Optimization analysis of 3D modelling of SOEC stacks taking into account inhomogeneities

doi:10.11949/0438-1157.20250142

Abstract

Abstract:

To address the impact of temperature and current inhomogeneity inside the solid oxide electrolysis cell (SOEC) stack on the system's hydrogen production efficiency, safe and stable operation, and lifetime, first, based on the geometric structure of the SOEC power reactor, a three-dimensional (3D) model coupled with multi-physics fields that can accurately analyze the charge transport process, fluid flow, material transport process and heat energy transfer process of the SOEC is established. Secondly, in order to optimize the simulation process of the model, boundary constraints are imposed on the model and its structure is meshed to obtain an adaptive incremental Kriging agent model optimization that satisfies the constraints, which confirms the accuracy of the model optimization and reduces the simulation time and the total amount of computational resources. Finally, the multi-objective optimization algorithm for the steady-state operation of SOEC reactors is proposed to increase the efficiency of electrolytic hydrogen production and improve the inhomogeneity by analyzing the characteristics and causes of the inhomogeneous distribution of temperature, material, current density and voltage inside the stacks, and through numerical simulation and experimental verification, considering the optimization method of temperature and current uniformity distribution inside the stacks, it can greatly improve the safe and stable operation and hydrogen production of the stacks.

Key words: SOEC, inhomogeneity, Kriging agent model, efficiency, multi-objective optimization, steady-state operation

摘要：

针对SOEC电堆内部温度、电流不均匀性对系统制氢效率、安全稳定运行及寿命造成的影响，首先根据SOEC电堆的几何结构建立能精准分析SOEC电荷传输过程、流体流动、物质传输过程、热能传递过程的多物理场耦合的3D模型，其次为优化模型仿真过程对模型进行边界约束并将其结构网格化，得到满足约束条件的自适应增量Kriging代理模型优化方式，印证该模型优化的精准性并减少了仿真时间与计算资源总量，最后通过分析电堆内部温度、物料分布、电流密度、电压等不均匀分布特性及原因提出考虑增加电解制氢效率及改善不均匀性的SOEC电堆稳态运行多目标优化算法，并通过算例仿真和实验验证，考虑电堆内部温度、电流均匀性分布的优化方式，可大大提高电堆安全稳定运行及产氢量。

关键词: SOEC, 不均匀性, Kriging代理模型, 效率, 多目标优化, 稳态运行

CLC Number:

TQ 116.2⁺1

Yaqing HE, Weiqing WANG, Yingtian CHI, Jiarong LI, Haiyun WANG, Xinyan ZHANG, Bowen LIU. Optimization analysis of 3D modelling of SOEC stacks taking into account inhomogeneities[J]. CIESC Journal, 2025, 76(8): 4129-4144.

赫亚庆, 王维庆, 池映天, 李佳蓉, 王海云, 张新燕, 刘博文. 考虑不均匀性的SOEC电堆3D建模优化分析[J]. 化工学报, 2025, 76(8): 4129-4144.

Figures/Tables 21

Fig.1 Schematic diagram of a plate SOEC single stack

Fig.2 Schematic diagram of hydrogen production by SOEC electrolysis

Fig.3 Geometry of SOEC stack 3D model[18-20]

Fig.4 Flowchart of 3D model simulation of SOEC stack[21-23]

Table 1 Boundary constraints of 3D spatial multiphysics field model of SOEC stack

参数约束条件	数值
氧电极侧集流体电势/V	0
氢电极侧集流体电势/V	1～2
空气流道入口O₂与N₂摩尔比	21∶79
氢气流道入口H₂O与H₂摩尔比	9∶1
空气流道出口压强/kPa	101
氢气流道出口压强/ kPa	101
空气流道入口温度/℃	810
氢气流道入口温度/℃	810
空气流道入口速度/（m/s）	4～6
氢气流道入口速度/（m/s）	2～4

Fig.5 Schematic of 3D state-space model of SOEC stack

Fig.6 Flowchart of SOEC agent model

Table 2 Single-stack parameters

相关参数	数值
SOEC长度/ mm	75.0
SOEC宽度/ mm	30.0
SOEC厚度/ mm	2.1
氢电极功能层厚度/μm	50.0
氧电极长度/ mm	72.0
氧电极宽度/ mm	28.0
氧电极厚度/μm	30.0
电解质厚度/ μm	8.0
氢电极支撑层厚度/μm	500.0
金属支撑体长度/ mm	75.0
金属支撑体宽度/ mm	30.0
金属支撑体厚度/ mm	1.5
流道宽度/ mm	1.5
流道高度/ mm	0.8

Fig.7 Comparison of 3D model optimisation simulations of SOEC stacks

Fig.8 H2O(g) distribution

Fig.9 Current density distribution at intermediate electrolyte interface

Fig.10 Simulation comparison of SOEC current density distribution under different models

Fig.11 Simulation comparison of SOEC volt-ampere characteristic curves under different models

Fig.12 Comparison of simulation of temperature variation of SOEC stack under different models

Fig.13 Schematic diagram of Pareto Frontier

Table 3 Weight coefficient of different optimization objects

类别	$U s c$	$V H 2 O$	$V a i r$	$T s c$	$U E I$	$U E T$
方式1	1	1	1	1	1	1
方式2	1	1	1	1	0	0

Table 3 Weight coefficient of different optimization objects

类别	$U s c$	$V H 2 O$	$V a i r$	$T s c$	$U E I$	$U E T$
方式1	1	1	1	1	1	1
方式2	1	1	1	1	0	0

Fig.14 Ideal solution of Pareto Frontier for SOEC at 60 W single stack power

Fig.15 Steady state operating curves of different stack power under Pareto Frontier

Table 4 Comparison of decision-making results under different models and approaches for a stack power of 16 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	807.50	0.04	12.62	0.19	77.80	1.27
	方式2	808.00	0.07	12.10	0.32	87.10	1.29
	优化占比	0.06%	42.86%	-4.30%	40.63%	10.68%	1.55%
经典3D模型	方式1	807.50	0.03	12.63	0.19	77.80	1.27
	方式2	808.00	0.06	12.10	0.32	87.10	1.29
	优化占比	0.06%	50.00%	-4.38%	40.63%	10.68%	1.55%

Table 4 Comparison of decision-making results under different models and approaches for a stack power of 16 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	807.50	0.04	12.62	0.19	77.80	1.27
	方式2	808.00	0.07	12.10	0.32	87.10	1.29
	优化占比	0.06%	42.86%	-4.30%	40.63%	10.68%	1.55%
经典3D模型	方式1	807.50	0.03	12.63	0.19	77.80	1.27
	方式2	808.00	0.06	12.10	0.32	87.10	1.29
	优化占比	0.06%	50.00%	-4.38%	40.63%	10.68%	1.55%

Table 5 Comparison of decision-making results under different models and approaches for a stack power of 32 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	808.30	0.17	24.67	0.20	77.60	1.29
	方式2	807.85	0.20	24.15	0.33	86.10	1.32
	优化占比	-0.06%	15.00%	-2.15%	39.39%	9.87%	2.27%
经典3D模型	方式1	808.30	0.18	24.66	0.20	77.60	1.29
	方式2	807.85	0.21	24.15	0.33	86.10	1.32
	优化占比	-0.06%	14.29%	-2.11%	39.39%	9.87%	2.27%

Table 5 Comparison of decision-making results under different models and approaches for a stack power of 32 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	808.30	0.17	24.67	0.20	77.60	1.29
	方式2	807.85	0.20	24.15	0.33	86.10	1.32
	优化占比	-0.06%	15.00%	-2.15%	39.39%	9.87%	2.27%
经典3D模型	方式1	808.30	0.18	24.66	0.20	77.60	1.29
	方式2	807.85	0.21	24.15	0.33	86.10	1.32
	优化占比	-0.06%	14.29%	-2.11%	39.39%	9.87%	2.27%

Table 6 Comparison of decision-making results under different models and approaches for a stack power of 48 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	809.10	0.38	36.39	0.22	78.00	1.32
	方式2	809.00	0.42	35.87	0.34	86.30	1.35
	优化占比	-0.01%	9.52%	-1.45%	35.29%	9.62%	2.22%
经典3D模型	方式1	809.10	0.37	36.40	0.22	78.00	1.32
	方式2	809.00	0.41	35.88	0.34	86.30	1.35
	优化占比	-0.01%	9.76%	-1.45%	35.29%	9.62%	2.22%

Table 6 Comparison of decision-making results under different models and approaches for a stack power of 48 W

模型类型	方式/占比	$T s c$ /℃	$U E T$ /℃	$I s c$ /A	$U E I$	$U R H 2 O$ /%	$U s c$ /V
I-KAM代理模型	方式1	809.10	0.38	36.39	0.22	78.00	1.32
	方式2	809.00	0.42	35.87	0.34	86.30	1.35
	优化占比	-0.01%	9.52%	-1.45%	35.29%	9.62%	2.22%
经典3D模型	方式1	809.10	0.37	36.40	0.22	78.00	1.32
	方式2	809.00	0.41	35.88	0.34	86.30	1.35
	优化占比	-0.01%	9.76%	-1.45%	35.29%	9.62%	2.22%

References 31

[1]	张俊杰, 孙旺, 高啸天, 等. 固体氧化物电解池制氢关键技术及产业化进展[J]. 化工学报, 2023, 74(12): 4749-4763.
	Zhang J J, Sun W, Gao X T, et al. Key technology and industrialization progress of hydrogen production by solid oxide electrolytic cell[J]. CIESC Journal, 2023, 74(12): 4749-4763.
[2]	李佳蓉, 林今, 邢学韬, 等. 主动配电网中基于统一运行模型的电制氢(P2H)模块组合选型与优化规划[J]. 中国电机工程学报, 2021, 41(12): 4021-4033.
	Li J R, Lin J, Xing X T, et al. Technology portfolio selection and optimal planning of power-to-hydrogen(P2H) modules in active distribution network[J]. Proceedings of the CSEE, 2021, 41(12): 4021-4033.
[3]	邢学韬, 林今, 宋永华, 等. 基于高温电解的大规模电力储能技术[J]. 全球能源互联网, 2018, 1(3): 303-312.
	Xing X T, Lin J, Song Y H, et al. Large scale energy storage technology based on high-temperature electrolysis[J]. Journal of Global Energy Interconnection, 2018, 1(3): 303-312.
[4]	Chi Y T, Qiu Y W, Lin J, et al. Online identification of a link function degradation model for solid oxide fuel cells under varying-load operation[J]. International Journal of Hydrogen Energy, 2022, 47(4): 2622-2646.
[5]	章大海, 史晓锋, 侯啸海, 等. 固体氧化物电解池平行流道流动不均匀性优化模拟[J]. 硅酸盐学报, 2024, 52(5): 1687-1697.
	Zhang D H, Shi X F, Hou X H, et al. Simulations on flow non-uniformity in parallel channel of solid oxide electrolysis cells[J]. Journal of the Chinese Ceramic Society, 2024, 52(5): 1687-1697.
[6]	冯祥, 杨超, 梁超余, 等. 可逆固体氧化物燃料电池性能的数值模拟研究[J]. 推进技术, 2020, 41(11): 2630-2640.
	Feng X, Yang C, Liang C Y, et al. Numerical simulation of reversible solid oxide fuel cell performance[J]. Journal of Propulsion Technology, 2020, 41(11): 2630-2640.
[7]	Chi Y T, Qiu Y W, Lin J, et al. A robust surrogate model of a solid oxide cell based on an adaptive polynomial approximation method[J]. International Journal of Hydrogen Energy, 2020, 45(58): 32949-32971.
[8]	张玉魁, 张晨佳, 孙振新, 等. 高温固体氧化物电解制氢模拟研究进展[J]. 化工进展, 2021, 40(S1): 126-141.
	Zhang Y K, Zhang C J, Sun Z X, et al. Review on modeling and simulation of high temperature solid oxide electrolysis for hydrogen production[J]. Chemical Industry and Engineering Progress, 2021, 40(S1): 126-141.
[9]	王雅倩, 任娜, 徐宗磊, 等. 电/热/气多能转换的可逆固体氧化物燃料电池信息物理融合建模与仿真[J]. 电网技术, 2018, 42(11): 3535-3542.
	Wang Y Q, Ren N, Xu Z L, et al. Cyber-physical system modeling and simulation of power-heat-gas multi-energy conversion for reversible solid oxide fuel cell[J]. Power System Technology, 2018, 42(11): 3535-3542.
[10]	Srikanth S, Heddrich M P, Gupta S, et al. Transient reversible solid oxide cell reactor operation—experimentally validated modeling and analysis[J]. Applied Energy, 2018, 232: 473-488.
[11]	Nasser M, Hassan H. Assessment of hydrogen production from waste heat using hybrid systems of Rankine cycle with proton exchange membrane/solid oxide electrolyzer[J]. International Journal of Hydrogen Energy, 2023, 48(20): 7135-7153.
[12]	Buffo G, Ferrero D, Santarelli M, et al. Energy and environmental analysis of a flexible Power-to-X plant based on Reversible Solid Oxide Cells (rSOCs) for an urban district[J]. Journal of Energy Storage, 2020, 29: 101314.
[13]	Jolaoso L A, Bello I T, Ojelade O A, et al. Operational and scaling-up barriers of SOEC and mitigation strategies to boost H₂ production — a comprehensive review[J]. International Journal of Hydrogen Energy, 2023, 48(85): 33017-33041.
[14]	Wang H, Xiao L S, Liu Y Q, et al. Performance and thermal stress evaluation of full-scale SOEC stack using multi-physics modeling method[J]. Energies, 2023, 16(23): 7720.
[15]	姚文岐, 王江江, 邓宇, 等. 基于太阳能全光谱利用的固体氧化物电解池系统性能分析[J]. 工程热物理学报, 2024, 45(5): 1264-1274.
	Yao W Q, Wang J J, Deng Y, et al. Performance analysis of solid oxide electrolysis cell system based on full-spectrum utilization of solar energy[J]. Journal of Engineering Thermophysics, 2024, 45(5): 1264-1274.
[16]	尹燕, 杜迎梦, 焦魁, 等. 固体氧化物电解池结构对其性能的影响研究[J]. 天津大学学报(自然科学与工程技术版), 2019, 52(11): 1171-1178.
	Yin Y, Du Y M, Jiao K, et al. Influence of the structure of solid oxide electrolysis cell on its performance[J]. Journal of Tianjin University (Science and Technology), 2019, 52(11): 1171-1178.
[17]	Chi Y T, Yokoo K, Nakajima H, et al. Optimizing the homogeneity and efficiency of a solid oxide electrolysis cell based on multiphysics simulation and data-driven surrogate model[J]. Journal of Power Sources, 2023, 562: 232760.
[18]	牟树君, 林今, 邢学韬, 等. 高温固体氧化物电解水制氢储能技术及应用展望[J]. 电网技术, 2017, 41(10): 3385-3391.
	Mu S J, Lin J, Xing X T, et al. Technology and application prospect of high-temperature solid oxide electrolysis cell[J]. Power System Technology, 2017, 41(10): 3385-3391.
[19]	张梦茹, 王恩华, 胡浩然, 等. 金属支撑型固体氧化物电解池的3D建模与性能分析[J]. 北京理工大学学报, 2024, 44(1): 69-75.
	Zhang M R, Wang E H, Hu H R, et al. 3D simulation and performance analysis of a metal-supported solid oxide electrolysis cell[J]. Transactions of Beijing Institute of Technology, 2024, 44(1): 69-75.
[20]	齐宇博, 张淑兴. 平板型固体氧化物燃料电池堆仿真分析[J]. 陶瓷学报, 2022, 43(5): 899-907.
	Qi Y B, Zhang S X. Simulation of flat-type solid oxide fuel cell stack[J]. Journal of Ceramics, 2022, 43(5): 899-907.
[21]	Chi Y T, Li P Y, Lin J, et al. Fast and safe heating-up control of a planar solid oxide cell stack: a three-dimensional model-in-the-loop study[J]. Journal of Power Sources, 2023, 560: 232655.
[22]	窦真兰, 李佳文, 张春雁, 等. 固体氧化物电解池时空分布式参数建模[J]. 综合智慧能源, 2024, 46(7): 53-62.
	Dou Z L, Li J W, Zhang C Y, et al. Spatiotemporal distributed parameter modeling of solid oxide electrolysis cells[J]. Integrated Intelligent Energy, 2024, 46(7): 53-62.
[23]	Chi Y T, Hu Q, Lin J, et al. Numerical simulation acceleration of flat-chip solid oxide cell stacks by data-driven surrogate cell submodels[J]. Journal of Power Sources, 2023, 553: 232255.
[24]	田宗睿, 智鹏鹏, 云国丽, 等. 基于自适应增量Kriging模型的多目标稳健优化设计方法[J]. 中国机械工程, 2023, 34(8): 931-940.
	Tian Z R, Zhi P P, Yun G L, et al. Multi-objective robust optimization design method based on adaptive incremental Kriging model[J]. China Mechanical Engineering, 2023, 34(8): 931-940.
[25]	万良琪, 欧阳林寒. 基于0-1规划模型筛选策略的Kriging组合模型及可靠性优化设计[J]. 计算机集成制造系统, 2022, 28(7): 2162-2168.
	Wan L Q, Ouyang L H. Kriging ensemble model based on 0-1 programming model selection strategy for reliability-based design optimization[J]. Computer Integrated Manufacturing Systems, 2022, 28(7): 2162-2168.
[26]	Wu Y H, Liu H K, Wang Y F, et al. Spatially resolved electrochemical performance and temperature distribution of a segmented solid oxide fuel cell under various hydrogen dilution ratios and electrical loadings[J]. Journal of Power Sources, 2022, 536: 231477.
[27]	池映天. 面向灵活调节的固体氧化物电堆建模与控制[D]. 北京: 清华大学, 2023.
	Chi Y T. Modeling and control of solid oxide cell stacks for flexible regulation[D]. Beijing: Tsinghua University, 2023.
[28]	da Rosa Silva E, Sassone G, Prioux M, et al. A multiscale model validated on local current measurements for understanding the solid oxide cells performances[J]. Journal of Power Sources, 2023, 556: 232499.
[29]	齐珂, 王迪, 谢喆, 等. 考虑多物理场耦合特性的固体氧化物燃料电池瞬态特性研究[J]. 化工学报, 2025, 76(3): 1264-1274.
	Qi K, Wang D, Xie Z, et al. Research on transient characteristics of solid oxide fuel cells considering coupling features of multiphysics fields[J]. CIESC Journal, 2025, 76(3): 1264-1274.
[30]	Li Q S, Kuang K B, Sun Y N, et al. Deficiency of hydrogen production in commercialized planar Ni-YSZ/YSZ/LSM-YSZ steam electrolysis cells[J]. International Journal of Hydrogen Energy, 2022, 47(56): 23514-23519.
[31]	Son J, Hwang S, Hong S, et al. Parameter study on solid oxide fuel cell heat-up process to reaction starting temperature[J]. International Journal of Precision Engineering and Manufacturing-Green Technology, 2020, 7(6): 1073-1083.