Optimizing the Homogeneity and Efficiency of an SOEC Based on Multiphysics Simulation and Data-driven Surrogate Model

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Optimizing the Homogeneity and Eﬃciency of an SOEC Based

on Multiphysics Simulation and Data-driven Surrogate Model

Yingtian Chi

a,b,c

, Kentaro Yokoo

, Hironori Nakajima

b,c

, Kohei Ito

b,c

, Jin Lin

a,d,∗

, Yonghua

Songa,e

State Key Laboratory of Control and Simulation of Power Systems and Generation Equipment, Department

of Electrical Engineering, Tsinghua University, Beijing 100087, China

bDepartment of Hydrogen Energy Systems, Graduate School of Engineering, Kyushu University, Fukuoka,

Japan

cDepartment of Mechanical Engineering, Faculty of Engineering, Kyushu University, Fukuoka, Japan

dTsinghua-Sichuan Energy Internet Research Institute, Chengdu 610213, China

State Key Laboratory of Internet of Things for Smart City, University of Macau, Macau SAR 999078, China

Abstract

Inhomogeneous current and temperature distributions are harmful to the durability of

the solid oxide electrolysis cell (SOEC). Segmented SOEC experiments reveal that a high

steam utilization, which is favorable for system eﬃciency, leads to local steam starvation

and enhanced the inhomogeneity. It is necessary to consider inhomogeneity and eﬃciency

jointly in optimization studies. Three-dimensional (3D) multiphysics models validated with

experiments can simulate the inhomogeneity in a reliable manner, but they are unsuitable

for optimization due to the high computational cost. This study proposes a method that

combines segmented SOEC experiments, multiphysics simulation, and artiﬁcial intelligence to

optimize the inhomogeneity and eﬃciency of SOEC jointly. A 3D cell model is ﬁrst built and

veriﬁed by segmented SOEC experiments. Then, fast neural network surrogate models are

built from the simulation data and integrated into a multi-objective optimization problem.

Its solutions form a Pareto front reﬂecting the conﬂicting relationships among diﬀerent

objectives. It is found that the down-stream current is 60%-65% of the up-stream current

when the steam utilization is 0.7. To increase the steam utilization to 0.8, the down-stream

current will further drop to 50%-60% of the up-stream current. The Pareto fronts enable

system operators to achieve a balance between eﬃciency and inhomogeneity.

Keywords: Solid oxide electrolysis cell, steam utilization, multiphysics simulation,

segmented electrode method, homogeneity, multi-objective optimization

1. Introduction

Solid oxide electrolysis cells (SOECs) constitute a promising energy storage technology

∗Corresponding author

Email address: linjin@tsinghua.edu.cn (Jin Lin)

Preprint submitted to International Journal of Hydrogen Energy October 26, 2022

arXiv:2210.13766v1 [eess.SY] 25 Oct 2022

for carbon neutralization owing to its high eﬃciency and ability to convert carbon dioxide

into chemicals and fuels [

],[

]. However, the high operating temperature brings

durability problems. Mechanical stresses, induced by thermal transients and inhomogeneous

temperature distributions, are the direct causes of various failures [

],[

]. The inhomoge-

neous distribution of current also contributes the cell degradation and reduces eﬃciency [

It is critical to improve the homogeneity of current and temperature for safety and durability.

Experimental studies that investigate the spatial inhomogeneity in SOFC and SOEC

have been reported. For measuring the temperature distribution, several methods have been

reported. Inserting thermocouples into the gas channels or the interconnectors is a widely-

used method [

],[

]. Its spatial resolution is limited by the number of thermocouples,

due to the diﬃculties in handling electrical wiring, insulation, and gas-tight sealing. Guk

et al. [

] designed a multi-point thermal sensor to improve the spatial resolution of

temperature distribution while keeping the wiring simple. Other methods including infrared

imaging [

],[

], Raman spectroscopy [

], and optical ﬁber sensors [

], have also been

proposed to obtain high resolution temperature distribution data. For measuring the current

distribution, the segmented cell method is a powerful approach [

],[

]. Wuillemin et al.

[

] tested an anode-supported planar SOFC with 18 cathode segmentations and measured

the current-voltage (IV) curves and electrochemical impedance spectroscopy (EIS). Using an

anode-supported SOFC with 16 segmentations, Schiller et al. [

] found that the inhomogeneity

of current was enhanced remarkably under high fuel utilization due to the mass transport

limitation occurring at the down-stream part. They found that severe mass transport

limitation induced inhomogeneous degradation. Aydin et al. [

] measured the current

variation along an anode-supported microtubular SOFC with three segments. It was observed

that the current of the down-stream segment decreased rapidly due to fuel starvation as the

voltage decreased, which could cause local redox cycles and lead to degradation. They further

found that the inhomogeneity was enhanced under methane operation due to the severe

fuel starvation caused by incomplete methane reforming [

]. Kim et al. [

] found that Ni

re-oxidation and interface delamination tended to occur near the outlet in an anode-supported

planar SOFC. Wu et al. [

] tested an anode-supported SOFC with four cathode segments.

They found that high electrical loadings and high hydrogen dilution ratios could induce large

temperature gradient and uneven current distribution, leading to harsh conditions near the

gas outlet where microstructure degradation including cathode delamination and electrolyte

crack were observed. Therefore, the inhomogeneity of current density and temperature should

be controlled for durability.

To reduce experimental costs, multiphysics models are used to simulate the inhomogeneity,

while their reliability can be veriﬁed by the experimental data [

],[

]. Bessler et al.

used the data of a segmented anode-supported SOFC to calibrate a two-dimensional (2D)

model [

],[

]. The result showed that the model accurately predicted the IV curves under

diﬀerent temperatures and gas compositions. Aydin et al. used the data of a segmented

tubular SOFC and a segmented planar SOFC to verify the corresponding numerical models

[

],[

]. However, the high computational cost of 3D multiphysics models hinders their

applications, for example, in optimization studies. To handle this problem, surrogate models

have been constructed using simulation data produced by multiphysics models to predict the

SOEC performances with low computational cost. Arriagada et al. [

] and Huo et al. [

]

used artiﬁcial neural networks (ANNs) and support vector machine (SVM) to build SOFC

surrogate models using simulation data of physical models. Zahadat et al. [

] and Milewski

et al. [

] used ANNs to predict the SOEC and SOFC performance under diﬀerent operating

parameters and design parameters from experimental data. In our previous study, a method

to build polynomial surrogate models is proposed [30].

For a ﬁxed stack/system design, the operating parameters, including temperature, ﬂow

rates, gas compositions, voltage, and current, can be optimized to improve the eﬃciency and

durability of SOEC systems. Cai et al. [

] studied the optimization of an SOEC system

consisting of a stack and an air compressor with a one-dimensional (1D) SOEC model, seeking

to maximize the eﬃciency and hydrogen production. The temperature inhomogeneity was

controlled by including a temperature gradient constraint. Xing et al. [

] optimized the

temperature, voltage, and steam ﬂow rate of an SOEC system to maximize the hydrogen

production under diﬀerent target powers. A 1D SOEC model was used and the temperature

gradient constraint was also considered. They found that the steam utilization aﬀected the

system eﬃciency signiﬁcantly, because steam generation consumes a large amount of energy

and it is hard to fully recover the heat contained in the unused steam. Their optimization

results indicated that the optimal steam utilization to maximize system eﬃciency should

exceed 80%. Such a high steam utilization will enhance the inhomogeneity of current and

harm the durability as discussed above. However, operation optimization studies that consider

both temperature inhomogeneity and current inhomogeneity have not been reported, to the

best of the authors’ knowledge. The reason is that operation optimization studies prefer to

use lumped or 1D SOEC models due to the low computational cost. It is diﬃcult for such

models to simulate the spatial inhomogeneity reliably due to the simpliﬁed geometry and

boundary conditions. 3D models can simulate the cell performance with higher reliability,

but they are too time-consuming for operation optimization studies [

]. Additionally, most

of the detailed spatial distributions simulated by 3D models are redundant for operation.

Combining experiments, multiphysics models, and fast surrogate models improve the

reliability of multiphysics models and also enable multiphysics models to be integrated into

optimization studies for fast numerical solutions [

],[

]. Xu et al. [

] built ANN surrogate

models of SOFC using multiphysics simulation data, and used the surrogate models to

optimize the power output under diﬀerent fuel ﬂow rates. Using ANN surrogate models of

SOFC, Sun et al. [

] conducted optimization with multiple objectives including production

rate, conversion rate, energy eﬃciency, and heat production. In their study, the optimization

problem was formulated to maximize the production rate while keeping the other objectives

within given thresholds. Xu et al. [

] optimized the operating parameters of an SOEC to

maintain thermo-neutral operation. From the optimization results, a four-dimensional map

was constructed, which illustrated the relationships between voltage, temperature, power

density, and gas composition under thermo-neutral operation. With this map, it is convenient

for the system operators to choose the operating parameters and ensure thermo-neutral

operation. However, the inhomogeneity of current and temperature was not considered in

these studies, and the multiphysics models used by them were veriﬁed with only the overall

IV curves.

This paper aims to combine segmented SOEC experiments, 3D multiphysics simulation,

and neural network surrogate models to optimize the homogeneity and eﬃciency of SOEC.

A 3D model of a cathode-supported SOEC is ﬁrst built to predict the inhomogeneous

distributions of current and temperature. Its reliability is veriﬁed with the current and

temperature distributions measured with a segmented SOEC. With the simulation results,

ANN surrogate models are trained to predict the current distribution and temperature

distribution under diﬀerent cell voltages, ﬂow rates, and temperatures. A multi-objective

optimization problem is formulated with the surrogate models to optimize the homogeneity,

temperature, steam utilization, voltage, and hydrogen production under diﬀerent electrolysis

powers. The multi-objective optimization problem is solved by decomposing the original

problem into a series of single objective optimization problems, whose solutions form the

Pareto front reﬂecting the conﬂicting relationship among diﬀerent objectives. The results

show that the homogeneity, cell voltage, and hydrogen production accord with each other,

while a high steam utilization degrades the homogeneity of current. If the steam utilization

is 0.7, the current of the down-stream segment will be 60%-65% of that of the up-stream

segment. To increase the steam utilization to 0.8, the current of the down-stream segment

will drop to 50%-60% of that of the up-stream segment. The optimal solution is chosen from

the Pareto front to achieve a trade-oﬀ between diﬀerent objectives. The Pareto fronts can

be easily delivered to system operators by stack manufacturers in product datasheets, so

that the former can choose the optimal operating point to balance between system eﬃciency

and inhomogeneity. In this way, the collaboration between stack manufacturers and system

operators can be enhanced.

The main contributions of this study include: (1) Segmented SOEC experiments, 3D

multiphysics simulation, and artiﬁcial intelligence are combined to build fast surrogate models

of an SOEC that can predict the electrical performance and spatial inhomogeneity of the

SOEC. With this method, the distribution of current density is considered in operation

optimization quantitatively. (2) Pareto fronts that reﬂect the conﬂicting relationships between

inhomogeneity, temperature, hydrogen production, and steam utilization are constructed.

It enables system operators to choose the optimal operating parameters, including the

temperature, the voltage, and the steam ﬂow rate, to balance between inhomogeneity and

eﬃciency.

This paper is organized as follows. Section 2 introduces the segmented SOEC experiment

and the multiphysics SOEC model. Section 3 introduces the training of the neural network

surrogate models, as well as how to formulate and solve the multi-objective optimization

problems. Section 4 discusses the validation of the models, as well as the solutions of the

multi-objective optimization problems.

2. Segmented-electrode experiments and multiphysics model

2.1. Overview of the study

An overview of this study is provided in Figure 1(a). Experiments are conducted on a

cathode-supported SOEC to measure the distributions of temperature and current density

under diﬀerent cell voltages and steam ﬂow rates. To reduce the experimental cost, the

limited experimental data are used to validate a 3D multiphysics model, which can simulate

the SOEC performance with high reliability. However, the high computational cost of the 3D

model hinders its application in optimization studies. To solve this problem, fast artiﬁcial

neural network (ANN) surrogate models are trained with the simulation data generated

by the 3D model. They can rapidly simulate the distributions of the cell characteristics,

including temperature and current density. Therefore, the surrogate models are used for

a multi-objective optimization problem to optimize objectives including the cell voltage,

temperature, hydrogen production, steam utilization, and inhomogeneity. The problem is

solved numerically, and the Pareto fronts reﬂecting the SOEC performances are constructed,

which reveals the conﬂicting relationships between multiple objectives. Optimal solutions

are chosen on the Pareto fronts, which form optimal operation curves which can achieve

a trade-oﬀ among conﬂicting objectives. The optimization results can be parameterized

and delivered to the system operators in product datasheets by the stack manufacturers, so

that system operators can choose the operating conditions to balance system eﬃciency and

inhomogeneity. In the following part of this section, the segmented SOEC experiment and

the 3D multiphysics model are introduced.

2.2. Segmented SOEC experiment

Figure 1(b) shows the segmented cell used in the experiment. The cell was a commercial

cathode-supported SOEC (ASC-10B, Elcogen AS), while the anode and cathode separators

were designed and manufactured in-house. The geometric parameters of the cell are listed

in Table 1. Figure 1(c) demonstrates the cross section of the cell assembly. Silver meshes

were attached to the cathode and anode for current collection. On the cathode side, only

one piece of silver mesh was attached, covering the active area, i.e., the area opposite to the

anode. On the anode side, three pieces of silver meshes were attached, covering the up-stream

segment, middle-stream segment and down-stream segment of the anode, respectively. The

meshes were carefully tailored to avoid short circuiting. Silver paste was applied between the

meshes and the electrodes for reliable electrical contact. The cell was assembled with the

metallic separators. The gaps between the separator and cell were sealed by mica sheets and

ceramic sealant (Alon Ceramic, Shin-Etsu Chemical). The anode separators were also divided

into three segments, corresponding to the up-stream segment, middle-stream segment and

down-stream segment, respectively. The gaps between the three anode separators were sealed

and insulated by mica sheets and ceramic sealant (Alon Ceramic, Shin-Etsu Chemical).

Figure 1(d) illustrates the schematic diagram of the test rig. The cell assembly was placed

in a quartz tube and inserted into a tubular furnace. Heat insulation wool was stuﬀed into

both ends of the quartz tube to reduce heat dissipation. Air and a mixture of steam and

hydrogen were fed to the anode side and the cathode side, respectively. The hydrogen/steam

mixture was generated by a bubbler with hydrogen being the carrier gas. The temperature

of the bubbler was controlled, and the steam partial pressure was calculated according to

the saturation vapor pressure. The pipe between the bubbler and the cell was wound with

electrical heating band to avoid water condensation. Three thermocouples were inserted

into the anode separators to measure the temperature distribution. The positive electrodes

of three power supplies were connected to the three silver meshes on the SOEC anode,

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OptimizingtheHomogeneityandEciencyofanSOECBasedonMultiphysicsSimulationandData-drivenSurrogateModelYingtianChia,b,c,KentaroYokoob,HironoriNakajimab,c,KoheiItob,c,JinLina,d,,YonghuaSonga,eaStateKeyLaboratoryofControlandSimulationofPowerSystemsandGenerationEquipment,DepartmentofElectricalEngineering...

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