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A solid oxide fuel cell (SOFC) is regarded as the first choice of highefficiency and clean power generation technology in the 21st century due to its characteristics of high power generation efficiency and low pollutant emission. In this paper, hydrogen is used as a fuel for SOFCs using the EBSILON platform. A sensitivity analysis of the solid oxide fuel cell–gas turbine (SOFC–GT) system with steam reinjection is carried out to investigate the effect of the steam reinjection mass flow rate on the improvement of the electrical efficiency of the system and on the values of the other parameters. The results show that the variation in the steam reinjection mass flow rate has an effect on other parameters. Changes in several parameters affect the electrical efficiency of the system, which reaches 74.11% at a pressure ratio of 10, SOFC inlet temperature of 783.15 K, turbine back pressure of 70 kPa, and steam reinjection mass flow rate of 6.16 kg/s. Future research can optimize the overall parameter selection of the system in terms of economy and other aspects.
In recent years, global energy shortages and global warming have led both developed and developing countries to recognize the importance of reliable and sustainable power generation (
The solid oxide fuel cell–gas turbine (SOFC–GT) system generally consists of a compressor, preheater, reformer, SOFC, combustion chamber, expander, and generator. Many scholars have analyzed and studied the SOFC–GT system (
There has been a great deal on the waste heat utilization of SOFC–GT system exhaust, and since the exhaust temperature of the SOFC–GT system is generally greater than 573.15 K, some scholars pass the exhaust into the heat recovery steam generator (HRSG) to generate superheated steam (
The SOFC–GT systems in the three studies that use steam to recover waste heat from downstream to upstream for power generation have essentially similar system structures, but there are differences. Although the structure of each system differs, the main idea of all three studies is to achieve waste heat recovery by preheating air and fuel and generating superheated steam as a way to achieve an increase in system electrical efficiency. For the way to inject steam back into the GT in the upstream SOFC–GT system for utilization, this paper is called the SOFC–GT system with steam reinjection. For the parameters of the SOFC–GT system with steam reinjection,
The literature review shows that the researchers have analyzed the parameters of the systems they have studied, establishing the relationship between the variation in the system parameters and the evaluation indicators. However, we also note that for the SOFC–GT system with steam reinjection, the researchers have studied it with a defined steam reinjection mass flow rate and have not considered the effect of changes in the steam reinjection mass flow rate on the system and other thermodynamic parameters. In this paper, hydrogen is used as the fuel of the SOFC, and the electrical efficiency of the system is used as the evaluation index to study the thermodynamic characteristics of the SOFC–GT system with steam reinjection. Moreover, this study carried out the thermodynamic analysis of system parameters such as steam reinjection mass flow rate, compressor pressure ratio, fuel cell inlet temperature, and turbine back pressure. This study focuses on the variable steam reinjection mass flow rate. By studying the influence of the change in the steam reinjection mass flow rate on the trend of the system evaluation indexes and other parameters, this study not only establishes the relationship between the system parameters and evaluation indexes but also identifies the optimal value or optimal selection range of the other thermodynamic parameters, so as to provide a reference for the engineering application of the SOFC–GT system with steam reinjection.
The research on the SOFC–GT system shows that even if the heat recovery system is set, the outlet gas temperature of pipeline 9 in
The SOFC model in this paper is based on the SOFC model in EBSILON software, but the influence of input air and fuel parameter changes needs to be considered. The power generated by the SOFC is determined according to the following equation:
It has been proven that when the SOFC inlet pressure is greater than 2 bar, the inlet pressure has a negligible effect on the SOFC electricity generation efficiency. However, the inlet temperature of the SOFC has a certain effect on the SOFC electricity generation efficiency. The relationship between SOFC electricity generation efficiency and SOFC inlet temperature was investigated by
Effect of SOFC inlet temperature on electricity generation efficiency.
The SOFC electricity generation efficiency in Eq.
The mass conservation equation for each component in the fuel cell is shown in Eq.
The compressor is used to increase the pressure of liquid from the condenser, and the outlet pressure of the compressor can be calculated as
Neglecting the heat loss of the compressor, its isentropic efficiency is defined as shown in Eq.
Since the gas mixture is an ideal gas, the isentropic enthalpy of the compressor can be derived from Eq.
The outlet pressure of the turbine can be found using
Similar to the compressor, the isentropic temperature for TUR adiabatic operation can be found when the gas mixture is an ideal gas, and the isentropic enthalpy can be determined from the isentropic temperature. The isentropic enthalpy is incorporated into Eq.
From this, the work done by the turbine can be found according to the following equation (
Neglecting the heat dissipation loss in the AB, the temperature of the gas mixture after complete combustion of the fuel is obtained according to the following equation (
The temperature after the mixing of steam with the outlet gas of the AB can be obtained according to Eq.
The HRSG consists of an economizer, evaporator, and superheater. The HRSG composite curve of hot and cold streams is depicted in
HRSG temperature profile.
The difference between the outlet temperature of the economizer and the temperature of saturated vapor is called the approach point (ΔT_{ap}). ΔT_{ap} can be ignored in the vertical tube economizer (
In addition, the pinch point of the waste heat boiler is defined as
From
For the evaporation region, the relation is given by
For the superheated region, the relation is given by
The power generated by the GEN is derived from the following equation:
The calculation flowchart of this paper is shown in
Calculation flowchart of system electrical efficiency.
The thermal performance of the system scheme can be studied by establishing a simulation model. In this paper, the simulation models of the SOFC–GT system without steam reinjection and SOFC–GT system with steam reinjection are built using EBSILON software developed by STEAG Power.
In order to verify the accuracy of the computational model and related calculation methods used in this paper, the simulation results of the SOFC–GT system without steam reinjection were compared with the relevant data in the work of
SOFC–GT system simulation results.
Literature ( 
Modeling system  Relative error (%)  

Operation temperature of the SOFC (K)  1,217.15  1,215.03  0.17 
Inlet temperature of the TUR (K)  1,409.15  1,412.90  0.27 
Generating power of the SOFC (kW)  359.00  359.354  0.09 
Generating power of the GEN (kW)  104.00  104.849  0.82 
System exhaust temperature (K)  890.15  886.23  0.44 
As can be seen from
In this section, the SOFC–GT system with steam reinjection is compared with the SOFC–GT system without steam reinjection through simulation, while the system parameter settings are given in
System design parameter.
Equipment parameter  Value  Unit 

General  
Ambient temperature  293.15  K 
Ambient pressure  101.33  kPa 
Air mass flow rate  40.00  kg/s 
Hydrogen mass flow rate  1.00  kg/s 
Temperature of working water  293.15  K 
Inlet water temperature  101.33  kPa 
SOFC  
Temperature of inlets  783.15  K 
Temperature of outlets  1,273.15  K 
Pressure drops  10.00  kPa 
Fuel utilization rate  85.00  % 
Cell voltage  1.20  V 
Other equipment  
Compressor isentropic efficiency  85.00  % 
Turbine isentropic efficiency  90.00  % 
Mechanical shaft efficiency  99.00  % 
Pump isentropic efficiency  80.00  % 
Mechanical pump efficiency  99.80  % 
Generator efficiency  98.56  % 
Combustion efficiency  100.00  % 
AB pressure drop  60.00  kPa 
Heat exchanger pressure drop  1.00  kPa 
For SOFC–GT systems with steam reinjection, when the pressure loss of each piece of equipment in the system is fixed, the pressure ratio determines the outlet pressure of the AB. The pressure of the injected steam is set to 1 kPa above the pressure at the outlet of the AB so that the pressure ratio determines the pressure of the injected steam. The temperature of the injected steam is determined by the terminal temperature difference of the HRSG. The saturation temperature of the steam,
Since the temperature and mass flow rate of the flue gas are constant, i.e.,
Calculation results of system parameters at each point.
SOFC–GT system without steam reinjection  SOFC–GT system with steam reinjection  

Node  Temperature (K)  Pressure (kPa)  Mass flow rate (kg/s)  Temperature (K)  Pressure (kPa)  Mass flow rate (kg/s) 
1  293.00  101.33  40.00  293.15  101.33  40.00 
2  293.00  101.33  1.00  293.15  101.33  1.00 
3  607.17  1,013.25  40.00  607.17  1,013.25  40.00 
4  612.93  1,013.25  1.00  612.93  1,013.25  1.00 
5  783.15  1,013.05  40.00  783.15  1,013.05  40.00 
6  783.15  1,013.05  1.00  783.15  1,013.05  1.00 
7  1,572.61  943.05  41.00  1,572.61  943.05  41.00 
8  1,033.36  110.00  41.00  913.63  110.00  49.13 
9  856.33  108.90  41.00  776.27  109.00  49.13 
10  —  —  —  293.15  101.33  8.13 
11  —  —  —  293.21  949.00  8.13 
12  —  —  —  766.27  944.00  8.13 
13  —  —  —  1,383.45  943.05  49.13 
14  —  —  —  373.62  108.90  49.13 
Calculation results of the energy efficiency of the key equipment of the system.
SOFC–GT system without steam reinjection  SOFC–GT system with steam reinjection  

Power consumption of the AC (MW)  12.993  12.993 
Power consumption of the FC (MW)  4.681  4.681 
Power consumption of the WP (MW)  —  0.009 
Mechanical power of the TUR (MW)  32.472  36.591 
Electrical power of the SOFC (MW)  69.778  69.778 
Electrical power of the GEN (MW)  14.585  18.645 
Electrical power of the system (MW)  84.363  88.423 
System electrical efficiency (%)  70.14  73.52 
In this section, to study the effect of steam reinjection mass flow rate on the SOFC–GT system with steam reinjection, the AC and FC pressure ratio is set to 10, the SOFC inlet temperature is 783 K, and the TUR back pressure is set to 110 kPa. The steam reinjection mass flow rate can vary from 0 kg/s to the maximum value that can be achieved.
Effect of steam reinjection mass flow rate on system electrical efficiency, steam temperature, and system exhaust temperature.
The SOFC inlet pressure at greater than 200 kPa has no significant effect on the efficiency of the SOFC, but the change in pressure ratio will cause a change in compressor power consumption. At the same time, it will also affect the pressure of reinjection steam and, thus, affect the electrical efficiency of the system. In this section, we aim to study the effect of the pressure ratio on the SOFC–GT system with steam reinjection. The inlet and outlet temperature and power generation of the SOFC do not change, and only the inlet and outlet pressures are changed. In other words, it is considered that the change in air and fuel pressure has no influence on the SOFC. In addition, the TUR back pressure is fixed at 110 kPa.
Effect of pressure ratio on maximum steam reinjection mass flow rate and system electrical efficiency.
In addition, it is easy to see from
The inlet temperature of the SOFC has a significant effect on the electrical efficiency of the SOFC in a certain temperature range, as shown in
The effect of the steam reinjection mass flow rate on system electrical efficiency at different SOFC inlet temperatures is given in
The variation in system electrical efficiency with SOFC inlet temperature for different steam reinjection mass flow rates is given in
The effect of SOFC inlet temperature on the maximum steam reinjection mass flow rate and the maximum system electrical efficiency is given in
Maximum steam reinjection mass flow rate and maximum system electrical efficiency curves at different SOFC inlet temperatures.
According to
For SOFC–GT systems with steam reinjection, it is possible to take a lower value than atmospheric pressure for the turbine back pressure due to the fact that the steam generated from the waste heat is passed into the turbine, which increases the humidity of the gas mixture in the turbine. Therefore, it is necessary to study the effect of the variation of the turbine back pressure on the power generation efficiency of the system. Under certain conditions, decreasing the TUR back pressure will make the TUR work capacity increase but will reduce the TUR exhaust temperature resulting in a reduction of heat recovery. In addition, when the back pressure is lower than atmospheric pressure, additional fans are needed to draw the spent gas out of the system and provide resistance to overcome the flue gas side of the HRSG, which will eventually exhaust the flue gas to the atmosphere. At this time, the influence of fan power WF should be considered in the calculation of system electrical efficiency. In other words, the system electrical efficiency at this time can be obtained according to the following equation:
For the system studied in this paper, the system exhaust pressure is equal to the TUR back pressure minus the pressure losses in the PH and HRSG. No additional treatment is performed when the system exhaust pressure is higher than atmospheric pressure. When the system exhaust is below atmospheric pressure, the system exhaust is pumped out of the system using a fan, and the fan outlet pressure is set to 105 kPa. When studying the effect of TUR back pressure on system electrical efficiency, the pressure ratio is taken as 10 and the SOFC inlet temperature is taken as 783.15 K.
Maximum steam reinjection mass flow rate and maximum system electrical efficiency curves at different TUR back pressures.
When the system exhaust pressure is lower than the ambient pressure, additional fans are needed to pump out the system exhaust; furthermore, when the exhaust pressure decreases, the power consumption of the fans increases. Since the inlet pressure of the TUR remains constant, when the back pressure of the TUR is reduced, the expansion ratio of the system increases, causing the TUR to perform more work and making the GEN generate more power. The more the steam injected, the greater the influence of TUR work increase caused by the decrease in TUR back pressure. Therefore, when the steam reinjection mass flow rate exceeds 3 kg/s, the electrical efficiency of the system increases with the decrease in the back pressure of the TUR.
Furthermore, the lower the TUR exhaust pressure, the higher the electrical efficiency of the system. However, if the exhaust pressure is lower than 1 atm, the equipment will be in vacuum, which increases the cost and manufacturing difficulty of the equipment. Therefore, the choice of system exhaust pressure is generally greater than the atmospheric pressure.
(1) Due to the steam reinjection system, the mass flow rate of the working medium in the turbine increases, and the exhaust temperature of the system decreases significantly. Therefore, the electrical efficiency of the SOFC–GT system with steam reinjection is higher than that of the SOFC–GT system without steam reinjection, and the higher the mass flow rate of steam reinjection, the higher the electrical efficiency of the system. However, because the steam pressure is limited by the compressor pressure ratio, there is a maximum steam reinjection mass flow rate.
(2) When the SOFC inlet temperature and turbine back pressure are given, there is an optimal pressure ratio to maximize the electrical efficiency of the system. The optimal pressure ratio increases with the increase in the steam reinjection mass flow rate. For a given SOFC inlet temperature and turbine back pressure, the maximum system electrical efficiency can reach 73.93% considering the effect of steam reinjection mass flow rate and pressure ratio on the system electrical efficiency. At this time, the pressure ratio is 15, and the steam reinjection mass flow rate is 7.56 kg/s.
(3) Through the study of the steam reinjection mass flow rate and SOFC inlet temperature, it is found that there is an SOFC inlet temperature which can make the system achieve the maximum electrical efficiency. When the steam reinjection mass flow rate increases, the optimal SOFC inlet temperature tends to decrease, but the influence degree is small. When the pressure ratio is 10 and the turbine back pressure is 110 kPa, considering the influence of steam reinjection mass flow rate on the SOFC inlet temperature, the steam reinjection mass flow rate is 8.56 kg/s, and the electrical efficiency of the system is 73.71%. At this point, the SOFC inlet temperature is 763.15 K.
(4) The influence of turbine exhaust pressure on the electrical efficiency is more complex. The optimal turbine back pressure exists when the steam reinjection mass flow rate is small; however, when the steam reinjection mass flow rate is greater than or equal to 3 kg/s, the lower the turbine exhaust pressure, the higher the system electrical efficiency. At the pressure ratio of 10 and SOFC inlet temperature of 783.15 K, the maximum steam reinjection mass flow rate is 6.16 kg/s, and the electrical efficiency of the system reaches 74.11%.
The original contributions presented in the study are included in the article/Supplementary Material; further inquiries can be directed to the corresponding author.
HZ: writing–original draft and writing–review and editing. PZ: writing–review and editing. QZ: writing–review and editing. XZ: writing–review and editing. ZL: writing–review and editing. ZF: writing–review and editing. TL: writing–review and editing. RS: writing–review and editing. JC: writing–review and editing.
The author(s) declare financial support was received for the research, authorship, and/or publication of this article. This research was supported by the Department of Science and Technology of Gansu Province under the contract No. 22ZD11GA314.
The authors gratefully acknowledge the financial support of the Department of Science and Technology of Gansu Province (No. 22ZD11GA314). Thanks are also given to the editors and reviewers for their comments and contributions to this work.
Author ZL was employed by Gansu Diantong Power Engineering Design Consulting Co., Ltd.
The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.
All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors, and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

Specific enthalpy (kJ/kg) 

Mass flow rate (kg/s) 

Pressure (kPa) 

Chemical reaction rate (mol/(L*s)) 

Absolute temperature (K) 

Fuel utilization (%) 

Chemical reaction equivalence factor 

Power (kW) 



Afterburner 

Air compressor 

Specific heat at constant pressure (kJ/(kg*K)) 

Fuel compressor 

Generator 

Heat recovery steam generator 

Low calorific value 

Mixer 

Preheater 

Solid oxide fuel cell 

Turbine 

Water pump 



System electrical efficiency (%) 

Isentropic efficiency of equipment (%) 

Pressure ratio or expansion ratio 

Heat capacity ratio 



Approach point 

Terminal temperature difference 

Fuel 

Gas composition 

Chemical reaction component 

Mechanical 

Pinch point 

Steam 