A multi-level sequential optimization design method for solid oxide electrolysis systems

Abstract

This invention relates to the field of hydrogen energy technology and discloses a multi-level sequential optimization design method for solid oxide electrolysis systems. The method includes: S1, multi-objective optimization of system-level design parameters; S2, accurate simulation of the entire system process; S3, comprehensive optimization of the heat exchanger network, constructing a comprehensive optimization model for the heat exchanger network; and S4, heat exchanger layer design optimization, including optimization of heat exchanger geometry and heat exchanger channel arrangement. The full-process simulation results and heat exchanger network optimization results are fed back to the system-level multi-objective optimization model to iteratively optimize candidate design parameters. The heat exchanger network optimization results are used as input for heat exchanger layer optimization, achieving cross-level coupling and collaborative optimization between the system layer, heat exchanger network layer, and heat exchanger layer. This method realizes multi-level sequential optimization design of solid oxide electrolysis systems from system operating parameters and heat exchanger network to heat exchanger equipment, effectively improving system energy utilization efficiency and reducing overall operating costs.

Description

Technical Field

[0001] This invention relates to the field of hydrogen energy technology, and in particular to a multi-level sequential optimization design method for a solid oxide electrolysis system. Background Technology

[0002] The performance of solid oxide electrolysis (SOE) systems is influenced by multiple factors, including design parameters, thermal integration methods, and heat exchanger structures. For example, changes in system design parameters such as current, stack operating temperature, and fuel utilization rate are affected by the operating status of auxiliary components, which in turn affects the operating status of the stack core, thus impacting the overall system performance. Optimizing design parameters helps identify optimal operating conditions and optimize the system for efficient and economical hydrogen production. Secondly, SOE systems operate at high temperatures, and the SOE system recovers and utilizes the heat from the high-temperature gases produced. A reasonable thermal integration method is crucial for the safe, stable, and efficient operation of the system. Finally, the cascade utilization of heat in the energy system largely depends on the performance differences of equipment such as heat exchangers; heat exchanger design directly affects the system's heat transfer and flow performance. For SOE systems, design parameter optimization, thermal integration, and heat exchanger design are interconnected and interact to influence the overall system performance. However, existing technologies often optimize only one level, failing to consider the interactive relationships between different levels and lacking a comprehensive optimization method for SOE systems that considers the combined effects of multiple factors.

[0003] Existing research, such as Bui T, Kim YS, Giap VT, et al. Parametric study on highpower SOEC system[J]. Trans Korean Hydrogen New Energy Soc, 2021, 32(6): 470, and Kong Weiming, Li Ke. Simulation and optimization of solid oxide fuel cell system[J]. Energy and Energy Conservation, 2021,(06): 7-10+34, analyzes the influence of fuel utilization rate and recycling ratio on the efficiency of solid oxide fuel cell system. However, there is still a lack of optimization through multi-factor global search to find the optimal operating conditions of the system; at the same time, most existing studies on system thermal integration are limited to the analysis of the total heat load curve (GCC), which shows that the system's energy is insufficient, but no specific heat exchanger network scheme is given. In addition to the above-mentioned system optimization challenges, how to optimize the specific heat exchanger design of the obtained heat exchanger network structure of the system also requires the guidance of scientific optimization design methods.

[0004] A Chinese patent with publication number CN 118551544 A provides a heat exchange design method, system, device, and medium for reversible solid oxide batteries. This method allows the heat exchanger to be shared in both fuel cell and electrolysis cell modes, reducing the number of heat exchangers and achieving heat recovery. However, this method has the following drawbacks:

[0005] 1. Only considering the influence of a single level of factors, only optimizing the heat exchange network of the system, without searching for and optimizing the multi-dimensional operating parameters of the system;

[0006] 2. At the heat exchanger design level, only the heat transfer area and heat transfer load of the heat exchanger were calculated, and no specific optimization of the heat exchanger geometry design was carried out.

[0007] A Chinese patent with publication number CN 115938493 A provides an online optimization method for a high-temperature solid oxide electrolysis hydrogen production system. It establishes an online optimization model with hydrogen production efficiency as the objective to better guide the system operation. However, this method has the following drawbacks:

[0008] 1. Using fixed first and second heat exchangers to recover heat from the high-temperature gas at the fuel cell outlet, without performing optimal heat exchange network design under different sets of design parameters, and without achieving synchronous optimization of design parameters and heat exchange network;

[0009] 2. No specific geometric design was carried out for the heat exchangers involved in the system. Summary of the Invention

[0010] To overcome or alleviate one or more of the above technical problems, the present invention aims to provide a multi-level sequential optimization design method for solid oxide electrolysis systems. This method breaks through the traditional approach of considering only some influencing factors in design optimization, sorts out the correlation between multi-level and multi-dimensional influencing factors, and obtains a combined optimization design scheme of top-level SOEC design parameters, heat exchange network structure and bottom-level multi-stream heat exchanger structure parameters by comprehensively considering SOEC design parameters, heat exchange network structure and the interaction between heat exchangers.

[0011] This invention provides the following technical solution:

[0012] A multi-level sequential optimization design method for a solid oxide electrolysis system includes the following steps:

[0013] S1. Multi-objective optimization of system-level design parameters

[0014] In the optimized computing platform, a multi-objective optimization algorithm is used to construct a multi-objective optimization model at the system layer, with the goal of maximizing the system's hydrogen production efficiency and hydrogen production rate. By iteratively solving the multi-objective optimization model at the system layer, the Pareto solution set and optimal solution of the system design parameters are obtained. The system design parameters include at least one or more of the following: current density, stack inlet temperature, reactant utilization rate, recycle ratio, and anode / cathode feed ratio. The multi-objective optimization model at the system layer searches within a set feasible region of parameters to generate multiple sets of candidate design parameters.

[0015] S2, System Full-Process Precise Simulation

[0016] A quasi-two-dimensional model of the SOEC fuel cell stack and its steady-state model are constructed in the process simulation software. The candidate design parameters generated in step S1 are then transferred to the SOEC system steady-state model in the process simulation software. After performing simulation calculations, accurate simulation results of the entire system process are obtained, including two types of key data: first, system performance data, including the power consumption and hydrogen production of each major component, which are used to provide feedback for the optimization target of step S1; second, stream data, namely the complete thermodynamic state parameters of all process streams, including their inlet temperature, pressure, mass flow rate and specific heat capacity, which are used for the comprehensive optimization of the heat exchange network in the subsequent step S3.

[0017] S3, Comprehensive Optimization of Heat Exchanger Network

[0018] Based on the flow data provided in step S2, in the mathematical modeling and optimization platform, a comprehensive optimization model of the heat exchange network is constructed with the goal of minimizing the consumption of thermal utilities, based on the hierarchical superstructure method. The comprehensive optimization model of the heat exchange network is a mixed integer programming problem, and its decision variables include the matching relationship between the flow streams, the heat exchange distribution, and the utilities load. By solving the comprehensive optimization model of the heat exchange network, the optimal heat exchange network topology corresponding to the current system design parameters is obtained, including the required number of heat exchange units, the flow parameters matched to each unit, and their heat load.

[0019] S4, Heat exchanger layer design optimization

[0020] Optimization of heat exchanger geometry and channel arrangement includes:

[0021] S4.1 Multi-objective optimization of heat exchanger geometric parameters

[0022] Based on the flow data matched in the heat exchange network obtained in step S3, the heat exchanger is designed. The fin parameters of the main heat exchange zone and the structural parameters of the flow guiding zone are used as decision variables. A multi-objective optimization model of the heat exchanger is established with the conflicting objectives of maximizing the specific surface area of ​​the heat exchanger and minimizing the flow power consumption. Driven by the multi-objective optimization algorithm and coupled with simulation design software, the heat transfer and pressure drop calculations are automated. Finally, the Pareto solution set of the geometric structural parameters of the heat exchanger and the optimal design results are obtained.

[0023] S4.2 Optimization of heat exchanger channel arrangement

[0024] Using the arrangement order of multiple fluid channels as the decision variable, a channel arrangement optimization model is constructed with the objective of minimizing the root mean square error of the cumulative heat load of each channel along the heat transfer direction to achieve uniform heat load distribution and avoid temperature crossover. A genetic optimization algorithm based on permutation is used to search and determine the optimal channel arrangement.

[0025] Preferably, in step S2, the process simulation software is called to perform a full-process simulation of the system. The SOEC system steady-state model is a refined steady-state model that covers the solid oxide electrolytic reactor, gas compressor, circulating fan, water pump, heater and steam-water separator. By changing the input system design parameters, the key parameters of energy consumption, hydrogen production and flow thermodynamic data of each component in the system are simulated and calculated.

[0026] Preferably, the heat exchange network comprehensive optimization model in step S3 is a mixed integer optimization model, whose decision variables include flow matching relationship, heat exchange allocation and utility load, and satisfy flow heat balance constraint, temperature feasibility constraint and heat exchange driving force constraint.

[0027] Preferably, the optimization of heat exchanger structural parameters in step S4.1 includes the optimization of the main heat exchange zone and the flow guiding zone, wherein: the main heat exchange zone uses fin parameters as decision variables, the fin parameters include fin height, fin thickness and fin frequency; the flow guiding zone uses structural parameters as decision variables, the structural parameters include connecting pipe diameter and flow divider characteristic dimensions, and the constraint condition is heat exchanger size constraint, with the optimization objectives being to improve the compactness of the heat exchanger and reduce flow power consumption, and to perform multi-objective optimization design of the heat exchanger.

[0028] Preferably, after obtaining the Pareto solution set for multi-objective optimization of the heat exchanger in step S4.1, further optimization decisions are made on the Pareto solution set to determine the optimal design scheme of the heat exchanger, wherein the optimization decisions include any one or a combination of the following methods:

[0029] (1) The heat exchanger flow power consumption and volume specific surface area are dimensionless, and the candidate schemes are comprehensively evaluated based on the weight of each index. The optimal design result is selected according to the degree of closeness between each candidate scheme and the ideal solution.

[0030] (2) Convert the flow power consumption into the energy consumption cost during equipment operation, convert the specific surface area into the heat exchanger manufacturing cost, construct economic evaluation index, and select the design scheme with the lowest total cost as the optimal heat exchanger structural parameters.

[0031] Preferably, the accurate simulation results of the entire system process in step S2 and the comprehensive optimization results of the heat exchanger network in step S3 are fed back into the multi-objective optimization model of the system layer in step S1 to perform multi-objective optimization of the candidate design parameters; the comprehensive optimization results of the heat exchanger network in step S3 are used as the input conditions for the design optimization of the heat exchanger layer in step S4 to perform multi-objective optimization of the heat exchanger geometric parameters in step S4.1 and optimization of the heat exchanger channel arrangement in step S4.2, thereby achieving cross-level collaborative optimization.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] (1) This invention realizes a detailed design scheme for SOEC system from top-level design parameters and heat exchange network to bottom-level heat exchanger equipment structural parameters and channel arrangement through this multi-level sequential optimization method. It overcomes the shortcomings of previous optimization processes that only considered the influence of single-level factors and did not comprehensively consider the multi-level correlation of system design parameters, heat exchange network optimization, heat exchanger design, etc. The optimization results obtained have important practical value for guiding the design and operation of actual systems.

[0034] (2) By synchronously and collaboratively optimizing the top-level system design parameters and the heat exchange network, the strong coupling conflict between the two is resolved. This invention adopts a collaborative optimization strategy of "parameter optimization - heat exchange network synthesis" to ensure that the system design parameters of each Pareto optimal solution are perfectly matched with the current best heat exchange network, thereby obtaining a truly global optimal solution set, rather than a local or suboptimal solution.

[0035] (3) The multi-objective refined design of the bottom heat exchanger effectively translates the top-level optimization results into high-performance equipment. This invention not only completes the process design of the heat exchange network, but also goes deeper into the geometric structure of the heat exchanger. By optimizing the fin parameters and channel arrangement, the heat exchanger compactness is maximized and the flow resistance is minimized while meeting the heat exchange requirements, thereby ensuring and improving the overall system performance determined by the first part of the optimization. Attached Figure Description

[0036] Figure 1 This is a schematic diagram of the main process of the multi-level sequential optimization design method for a solid oxide electrolysis system provided in an embodiment of the present invention.

[0037] Figure 2This is a schematic diagram illustrating the specific process of the multi-level sequential optimization design method for a solid oxide electrolysis system provided in an embodiment of the present invention.

[0038] Figure 3 The Pareto front for multi-objective optimization of SOEC system design parameters provided in the embodiments of the present invention.

[0039] Figure 4 The optimal heat exchange network structure for the SOEC system provided in this embodiment of the invention.

[0040] Figure 5 The Pareto front for multi-objective optimization of heat exchangers provided in embodiments of the present invention.

[0041] Figure 6 The cumulative heat load distribution before and after the optimization of the heat exchanger channel arrangement provided in the embodiments of the present invention.

[0042] Figure 7 This is a schematic diagram of the optimal structural parameters and channel arrangement of the heat exchanger provided in an embodiment of the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to embodiments and accompanying drawings. However, it should be understood that the embodiments and drawings are for illustrative purposes only and do not constitute any limitation on the scope of protection of the present invention. All reasonable modifications and combinations included within the inventive spirit of the present invention fall within the scope of protection of the present invention.

[0044] The present invention will be further described below with reference to the accompanying drawings.

[0045] Example 1

[0046] like Figure 1 As shown, this embodiment provides a multi-level sequential optimization design method for a solid oxide electrolysis system, specifically including the following four stages:

[0047] Phase 1: Multi-objective optimization of system-level design parameters. First, a multi-objective optimization model at the system level is constructed using a multi-objective optimization algorithm (such as NSGA-II) on an optimization computing platform (such as MATLAB). This model aims to simultaneously maximize the system's hydrogen production efficiency and hydrogen yield rate. Its decision variables are the core operating parameters affecting system performance, such as current density, stack inlet temperature, reactant utilization rate, recycle ratio, and anode / cathode feed ratio. The algorithm searches within the set feasible region of the parameters. For each set of candidate design parameters generated, it must be passed to the next stage to obtain accurate system response data, thereby calculating the objective function value and guiding the algorithm towards the Pareto optimal front.

[0048] Phase Two: Full-Process System Simulation. First, a full-process steady-state model of the SOEC system is established in process simulation software (such as Aspen Plus). This model includes the solid oxide reactor, gas compressor, circulating fan, water pump, heater, and steam-water separator. Then, the candidate design parameter set generated in Phase One is automatically transferred to the SOEC system model established in the process simulation software via an interface. After performing simulation calculations, two types of key data are extracted: first, system performance data, such as the power consumption and hydrogen production of each major component, used to feed back the optimization objectives of Phase One; second, complete thermodynamic state parameters of all process streams, including their inlet temperature, pressure, mass flow rate, and specific heat capacity. These data form the basis for the comprehensive optimization of the heat exchanger network in Phase Three.

[0049] Phase 3: Comprehensive Optimization of the Heat Exchanger Network. Based on the flow data provided in Phase 2, a comprehensive optimization model of the heat exchanger network is constructed using a mathematical modeling and optimization platform (such as GAMS) and methods such as hierarchical superstructures, with the objective of minimizing thermal utility consumption. This model is a mixed-integer programming problem, and its decision variables include the matching relationships between flow streams, heat exchange allocation, and utility load. By solving this model, the optimal heat exchanger network topology corresponding to the current system design parameters can be obtained, including the required number of heat exchange units, the flow parameters matched to each unit, and their heat loads.

[0050] Phase 4: Detailed design optimization of the heat exchanger layer, including two sub-steps: optimization of the heat exchanger geometry and optimization of the heat exchanger channel arrangement.

[0051] Step 4.1: Multi-objective optimization of heat exchanger geometric parameters. Based on the flow parameters matched in the third-stage heat exchange network, the heat exchanger is designed. Using the geometric parameters of the main heat exchange zone fins (such as height, thickness, and frequency) and the structural parameters of the guide zone (connecting pipe diameter and distributor characteristic dimensions) as decision variables, a multi-objective optimization model is established with conflicting objectives of maximizing heat exchanger compactness (specific surface area) and minimizing flow resistance (flow power consumption). Driven by an optimization algorithm (such as NSGA-II) and coupled with detailed heat exchanger design software (such as Aspen EDR), automated heat transfer and pressure drop calculations are performed to ultimately obtain the optimal design scheme for the fin structure parameters.

[0052] Step 4.2: Heat Exchanger Channel Arrangement Optimization. Based on the basic geometric configuration of the heat exchanger determined in Step 4.1, the arrangement order of the multiple fluid channels is further used as the decision variable. An optimization model is constructed with the objective of minimizing the root mean square error of the cumulative heat load along the heat transfer direction of each channel, aiming to achieve a uniform distribution of heat load and avoid temperature crossover. An optimization algorithm based on arrangement (such as a genetic algorithm) is used to search for and determine the optimal channel arrangement.

[0053] This design method achieves optimal global performance by constructing and solving a collaborative optimization framework that includes the coupling relationships between the system layer, the heat exchange network layer, and the heat exchanger layer.

[0054] Example 2

[0055] This embodiment implements the multi-level sequential optimization design method for solid oxide electrolysis systems proposed in this application, and optimizes the design of a 100kW-class solid oxide electrolysis hydrogen production system. This system mainly consists of an electrolytic reactor, compressor, fan, pump, multi-stream heat exchanger, and steam-water separator. The initial design parameters of the system are: current density J... cell =0.8 A / cm 2 The inlet temperature of the fuel cell stack, T inlet =750℃, reactant utilization rate RU=0.7, recycle ratio RR=0.4, anode / cathode feed ratio AFR=0.5, system efficiency is 74.27%, hydrogen production rate is 17.16 Nm 3 / h. Under the baseline design scheme, the heat exchanger fin parameters are: fin height h = 6mm, fin thickness t = 0.15mm, fin frequency n = 600m. -1 The specific surface area of ​​the heat exchanger is 752 m². 2 / m 3 The power consumption during operation is 0.85kW.

[0056] The entire optimization process is divided into four stages, as detailed below. Figure 2 As shown.

[0057] Phase 1: Optimization of the SOEC System Operation Window

[0058] Step 1.1: Establish a multi-objective optimization model for system design parameters

[0059] In the Matlab platform, a multi-objective optimization model for the system layer is constructed based on the improved NSGA-II algorithm. Considering system-level operating parameters and performance indicators, five decision variables are defined: current density J. cell The inlet temperature of the fuel cell stack, T inlet Reactant utilization rate (RU), recycling ratio (RR), and anode / cathode feed ratio (AFR) are all considered. The optimization objective is defined as maximizing system efficiency (η). H2 and hydrogen production rate P H2 The constraints include: conservation of mass and energy of the core components and the whole system; safety constraint that the temperature difference between the inlet and outlet of the fuel cell stack must be less than the allowable standard (120℃); and that the decision variables must be within the preset feasible region, and that the simulation of the whole SOEC system converges.

[0060] Step 1.2: Implementation process of the improved NSGA-II algorithm

[0061] Step 1.2.1: Set algorithm parameters: Population size N pop =60, maximum number of generations G max =40, crossover probability value f cross =0.7, mutation probability value f mut =0.4.

[0062] Step 1.2.2: Decision variable vector X = [J] cell T inlet The boundary constraints of [RU, RR, AFR] are determined through engineering experience and equipment safety range: current density J cell ∈[0.1,1.4]A / cm 2 The inlet temperature of the fuel cell stack, T inlet ∈[650,850]℃, reactant utilization rate RU∈[0.5,0.8], recycling ratio RR∈[0.1,0.8], anode / cathode feed ratio AFR∈[0.1,4.0].

[0063] Step 1.2.3: An initial population is generated using Latin hypercube sampling (LHS), with each individual representing a set of SOEC system design parameters. Initialization employs a special initialization strategy using a "judgment-loop" combination of statements to ensure individual validity. The generated individual parameters are then passed to the second stage (process simulation) and the third stage (heat exchanger network optimization) to obtain system energy consumption, hydrogen production, and simulation convergence status. If individual parameters cause the system simulation to fail to converge, the individual is automatically updated using a loop judgment statement until an effective parameter combination that allows the system to converge is obtained.

[0064] Step 1.2.4: Based on the energy consumption and hydrogen production data fed back from Step 5.1 of the second stage and Step 8.2 of the third stage, calculate the fitness (i.e., η) of each individual according to formulas (1) and (2). H2 and P H2 ):

[0065] (1)

[0066] Where, η H2 The hydrogen production efficiency (%) of the SOEC system, m H2 This is the hydrogen mass flow rate (kg / s) at the SOEC system outlet, in LHV. H2 The lower heating value of H2 is taken as 120,000 kJ / kg, W. total This is the total input power (kW) of the SOEC system, including the power consumed by the fuel cell stack (W). stack Pump power consumption (W) pump ), power consumption of air compressor (W) comp ) and the power consumed by the electric heater (W) heater );

[0067] (2)

[0068] Among them, P H2 This refers to the hydrogen production per unit time of the SOEC system (Nm³). 3 / h), m H2 This is the hydrogen mass flow rate at the SOEC system outlet, in kg / s. R is the universal gas constant (R = 8.314 J / (mol·K)), T0 is the standard temperature (T0 = 273.15 K), and M... H2 It is the molar mass (M) of H2 H2 =2.016×10 -3 kg / mol), P0 is the standard pressure (P0 = 101325 Pa).

[0069] Step 1.2.5: Perform fast nondominated sorting and crowding calculation.

[0070] Step 1.2.6: Based on the fast non-dominated sorting, crowding calculation results and preset crossover probability, select suitable individuals for crossover operation to generate a new population PoP_c, and select suitable individuals for mutation operation to generate a new population PoP_m.

[0071] Step 1.2.7: Pass the individuals in PoP_c and PoP_m to the second and third stages again for simulation and heat exchange network optimization, obtain feedback data and evaluate their fitness.

[0072] Step 1.2.8: Merge PoP_c, PoP_m with the parent population, re-perform fast non-dominated sorting and crowding calculation, and retain the best individual as the parent population for the next generation.

[0073] Step 1.2.9: Determine the number of iterations. Repeat steps 2.6-2.8 until the maximum number of iterations is reached or the termination criterion is met. Output the Pareto front solution set, such as... Figure 3 As shown.

[0074] Step 1.3: Optimize Decisions

[0075] The optimal design parameters were determined from the Pareto front solution set using the Top-Order Ideal Solution Approximation Method (TOPSIS). A system efficiency weight of w1=0.5 and a hydrogen production rate weight of w2=0.5 were set to select the best compromise solution.

[0076] In this embodiment, the optimal solution corresponds to a system efficiency of 80.37% and a hydrogen production rate of 29.72 Nm. 3 / h, at this time J cell =1.39A / cm 2 T inlet=849℃, RU=0.70, RR=0.64, AFR=0.93. Compared with the initial scheme, the system efficiency is improved by 8.2% and the hydrogen production rate is improved by 79.2%.

[0077] Phase Two: Overall SOEC System Process Simulation

[0078] Step 2.1: Interface Automation Process

[0079] The ASPEN Plus V8.8 software is automatically invoked through MATLAB's ActiveX interface to assign values ​​to the parameter set X corresponding to each individual in the population, and then simulation calculations are performed on the pre-established refined steady-state process model of the SOEC system.

[0080] Step 2.2: Data Extraction and Transmission

[0081] After the simulation converges, MATLAB automatically extracts the following two types of key data:

[0082] (1) System performance parameters: including stack power consumption W stack Compressor power consumption (W) comp Pump power consumption W pump Electric heater power consumption W ele and hydrogen production m H2 These parameters will be used to calculate the optimization objective for the first stage.

[0083] (2) Stream thermodynamic parameters: the inlet and outlet temperatures (T) of all cold and hot process streams participating in heat exchange within the system. in ,T out Pressure (P), mass flow rate (m³), and specific heat capacity (C) p These are the input data for the subsequent third-stage heat exchanger network optimization.

[0084] Phase 3: Heat exchanger network optimization

[0085] Step 3.1: Reading heat exchanger network data

[0086] MATLAB writes the stream data extracted in step 5.1 of the second stage into a GDX format file and calls the GAMS platform.

[0087] Step 3.2: Heat transfer network model construction

[0088] Step 3.2.1: Based on the data of each stream, the data preprocessing is performed first: the temperature range is divided and the cold and hot streams are defined.

[0089] Step 3.2.2: In the GAMS environment, based on the hierarchical superstructure modeling method, the heat exchanger network synthesis problem is transformed into a mathematical optimization problem with the goal of minimizing utilities. The expression of the objective function is formula (3):

[0090] (3)

[0091] Q hu qhuj is the thermal utility required for the heat exchange network, in kW; qhuj is the heat exchange between the cold fluid j and the thermal utility, in kW.

[0092] Step 3.2.3: The constraints of the mathematical model for the heat exchanger network integration are Equations (4) to (11):

[0093] Heat balance of each stream:

[0094] (4)

[0095] Where Tin i and Tout i are the inlet and outlet temperatures of hot stream i, in °C, and Tin j and Tout j are the inlet and outlet temperatures of cold stream j, in °C, F i F j q represents the heat capacity flow rate of hot flow stream i and cold flow stream j, in kW / ℃. i,j,k qcu i represents the heat exchange between hot stream i and cold stream j in stage k, in kW; qcu i represents the heat exchange between hot stream i and the cold utility, in kW; qhuj represents the heat exchange between cold stream j and the hot utility, in kW.

[0096] Heat balance at each level:

[0097] (5)

[0098] Where t i,k t i,k+1 It is the temperature at the end of heat flow i in stage k and stage (k+1), in °C and t. j,k t j,k+1 It is the temperature of cold flow j at the end of stage k and stage (k+1), in °C.

[0099] Inlet temperature constraint:

[0100] (6)

[0101] Where t i,1 It is the temperature at which heat flow i enters the first stage, in °C (°C) and t (t). j,ST It is the temperature at which the cold flow j exits the ST stage, in °C;

[0102] Temperature feasibility constraints:

[0103] (7)

[0104] Cooling and heating utility loads:

[0105] (8)

[0106] Logical constraints:

[0107] (9)

[0108] Where H i and H j These are the heat loads of hot flow stream i and cold flow stream j, respectively, in kW. i,j,k The 0 and 1 of zcu i and zhu j represent whether heat exchange matching exists between the hot and cold streams, respectively.

[0109] Approach temperature:

[0110] (10)

[0111] In the formula: Γ is the upper limit of the driving force, and the calculation formula is:

[0112] (11)

[0113] Step 3.3: Model Solving and Data Output

[0114] Step 3.3.1: Call the MIP solver (such as BARON) to solve the model.

[0115] Step 3.3.2: After the solution is completed, GAMS automatically writes the optimal heat exchange network structure (heat exchanger arrangement matrix, heat load distribution, minimum thermal utility load) into the GDX file, and MATLAB reads it and calculates the fitness in combination with the system performance parameters.

[0116] Step 3.3.3: Based on the optimal design parameters, the optimal heat exchanger network structure output by GAMS is as follows: Figure 4 As shown, the heat exchange network includes 5 heat exchangers, 2 thermal utilities (electric heaters), and 1 cold utility (cooling water).

[0117] Phase 4: Optimization Design of Multi-Stream Heat Exchangers

[0118] Step 4.1: Multi-objective optimization of heat exchanger geometry parameters.

[0119] Step 4.1.1: Initialize NSGA-II parameters in the VB environment: Population size N pop =50, maximum number of generations G max=80, crossover probability f cross =0.8, mutation probability f mut =0.2.

[0120] Step 4.1.2: Set the decision variables as the fin geometric parameter vector [fin height h, fin thickness t, fin frequency n], with values ​​ranging from: h ∈ [2, 15] mm, t ∈ [0.1, 0.2] mm, n ∈ [100, 1000] m. -1 .

[0121] Step 4.1.3: Generate an initial fin population through random sampling.

[0122] Step 4.1.4: For each individual fin parameter, VB automatically starts ASPEN EDR via the COM interface to create a multi-flow plate-fin heat exchanger model. Input the flow heat load Q obtained in step 9.3 of the third stage. ij The inlet and outlet temperatures and pressure parameters are used to design the heat exchanger using ASPEN EDR. The heat exchanger design process includes formulas (12)-(18):

[0123] Assuming the total mass flux of the heat exchanger, calculate the flow cross-sectional area of ​​the heat exchanger based on the mass flow rate:

[0124] (12)

[0125] Where S is the flow cross-sectional area, in meters. 2 M represents mass flow rate in kg / s, and m represents mass flux in kg / (s·m). 2 );

[0126] Calculate the initial heat exchanger width based on the aspect ratio:

[0127] (13)

[0128] Where W0 is the initial heat exchanger width, in meters; R dw The aspect ratio is [height-to-width ratio].

[0129] Calculate the number of fluid layers based on the relationship between the flow cross-sectional area and the number of layers:

[0130] (14)

[0131] Where h is the fin height in meters (m), t is the fin thickness in meters (m), and n is the fin frequency in meters (m). -1 N i Let i be the number of fluid layers. It is important to note that the ratio of the total number of hot layers to the total number of cold layers should not exceed 2. Otherwise, if there are three hot or three cold layers connected together, it will lead to deterioration of heat transfer.

[0132] Based on the calculated number of layers N i The width w of each fluid is recalculated using formula (15). i Select the largest w i As the width of the heat exchanger;

[0133] (15)

[0134] Calculate the heat exchanger height based on the number of heat exchanger layers:

[0135] (16)

[0136] In the formula: N is the number of layers, γ is the thickness of the partition, in meters;

[0137] Calculate the heat exchanger length L based on the heat exchanger capacity ΔQ:

[0138] (17)

[0139] Where A p The primary heat transfer area is expressed in meters (m²). 2 A f This refers to the secondary heat transfer area, in meters (m²). 2 A e Total heat transfer area, in meters (m²) 2 η f For fin efficiency, α u The heat transfer coefficient is expressed in W / (m²). 2 ·K), T is the fluid temperature in °C, T w The wall temperature is expressed in °C.

[0140] Finally, calculate the fluid pressure drop:

[0141] (18)

[0142] Where f is the friction factor, d h ρ is the hydraulic diameter, in meters; ρ is the fluid density, in kilograms per cubic meter of water. 3 ;

[0143] Step 4.1.5: After calculating the ASPEN EDR value for each individual in the population, extract the performance parameters and calculate the objective function value: Specific surface area A is calculated according to formula (19):

[0144] (19)

[0145] Where A total For effective heat transfer area, the unit is m. 2 V is the heat exchanger volume, in meters. 3 .

[0146] The power consumption ΔW is calculated according to formula (20):

[0147] (20)

[0148] Among them W i The power consumption of flow stream i is expressed in kW and Q. i The volumetric flow rate of stream i, in cubic meters per second (m³). 3 / s, ΔP i Let η be the pressure drop of flow stream i, in Pa, and η0 be the fan efficiency, taken as 0.7.

[0149] Step 4.1.6: Perform fast nondominated sorting and crowding calculation.

[0150] Step 4.1.7: Based on the fast non-dominated sorting, crowding calculation results and preset crossover probability, select suitable individuals for crossover operation to generate a new population PoP_c, and select suitable individuals for mutation operation to generate a new population PoP_m.

[0151] Step 4.1.8: Merge PoP_c, PoP_m with the parent population, re-perform fast non-dominated sorting and crowding calculation, and retain the best individual as the parent population for the next generation.

[0152] Step 4.1.9: Determine the number of iterations. Repeat steps 9.6-9.7 until the maximum number of iterations is reached or the termination criterion is met. Output the Pareto front solution set, such as... Figure 5 As shown.

[0153] Step 4.1.10: Optimize Decisions

[0154] The optimal design parameters are determined from the Pareto front solution set using the Top-Order Ideal Solution Approximation Method (TOPSIS). A weight of specific surface area w1 = 0.5 and a weight of flow energy consumption w2 = 0.5 are set to select the best compromise solution.

[0155] In this embodiment, the optimal fin parameters are h=11.03mm, t=0.11mm, and n=259m. -1 The specific surface area of ​​the heat exchanger is 836 m². 2 / m 3 The power consumption is 0.12kW. Compared to the initial design, the compactness is improved by 11.2%, and the power consumption is reduced by 85.9%.

[0156] Step 4.2: Channel Arrangement Optimization

[0157] Step 4.2.1: Define the number of fluids and the corresponding number of channel layers, and assign a specific channel heat load value to each fluid layer.

[0158] Step 4.2.2: Initialize genetic algorithm parameters in the Python environment: population size N pop =50, maximum number of generations G max =80, crossover probability f cross =0.8, mutation probability f mut =0.2.

[0159] Step 4.2.3: Generate an initial channel arrangement population through random sampling.

[0160] Step 4.2.4: Calculate the fitness value for each individual in the population, and calculate the root mean square error of its cumulative heat load according to formula (21):

[0161] (twenty one)

[0162] Where σ i The cumulative heat load of the channel is expressed in kW.

[0163] The formula for calculating the cumulative heat load of the channel is:

[0164] (twenty two)

[0165] Where q i Heat exchange per channel, in kW;

[0166] Step 4.2.5: Store the individuals in the current population and their fitness into a set, sort the population according to fitness, and select the individual with the best fitness as the parent.

[0167] Step 4.2.6: Perform crossover and mutation operations on the parent population to generate offspring, calculate the fitness of the generated offspring individuals and sort them, and select individuals with higher fitness to update the population.

[0168] Step 4.2.7: Determine the iteration count. Repeat steps 4.2.4-4.2.6 until the maximum iteration count is reached or the termination criterion is met. Output the channel arrangement that minimizes the root mean square error of the cumulative heat load. In this case, the cumulative heat load distribution before and after channel arrangement optimization is as follows: Figure 6 As shown. The optimal channel arrangement is combined with the optimal fin parameters obtained in step S4.1.10 to form a complete detailed heat exchanger design scheme. The final heat exchanger design parameters in this case are as follows: Figure 7 As shown.

[0169] The above embodiments are merely preferred embodiments of the present invention, and the scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, improvements and modifications made without departing from the principles of the present invention should also be considered within the scope of protection of the present invention.

Claims

1. A method of multi-level sequential optimization design of a solid oxide electrolysis system, characterized in that, Includes the following steps: S1. Multi-objective optimization of system-level design parameters In the optimized computing platform, a multi-objective optimization algorithm is used to construct a multi-objective optimization model at the system layer, with the goal of maximizing the system's hydrogen production efficiency and hydrogen production rate. By iteratively solving the multi-objective optimization model at the system layer, the Pareto solution set and optimal solution of the system design parameters are obtained. The system design parameters include at least one or more of the following: current density, stack inlet temperature, reactant utilization rate, recycle ratio, and anode / cathode feed ratio. The multi-objective optimization model at the system layer searches within a set feasible region of parameters to generate multiple sets of candidate design parameters. S2, System Full-Process Precise Simulation A quasi-two-dimensional model of the SOEC fuel cell stack and its steady-state model are constructed in the process simulation software. The candidate design parameters generated in step S1 are then transferred to the SOEC system steady-state model in the process simulation software. After performing simulation calculations, accurate simulation results of the entire system process are obtained, including two types of key data: first, system performance data, including the power consumption and hydrogen production of each major component, which are used to provide feedback for the optimization target of step S1; second, stream data, namely the complete thermodynamic state parameters of all process streams, including their inlet temperature, pressure, mass flow rate and specific heat capacity, which are used for the comprehensive optimization of the heat exchange network in the subsequent step S3. S3, Comprehensive Optimization of Heat Exchanger Network Based on the flow data provided in step S2, in the mathematical modeling and optimization platform, a comprehensive optimization model of the heat exchange network is constructed with the goal of minimizing the consumption of thermal utilities, based on the hierarchical superstructure method. The comprehensive optimization model of the heat exchange network is a mixed integer programming problem, and its decision variables include the matching relationship between the flow streams, the heat exchange distribution, and the utilities load. By solving the comprehensive optimization model of the heat exchange network, the optimal heat exchange network topology corresponding to the current system design parameters is obtained, including the required number of heat exchange units, the flow parameters matched to each unit, and their heat load. S4, Heat exchanger layer design optimization Optimization of heat exchanger geometry and channel arrangement includes: S4.1 Multi-objective optimization of heat exchanger geometric parameters Based on the flow data matched in the heat exchange network obtained in step S3, the heat exchanger is designed. The fin parameters of the main heat exchange zone and the structural parameters of the flow guiding zone are used as decision variables. A multi-objective optimization model of the heat exchanger is established with the conflicting objectives of maximizing the specific surface area of ​​the heat exchanger and minimizing the flow power consumption. Driven by the multi-objective optimization algorithm and coupled with simulation design software, the heat transfer and pressure drop calculations are automated. Finally, the Pareto solution set of the geometric structural parameters of the heat exchanger and the optimal design results are obtained. S4.2 Optimization of heat exchanger channel arrangement Using the arrangement order of multiple fluid channels as the decision variable, a channel arrangement optimization model is constructed with the objective of minimizing the root mean square error of the cumulative heat load of each channel along the heat transfer direction to achieve uniform heat load distribution and avoid temperature crossover. A genetic optimization algorithm based on permutation is used to search and determine the optimal channel arrangement.

2. The multi-level sequential optimization design method for the solid oxide electrolysis system according to claim 1, characterized in that, In step S2, the process simulation software is called to perform a full-process simulation of the system. The SOEC system steady-state model is a refined steady-state model that covers the solid oxide electrolytic reactor, gas compressor, circulating fan, water pump, heater and steam-water separator. By changing the input system design parameters, the key parameters of energy consumption, hydrogen production and flow thermodynamic data of each component in the system are simulated and calculated.

3. The multi-level sequential optimization design method for the solid oxide electrolysis system according to claim 1, characterized in that, The comprehensive optimization model of the heat exchange network mentioned in step S3 is a mixed integer optimization model. Its decision variables include the flow matching relationship, heat exchange allocation and utility load, and satisfy the flow heat balance constraint, temperature feasibility constraint and heat exchange driving force constraint.

4. The multi-level sequential optimization design method for the solid oxide electrolysis system according to claim 1, characterized in that, The heat exchanger structural parameter optimization in step S4.1 includes the optimization of the main heat exchange zone and the flow guiding zone. Specifically, the main heat exchange zone uses fin parameters as decision variables, including fin height, fin thickness, and fin frequency; the flow guiding zone uses structural parameters as decision variables, including connecting pipe diameter and flow divider characteristic dimensions. The constraint condition is the heat exchanger size constraint. The optimization objectives are to improve the heat exchanger compactness and reduce flow power consumption. The heat exchanger is then subjected to multi-objective optimization design.

5. The multi-level sequential optimization design method for the solid oxide electrolysis system according to claim 1, characterized in that, After obtaining the Pareto solution set for the multi-objective optimization of the heat exchanger in step S4.1, further optimization decisions are made on the Pareto solution set to determine the optimal design scheme of the heat exchanger. The optimization decisions include any one or a combination of the following methods: (1) The heat exchanger flow power consumption and volume specific surface area are dimensionless, and the candidate schemes are comprehensively evaluated based on the weight of each index. The optimal design result is selected according to the degree of closeness between each candidate scheme and the ideal solution. (2) Convert the flow power consumption into the energy consumption cost during equipment operation, convert the specific surface area into the heat exchanger manufacturing cost, construct economic evaluation index, and select the design scheme with the lowest total cost as the optimal heat exchanger structural parameters.

6. The multi-level sequential optimization design method for the solid oxide electrolysis system according to claim 1, characterized in that, The accurate simulation results of the entire system process in step S2 and the comprehensive optimization results of the heat exchange network in step S3 are fed back into the multi-objective optimization model of the system layer in step S1 to perform multi-objective optimization of the candidate design parameters. The results of the comprehensive optimization of the heat exchanger network in step S3 are used as input conditions for the design optimization of the heat exchanger layer in step S4. Multi-objective optimization of heat exchanger geometric parameters in S4.1 and optimization of heat exchanger channel arrangement in S4.2 are carried out to achieve cross-level collaborative optimization.

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