are 0.22 and 0.31, respectively, and the first-order sensitivity and total sensitivity of initial hydrogen concentration in oxygen are 0.06 and 0.08, respectively. In order to improve the operation efficiency of the electrolytic cell, it is recommended to monitor the input power in real time and adjust the cooling flow and system pressure in a timely manner.

[0131] Example 3

[0132] In this embodiment, a dynamic model-based global sensitivity analysis system for an alkaline electrolytic cell is proposed, which specifically comprises:

[0133] The sampling module: randomly samples the above control variables within the preset distribution intervals of the alkali flow, the cooling flow, the system pressure, the input power, the initial temperature and the initial hydrogen concentration in oxygen;

[0134] The dynamic simulation module: based on the dynamic simulation model of the alkaline electrolytic cell, the dynamic simulation of the alkaline electrolytic cell is carried out according to the sampling results, and the numerical integral calculation of the alkaline electrolytic cell is carried out through fixed time steps to obtain the simulation time series data of temperature, efficiency and hydrogen concentration in oxygen under each group of samples;

[0135] The fitting model construction module: using the simulation time series data, time series polynomial fitting models between each control variable and the temperature, efficiency and hydrogen concentration in oxygen of the electrolytic cell are constructed, respectively;

[0136] The analysis module: based on the time series polynomial fitting model, the global sensitivity analysis method is used to quantify the influence degree of each control variable on the temperature, efficiency and hydrogen concentration in oxygen of the electrolytic cell.

[0137] The methods of the present application can be implemented in hardware, firmware, or software, or any combination thereof, and can be stored in or implemented with the aid of software or computer code stored in a recording medium as a computer program product without departing from the scope of the present application. The computer program product includes a computer readable medium, such as but not limited to the non-transitory machine-readable medium of the present application, having stored therein the computer program code, firmware, or software. The computer readable medium can be a machine readable non-transitory storage medium including any mechanism for storing information in a form readable by a machine, such as for example magnetic storage medium (e.g., floppy disksettes, magnetic rigid disks; magnetic tape); optical storage medium (e.g., optical disks such as CD-ROM, DVD-ROM, etc.); electrical storage media (e.g., solid state storage such as flash memory, RAM, ROM, etc.); hydraulic storage media (e.g., water based memories); sheet media (e.g., paper, cellulose based films); and the like. The computer readable medium can also be transitory media, such as transitory signals or waves.

[0138] The foregoing is considered as illustrative only of the principles of the application. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the application to the exact construction and practice described. Accordingly, all such variations and modifications are intended to be included within the scope of the present application as defined in the following claims.

Claims

1. A method for global sensitivity analysis of an alkaline electrolyzer based on a dynamic model, characterized in that, The method comprises the following steps: randomly sampling the control variables within preset distribution intervals of the lye flow rate, the cooling liquid flow rate, the system pressure, the input power, the initial temperature, and the initial oxygen-hydrogen concentration; based on a dynamic simulation model of the alkaline electrolytic cell, performing dynamic simulation on the alkaline electrolytic cell according to the sampling results, performing numerical integral calculation on the alkaline electrolytic cell through fixed time steps, and obtaining simulation time series data of the temperature, the efficiency, and the oxygen-hydrogen concentration under each sample; using the simulation time series data, respectively constructing time series polynomial fitting models between each control variable and the temperature, the efficiency, and the oxygen-hydrogen concentration of the electrolytic cell; based on the time series polynomial fitting models, quantifying the influence degree of each control variable on the temperature, the efficiency, and the oxygen-hydrogen concentration of the electrolytic cell by using a global sensitivity analysis method.

2. The dynamic model-based global sensitivity analysis method of an alkaline electrolyzer according to claim 1, characterized in that, The random sampling is Latin hypercube sampling.

3. The dynamic model-based global sensitivity analysis method of an alkaline electrolyzer according to claim 1, wherein, The dynamic simulation model of the alkaline electrolytic cell comprises an electrochemical model, a thermal dynamic model, and an oxygen-hydrogen dynamic model. The electrochemical model is: U = U rev + U act + U Ω wherein U rev , U act , and U Ω are the inverse, activation, and ohmic voltages, respectively; U rev0 is the inverse voltage fixed value, U is the electrolysis voltage, R0 is the gas constant, T is the temperature, F is the Faraday constant, P is the gas pressure, P0 is the standard atmospheric pressure, s, t1, t2, t3, r1, and r2 are all empirical fitting parameters, A is the electrode area, and I is the current; The thermal dynamic model is: Q loss = (T - T amb ) / R Q lye = c lye p lye v lye (T t -T ch,t-τ ) In the formula, C cell C ch and C cool These are the heat capacities of the electrolysis chamber, heat exchanger, and coolant, respectively; Q ele Q loss Q lye These are the heat generated by electrolysis, the heat dissipated naturally, and the heat carried away by the alkali solution, respectively; p ele The total power of electrolysis, T represents the hydrogen production rate, H represents the calorific value of hydrogen, and T represents the hydrogen production rate. amb Where R is the ambient temperature, C is the thermal resistance, and R is the thermal resistance. lye ρ lye v lye These are the specific heat capacity, density, and flow rate of the alkaline solution, respectively; c cool ρ cool v cool These are the specific heat capacity, density, and flow rate of the coolant, respectively; T ch Here, T represents the heat exchanger temperature, ΔT represents the logarithmic mean temperature difference of the heat exchanger, and kA represents the heat transfer coefficient of the heat exchanger. cool T represents the coolant temperature. t Let T be the temperature of the electrolytic cell at time t. ch,t-τ Let T be the temperature of the exchanger at time t-τ. cell,t Let T be the temperature of the electrolytic cell at time t. ch,t Let T be the temperature of the exchanger at time t. cool,in,t Let T be the temperature of the coolant flowing in at time t. cool,t Let t be the temperature of the coolant at time t; The oxygen-hydrogen dynamic model is: where n in represents the hydrogen flow rate at the anode; represents the hydrogen flow rate entering through gas diffusion; represents the hydrogen flow rate entering through pressure differential; represents the hydrogen flow rate entering through lye mixing; ξ diff is the diffusion coefficient; ξ conv is the convection coefficient; S in is the solubility of hydrogen in lye; γ lye is the lye related time constant; P ele is the cell pressure; P0 is the reference pressure; a1 is a quadratic fit parameter between solubility and temperature; a2 is a linear fit parameter between solubility and temperature; a3 is a constant fit parameter between solubility and temperature; T is the temperature; HTO(s) is the hydrogen transfer function; is the oxygen generation flow rate; τ an is the anode time constant; τ sep is the gas-liquid separation time constant; τ out is the hydrogen exhaust time constant; V an is the anode volume; v lye is the lye fluid parameter; P is the pressure; V sep,g is the separator gas phase volume; R g is the gas constant; s is the Laplace transform variable.

4. The dynamic model-based global sensitivity analysis method of an alkaline electrolyzer according to claim 1, wherein, The time series polynomial fitting model has the following form: Wherein, X = [X1, X2, …, X6] respectively correspond to the lye flow, the cooling liquid flow, the system pressure, the input power, the initial temperature and the initial oxygen hydrogen concentration; represents X i a i the Legendre polynomial of the second kind, c α is the coefficient to be solved; Y is the output parameter of the system, g(·) is a polynomial function, Ψ α (X) is a polynomial composed of each input variable under the degree of α, α is the degree vector of the input variable, Θ is a set composed of the degree vector of the input variable; is the tensor product of the polynomial.

5. The dynamic model-based global sensitivity analysis method of an alkaline electrolyzer according to claim 4, wherein, The coefficient c to be solved α satisfies: In the formula, The simulation results under X l ED N represents the number of simulation samples, and λ is a sparsity index, Θ n,P Both are sets of polynomial coefficients; ‖α‖ q is the q-norm of α, is the ith element in the α vector to the qth power, and n is the number of input variables, is a sparsity coefficient threshold, Ψ(X l ) is a polynomial under the lth set of experimental input data, c T is the transpose of the c α composition vector.​ 6. The dynamic model-based global sensitivity analysis method of an alkaline electrolyzer according to claim 1, wherein, The process of the global sensitivity analysis method comprises the following steps: based on Sobol sensitivity index, decomposing the time series polynomial fitting model, and calculating the first-order sensitivity and the global sensitivity of each control variable: where 0 n denotes an all-zero vector, S i denotes the first order sensitivity of the i-th state variable, denotes the global sensitivity of the i-th state variable; A i is the set of α whose i-th element is not zero and j-th element is zero, α i is the i-th element in the α vector, α j is the j-th element in the α vector, B i is the set of α whose i-th element is not zero.

7. A system for global sensitivity analysis of an alkaline electrolyzer based on a dynamic model, characterized in that, The method comprises the following steps: a sampling module: randomly sampling the control variables within preset distribution intervals of the lye flow rate, the cooling liquid flow rate, the system pressure, the input power, the initial temperature, and the initial oxygen-hydrogen concentration; a dynamic simulation module: based on a dynamic simulation model of the alkaline electrolytic cell, performing dynamic simulation on the alkaline electrolytic cell according to the sampling results, performing numerical integral calculation on the alkaline electrolytic cell through fixed time steps, and obtaining simulation time series data of the temperature, the efficiency, and the oxygen-hydrogen concentration under each sample; a fitting model construction module: using the simulation time series data, respectively constructing time series polynomial fitting models between each control variable and the temperature, the efficiency, and the oxygen-hydrogen concentration of the electrolytic cell; an analysis module: based on the time series polynomial fitting models, quantifying the influence degree of each control variable on the temperature, the efficiency, and the oxygen-hydrogen concentration of the electrolytic cell by using a global sensitivity analysis method.

8. A computer storage medium storing a readable program, characterized in that, When the program is running, the program can instruct a computing device to perform the dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell according to any one of claims 1-6.

9. An electronic device, comprising: The method comprises the following steps: a processor, a memory, a communication interface, and a communication bus, the processor, the memory, and the communication interface complete communication with each other through the communication bus; the memory is used to store at least one executable instruction, and the executable instruction makes the processor perform the operation corresponding to the dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell according to any one of claims 1-6.

10. A computer program product comprising computer instructions, characterized in that, The computer instructions instruct a computing device to perform the operation corresponding to the dynamic model-based global sensitivity analysis method of the alkaline electrolytic cell according to any one of claims 1-6.

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