## Abstract

In this study, four solid oxide fuel cell (SOFC) power plants, with natural gas (NG) as the fuel source, that account for long-term degradation were designed and simulated. The four candidate SOFC plants included a standalone SOFC plant, a standalone SOFC plant with a steam bottoming cycle, an SOFC/ (gas turbine) GT hybrid plant, and an SOFC/GT hybrid plant with a steam bottoming cycle. To capture dynamic behaviors caused by long-term SOFC degradation, this study employed a pseudo-stead-state approach that integrated real-time dynamic 1D SOFC models (degradation calculation embedded) with steady-state balance-of-plant models. Model simulations and eco-techno-economic analyses were performed over a 30-year plant lifetime using matlab simulink R2017a, aspen plus V12.1, and python 3.7.4. The results revealed that, while the standalone SOFC plant with a steam bottoming cycle provided the highest overall plant efficiency (65.0% LHV), it also had high SOFC replacement costs due to fast degradation. Instead, the SOFC/GT hybrid plant with a steam bottoming cycle was determined to be the best option, as it had the lowest levelized cost of electricity ($US 35.1/MWh) and the lowest cost of CO_{2} avoided (−$US100/ton CO_{2}e).

## 1 Introduction

Solid oxide fuel cells (SOFCs) produce electricity through electrochemical reactions by utilizing fuel gases including, but not limited to, hydrogen gas, syngas, and natural gas (NG). SOFCs are considered as a next-generation power production technology that can provide greater efficiency and lower greenhouse gas emissions compared to conventional power plants [1]. However, the large-scale commercialization of SOFCs is limited, as their lifetime is constrained due to degradation. In constant power output operation mode—also known as baseload power production—SOFC degradation occurs quickly as a result of the increasing current density (to maintain a constant power output) [2,3]. One approach to overcoming these degradation issues is to slow the degradation rate by developing new materials that degrade more slowly [4], while another option is to keep the existing materials, but change the operating strategies or conditions [2].

Previous findings have shown that operating an SOFC in constant voltage mode instead of constant power mode can slow its degradation and significantly increase its lifetime. The strategy behind using constant voltage mode is to allow the current density to decrease over time, thereby slowing degradation [2]. However, as the current density decreases, the power output also decreases, which is not useful for baseload power production. In addition, fuel utilization (FU) also decreases over time in constant voltage mode, which causes the heating value of the anode exhaust gas stream from the SOFC to increase. SOFC/GT hybrid systems are predicated on using a gas turbine (GT) to capture this growing output of surplus chemical energy and using it to produce power. Integrating a GT into the SOFC system is advantageous, as it allows the SOFC stack to be operated in constant voltage mode, which slows SOFC degradation, and provides a means of harnessing the unspent fuel from the SOFC exhaust to compensate for the decline in power output as the SOFC ages. Thus, the net outcome is a (near) baseload power system wherein the power load gradually shifts from the SOFC to the GT [5]. Furthermore, the lifetime of the SOFC stack in a hybrid system in constant voltage mode can be more than ten times longer than the lifetime of an SOFC stack in a standalone system operated in constant power mode [6]. The SOFC/GT hybrid concept has been the focal point of various types of studies, including modeling and control [7–9], efficiency and exergy analysis [10–12], system optimization [13–17], and technoeconomic analysis [18–21]. However, very few of these studies have accounted for long-term degradation in their model simulations.

Researchers have developed different SOFC degradation models for various degradation mechanisms including Ni coarsening and oxidation [22–25] and sulfur poisoning [3,26,27]. On the other hand, researchers have also conducted a number of degradation studies focusing on different SOFC components, such as the anode [22,26,28–30], cathode [31,32], electrolyte [33,34], and interconnects [35]. Recently, Naeini et al. developed a degradation model that integrates existing models of most degradation mechanisms in the literature, including Ni coarsening and oxidation, sulfur poisoning, and changes in anode pore size, conductivity, and electrolyte conductivity [36]. Instead of focusing on the degradation mechanisms, Abreu-Sepulveda et al. examined how operating conditions such as current density and fuel utilization in real-time operation impact the overall SOFC degradation rate [37]. Subsequently, Zaccaria et al. upgraded Abreu-Sepulveda et al.’s model to account for temperature effects as well as local behaviors [38]. For this work, we have selected the degradation model developed by Zaccaria et al. [38], which is an empirical model derived from experimental data for SOFC standalone and SOFC/GT systems. Thus it is most suitable for our application. A comparison of the degradation models in the literature is outside the scope of this work.

In our previous work, we designed and conducted eco-technoeconomic analyses (eTEAs) of coal-powered SOFC/GT hybrid plants and standalone SOFC plants accounting for long-term degradation effects [6]. With the exception of our prior work using coal, we are unaware of any eTEAs of SOFC/GT hybrid plants that consider long-term degradation effects over the plant’s lifetime. Systems that incorporate the SOFC/GT concept have been studied with respect to one or more of the following topics: economy, energy, exergy, thermal management, and environment [21,39–43]. However, all of these works assumed the use of a steady-state system and did not consider long-term degradation. We believe that long-term degradation plays an important role in the eTEA of SOFC/GT hybrid systems, as it strongly affects the performance and the lifetime of the SOFC, especially when a long period of time is considered (e.g., a 30-year plant lifetime). Moreover, when considering long-term SOFC degradation, it is important to consider that the GT’s power production increases over time; as such, the GT should be designed to reach its maximal efficiency and power capacity at the end of the SOFC’s lifetime. To this end, a GT characteristic curve should be used, as the GT’s power and efficiency change with load. The dynamic behaviors of the SOFC and the GT in a hybrid system affect the eTEA results and cannot be captured by steady-state simulations. In our previous study, we utilized a pseudo-steady-state approach—which integrated both dynamic models and steady-state models—to capture the dynamic behaviors of SOFC/GT plants and to conduct an eTEA of coal-powered SOFC/GT plants and standalone SOFC plants [6]. In the present study, we build on our previous eTEA by examining large-scale SOFC/GT hybrid plants and standalone SOFC plants that use NG rather than coal as the fuel source, while also considering the effects of long-term degradation. To conduct our analysis, we designed several different NG-powered standalone SOFC plants and SOFC/GT plants and subjected them to simulations. In the dynamic simulations, controllers were upgraded from the previous work to increase system stability. The modeling process is detailed in the next section.

## 2 Process Modeling

### 2.1 Process Overview.

Four base cases were selected for the long-term eTEA studies: Base Case 1—standalone SOFC plant; Base Case 2—standalone SOFC plant with a steam bottoming cycle; Base Case 3—SOFC/GT hybrid plant; and Base Case 4—SOFC/GT hybrid plant with a steam bottoming cycle. The process flow diagrams for the four base cases are shown in Fig. 1.

As shown in Fig. 1(a), Base Case 1 has two main components: an SOFC stack with a post-combustor, and an upstream syngas production process. The upstream syngas process produces raw syngas by reforming natural gas from the natural gas pipeline. Table 1 shows the conditions of the natural gas received from the pipeline [44]. Once the raw syngas has been produced, it is converted to hydrogen-rich syngas (around 60 mol% H_{2}) using water-gas shift reactors. Although SOFCs can directly take CH_{4} as a fuel source, findings have shown that degradation can be slowed by using fuel gas with lower concentrations of CH_{4} and higher concentrations of H_{2}. Since the SOFC stack is operated at near atmospheric pressure, a multi-stage turbine is employed to reduce the anode upstream pressure and to produce extra power. The exhaust gas from the post-combustion provides heat for the inter-heater in between the turbines, as well as for the cathode inlet air stream. Base Case 2 (Fig. 1(b)) is identical to Base Case 1, except a steam bottoming cycle has also been added to capture the waste heat from the exhaust gas to produce extra power. The steam bottoming cycle consists of a water tank, a pump, a steam generator (heat exchanger between the flue gas and water), a multi-stage steam turbine, and a condenser.

Pressure | 3 MPa |

Temperature | 27 °C |

Composition (molar) | |

CH_{4} | 0.931 |

C_{2}H_{6} | 0.032 |

C_{3}H_{8} | 0.007 |

C_{4}H_{10} | 0.004 |

CO_{2} | 0.010 |

N_{2} | 0.016 |

Pressure | 3 MPa |

Temperature | 27 °C |

Composition (molar) | |

CH_{4} | 0.931 |

C_{2}H_{6} | 0.032 |

C_{3}H_{8} | 0.007 |

C_{4}H_{10} | 0.004 |

CO_{2} | 0.010 |

N_{2} | 0.016 |

The SOFC/GT hybrid plant (Base Case 3, Fig. 1(c)) consists of three main components: an SOFC stack with a post-combustor, an upstream syngas production process, and a gas turbine equipped with a compressor and recuperator. The SOFC portion and the upstream syngas process are almost identical to those in Base Case 1; however, the hybrid plant in Base Case 3 requires a single stage in the upstream, as the SOFC stack is operated at 4 bar. Cold air bypass streams are designed to control the cathode inlet temperature and the gas turbine inlet temperature. Base Case 4 (Fig. 1(d)) utilizes the same design as Base Case 3, only it also features the addition of a steam bottoming cycle.

### 2.2 Plant Models.

A dynamic SOFC model and a steady-state balance-of-plant model were developed for each base case. The reason for choosing this hybrid modeling approach rather than completely dynamic modeling or completely steady-state modeling was that the dynamic behaviors of the SOFC (due to degradation) are vital for the eTEA while the dynamic behaviors of the balance-of-plant have insignificant impacts. Developing dynamic models for the balance-of-plant is out of the scope of this study. Instead, we took a pseudo-steady-state approach to integrate and simulate the dynamic SOFC model and the steady-state balance-of-plant model, which will be described in later section. The dynamic SOFC models contained the SOFC stack and the post-combustor and provided real-time calculations of thermal and electrochemical changes in the SOFC, as well as degradation. The steady-state balance-of-plant models included everything shown in Fig. 1, with the exception of the SOFC stack and the post-combustor. For instance, the balance-of-plant model for Base Case 1 included the reformer, water-gas shift process, multi-stage turbine, air blower, and heat exchangers.

#### 2.2.1 Dynamic SOFC Model.

Equation (1) describes the effect of degradation on the SOFC in the model, where *r*_{d}, FU, *T*, and *i* represent the degradation rate (in percentage/(1000 h)), fuel utilization (in fraction), temperature (in Kelvin), and current density (in Ampere per square centimeter), respectively. This equation was derived via regression analysis and extrapolation using prior experimental data. The process used to obtain Eq. (1) is described in greater detail in Refs. [37,38]. The degradation rate is calculated in terms of percent of voltage drop per thousand hours, and is used to calculate the effect of degradation on ohmic resistance and cell voltage. The model was implemented in matlab simulink r2017a and subsequently modified and augmented with upgraded controllers.

The dynamic model of Base Case 1 has three feedback controllers: an SOFC power output controller that manipulates the SOFC load (current); an SOFC fuel utilization controller that manipulates the anode inlet fuel flowrate; and an SOFC average cell temperature controller that manipulates the cathode inlet air flowrate. A different control strategy was implemented in Base Case 3, which included: a feedback net power controller that manipulates the anode inlet fuel flowrate; a feedback voltage controller that manipulates the SOFC load (current); and a feedforward SOFC average cell temperature controller that manipulates the cold air bypass valves (thus adjusting the cathode inlet air temperature). As the SOFC degrades over time, the amount of unspent fuel in the anode exhaust increases, which results in a corresponding increase in the post-combustor exhaust temperature. This is a concern, as, without proper controls, this can eventually result in the gas turbine inlet temperature rising to unacceptable levels. Thus, the cold air bypass streams manipulated by the controllers help to ensure that the gas turbine inlet temperature and the SOFC average cell temperature remain in acceptable ranges.

In Base Case 3, the net power controller moderated the net power of the system by using the predicted gas turbine power production to determine the adjustment of the anode inlet fuel flowrate (which affects the power production of both the SOFC and the gas turbine). However, as the SOFC degrades, the fuel flowrate and the heating value of the post-combustor exhaust change, which affects the power and efficiency of the gas turbine due to off-design operations. As such, a gas turbine characteristic curve correlating efficiency with power production for off-design operations was employed to predict the GT’s power production while also accounting for off-design efficiency changes in different operating conditions (heating value of the gas turbine inlet stream). As this curve was generated using proprietary data from a turbine manufacturer (Siemens), it cannot be released for intellectual property reasons. However, this curve was embedded in the model and grouped with other information for reproduction purposes, which will be explained in Sec. 2.3.1. Base Cases 2 and 4 used the same control strategies as Base Cases 1 and 3, respectively. All controllers used in this work were proportional-integral-derivative controllers, with manual tuning techniques being used to determine the tuning parameters.

#### 2.2.2 Steady-State Balance-of-Plant Model.

For each base case, the balance-of-plant, which includes every unit (as shown in Fig. 1) except the SOFC stack and the post-combustor, was modeled in aspen plus v12.1. The advantage of modeling the balance-of-plant in aspen plus is that it reduces modeling complexity while still providing representations of the system and equipment sizes that are sufficient for conducting the eTEA. In aspen plus, the Peng–Robinson EOS was used along with the Boston–Mathias modification for most of the units except that the NBC/NRC steam tables were used for pure water streams. A detailed discussion on the selection of the thermodynamic method and the accompanying assumptions is available in Refs. [48,49].

The balance-of-plant model for Base Case 1 included the reformer, water-gas shift reactors, upstream multi-stage turbine, air blower, and heat exchangers and pumps responsible for heat management and steam generation (for the water-gas shift). The isentropic efficiency of the multi-stage turbine was assumed to be 88% without considering a turbine characteristic curve. The turbine accounted for around 12% of the plant’s gross power production, which refers to the plant’s total power production before subtracting any power consumption. A turbine characteristic curve was not implemented in this case because it would increase the model’s complexity while only altering the gross power production by around 0.6%. The air blower was assumed to have a constant isentropic efficiency of 90%. Since the blower consumed a negligible amount of electricity, an efficiency characteristic curve was not considered. The heat exchangers were designed by assuming a minimum temperature approach of 10 °C. The net power of the balance-of-plant contributed around 9% of the entire plant’s net power.

The balance-of-plant model for Base Case 2 included all the same units as the Base Case 1 model, along with a steam bottoming cycle. The steam cycle consisted of a water pump, a heat exchanger (a steam generator that uses heat from the flue gas), a multi-stage steam turbine, a cooler (condenser), and a water tank. The steam cycle was operated with the multi-stage turbine inlet steam conditions set to 550 °C and 100 bar, with hot bypasses between the stages to ensure 100% vapor fraction within the entire turbine unit. It was assumed that the pump had 90% efficiency, the heat exchanger (the steam generator) had a minimum temperature approach of 10 °C, the condenser had 5 °C of subcooling, and the steam turbines had 89% isentropic efficiency. The outlet pressure and hot bypass ratio of each stage in the multi-stage turbine were determined using the optimization tool in aspen plus in an attempt to maximize power production while still achieving 100% vapor fraction between the stages and at least 95% vapor fraction in the outlet stream. The optimal outlet pressures of the three stages were determined to be 24.7 bar, 4.7 bar, and 1.1 bar, with bypass ratios of 8% and 2% of the total steam to the medium- and low-pressure turbines, respectively. Similar to the upstream turbines, a characteristic curve was not implemented in steam turbines because it would increase the model’s complexity while only altering the gross power production by around 1.3%.

The upstream process in the Base Case 3 balance-of-plant model was almost identical to Base Case 1, except the Base Case 3 model only used a single-stage turbine, as the SOFC stack was operated at a pressure of 4 bar instead of 1 bar. The net power and electrical efficiency of the gas turbine (including the compressor) were determined using the aforementioned gas turbine characteristic curve. In addition, a heat exchanger model was used to represent the recuperator by assuming a minimum temperature approach of 10 °C.

The balance-of-plant model for Base Case 4 was largely the same as the Base Case 3 model, except it also included a steam bottoming cycle with a similar setup to the one used in Base Case 2. Since the heating value of the flue gas in Base Case 4 was much lower than that of Base Case 2, the inlet steam conditions to the multi-stage steam turbine were set to 294 °C and 25 bar. Additionally, the same optimization approach that was used for Base Case 2 was applied in Base Case 4, which yielded optimal outlet pressures of 5.3, 3.3, and 1.1 bar for the three steam turbine stages, with a bypass ratio of 35% of the total steam to the medium pressure turbine.

### 2.3 Pseudo-Steady-State Model Simulation.

To perform model simulations for the eTEA, the conditions for the four base cases are summarized in Table 2, which are the same for all four cases. The four base cases were designed with a net electricity production of 550 MW (combined AC and DC) and a plant lifetime of 30 years. The SOFC average cell temperature for each case was regulated at 830 °C by the controllers described in Sec. 2.2.1. The dynamic models were simulated using input variables (either their constant values or their initial values) and predicted variables, which are presented in Table 3. Base Case 1 utilized an SOFC stack operated in constant power mode; however, the stack power allowed for a small and slow drop (around 1.8%) over the cell’s lifetime in order to maintain constant net power production for the entire plant. The model simulations were conducted by integrating the dynamic model parts and steady-state model parts with a pseudo-steady-state approach. A time-step of one week was selected for the pseudo-steady-state simulation, as the SOFC degradation rate did not change much (change within 0.5% relatively) during this time interval. It was assumed that the dynamic behaviors of the dynamic models within a weekly time-step could be treated as steady-state at the start of the time-step. The simulation data from the dynamic models were recorded with a sampling time of 0.08 h, and the weekly data were then collected and used to run the simulations for the steady-state models. The simulation processes are described in detail in the following subsections.

Net power | 550 MW |

Plant lifetime | 30 years |

Initial FU (fuel utilization) of SOFC | 80% |

Initial current density of SOFC | 0.5 A/cm^{2} |

SOFC average cell temperature | 830 °C |

Net power | 550 MW |

Plant lifetime | 30 years |

Initial FU (fuel utilization) of SOFC | 80% |

Initial current density of SOFC | 0.5 A/cm^{2} |

SOFC average cell temperature | 830 °C |

Trend | Note | |||
---|---|---|---|---|

Base Case 1: SOFC standalone | Base Case 3: SOFC/GT hybrid | |||

Operating variables | Stack power | 1.8% | 71% | Controlled or being affected by other operating variables |

Voltage | 20% | → | ||

Current density | 23% | 70% | ||

Fuel utilization | → | 76% | ||

Average cell temperature | → | 2.4% | ||

Turbine power and efficiency | N/A | 67%(power) 31%(efficiency) | Predicted by reduced model to be matched by outputs from aspen plus model | |

Inlet variables | Fuel flow | 22% | 25% | The outputs of aspen plus simulations should match the values of these variables at each time-step. Fuel flow and air flow in Base Case 1, and fuel flow and air temperature in Base Case 3 were manipulated by controllers. The others were constant. |

Fuel temperature | → | → | ||

Fuel pressure | → | → | ||

Fuel composition | → | → | ||

Air flow | 28% | → | ||

Air temperature | → | 17% | ||

Air pressure | → | → | ||

Outlet variables | Combusted gas flow | 27% | 1.7% | Provided as inputs to aspen plus model |

Combusted gas temperature | 0.8% | 44% | ||

Combusted gas pressure | → | → | ||

Combusted gas composition | → | → |

Trend | Note | |||
---|---|---|---|---|

Base Case 1: SOFC standalone | Base Case 3: SOFC/GT hybrid | |||

Operating variables | Stack power | 1.8% | 71% | Controlled or being affected by other operating variables |

Voltage | 20% | → | ||

Current density | 23% | 70% | ||

Fuel utilization | → | 76% | ||

Average cell temperature | → | 2.4% | ||

Turbine power and efficiency | N/A | 67%(power) 31%(efficiency) | Predicted by reduced model to be matched by outputs from aspen plus model | |

Inlet variables | Fuel flow | 22% | 25% | The outputs of aspen plus simulations should match the values of these variables at each time-step. Fuel flow and air flow in Base Case 1, and fuel flow and air temperature in Base Case 3 were manipulated by controllers. The others were constant. |

Fuel temperature | → | → | ||

Fuel pressure | → | → | ||

Fuel composition | → | → | ||

Air flow | 28% | → | ||

Air temperature | → | 17% | ||

Air pressure | → | → | ||

Outlet variables | Combusted gas flow | 27% | 1.7% | Provided as inputs to aspen plus model |

Combusted gas temperature | 0.8% | 44% | ||

Combusted gas pressure | → | → | ||

Combusted gas composition | → | → |

Note: The sparklines represent the trends of each variable over time during simulation along with their relative change ranges (e.g., the stack power in Base Case 1 decreased by 1.8% over the lifetime of the SOFC) → indicating a constant value or variable controlled at a constant setpoint).

#### 2.3.1 Control Strategy in Dynamic Model Accounting for Balance-of-Plant Model.

The control strategy in Base Case 1 aimed to maintain a constant net power output (the net power of the SOFC and the balance-of-plant), a constant FU, and a constant *T* (SOFC average cell temperature). The power controller in the dynamic model adjusted the SOFC power to follow a decreasing trajectory such that the system could achieve constant net power with the addition of the power produced by the balance-of-plant. This outcome is possible due to the fuel flowrate increasing as the SOFC degrades over time, which in turn causes an increase in the power produced by the upstream multi-stage turbine. This decreasing SOFC power trajectory was determined manually through an iterative approach. The trajectory was described using second-order polynomial with respect to time. The coefficients of the polynomial were first guessed using information from preliminary simulations, and then iteratively refined by running additional simulations with repeatedly updated coefficients. Only a few iterations were required to reach a final trajectory which achieves essentially constant net system power output (with small variations) as determined by visual inspection.

As can be seen in Table 3, the power setpoint trajectory entailed a slow decrease in the SOFC’s power over its lifetime, while maintaining the plant’s net power at 550 MW. Base Case 2 had the same control strategy as Base Case 1, only it used a different second-order polynomial trajectory for the power controller setpoint. In Base Case 2, the steam bottoming cycle also contributed to the balance-of-plant power production by harnessing the increasing heating value of the SOFC’s exhaust stream as the SOFC degraded. Following a similar process to Base Case 1, the second-order polynomial trajectory for the power controller in Base Case 2 was determined iteratively as well.

The control strategy used in Base Case 3 entailed maintaining a constant net power, a constant voltage, and a constant *T*. In this SOFC/GT hybrid plant, the SOFC power decreased as it degraded, but the voltage was kept constant (Table 3). On the other hand, the GT harnessed the increasing heating value of the SOFC exhaust stream, allowing it to increase in its power output and efficiency (calculated according to the embedded turbine characteristic curve discussed earlier). In the dynamic model, the net power controller manipulated the anode inlet fuel flow based on information about the power produced by the balance-of-plant (mainly consisting of the power from the GT and upstream turbine) in order to obtain the SOFC power required for achieving a constant net plant power. A model-based controller was used for determining the SOFC power setpoint based on the heating value of the SOFC exhaust to try to achieve 550 MW net power. The model-based controller considered information about the GT characteristic curve, heating value of the SOFC exhaust, upstream turbine power, compressor parasitic loads, and pump parasitic loads. This significantly outperformed a PID controller (refer to Appendix A available in the Supplemental Materials on the ASME Digital Collection). The control strategy used in Base Case 4 was the same as in Base Case 3, except that the balance-of-plant power also included the power produced by the steam bottoming cycle.

#### 2.3.2 Simulation Methodology.

The model simulation of each base case involved a combination of dynamic model simulation of the SOFC stack and post-combustor in matlab simulink and steady-state model simulation of the balance-of-plant in aspen plus. To capture the slow dynamics due to SOFC degradation over a long time period, a pseudo-steady-state approach was employed for the combination of dynamic and steady-state model simulations. During the pseudo-steady-state simulations, the conditions of certain streams connecting the dynamic SOFC model and the steady-state balance-of-plant model should be consistent. For instance, in Base Case 4, the conditions of streams 3, 4, and 8 (Fig. 1) computed by the dynamic and steady-state models should be consistent for each time-step. Similarly, variables such as the GT power predicted by the dynamic model and the actual GT power computed by the steady-state model should be consistent for each time-step. Therefore, an iterative solution is required to converge the combined simulation of the dynamic model and steady-state model for each time-step. Solution algorithms were developed as python (python 3.7.4) scripts and matlab scripts to automate the entire simulation for each base case. Specifically, the matlab script was employed to initiate the dynamic simulink model simulation, record the resultant data, and save the data as text files that could be read by the python script. On the other hand, the python script read the data from matlab, initiated the steady-state aspen plus model simulation, and then recorded and checked whether the simulation results from the dynamic and steady-state models matched within a certain error tolerance. In addition to the pseudo-steady-state simulation, the initial conditions of the dynamic model for each case were changed and tested such that the initial current density, initial voltage, and initial fuel utilization were approximately the same for all cases.

Figure 2 shows the information flow between the dynamic model and the steady-state model at one pseudo-steady-state time-step for Base Case 3. As can be seen, some inlet variables (box A1, Fig. 2) were constant through every time-step, including the temperature, pressure, and composition of the inlet fuel stream (stream 8, Fig. 1), as well as the flowrate and pressure of the inlet air stream (stream 3, Fig. 1). At one pseudo-steady-state time-step (each pseudo-steady-state time-step is one week long), the dynamic simulation in matlab simulink began the simulation by using the reduced model to estimate the GT’s power and efficiency, as well as the total balance-of-plant power. The dynamic simulation ran using a fixed stepsize of 0.08 h with ode4 as the chosen integrator. The controllers manipulated the inlet fuel flowrate, the cathode inlet air temperature, and the SOFC load (current density) to achieve the desired set points for net power, SOFC average cell temperature, and voltage, respectively. During the simulation, operating and outlet variables, including SOFC stack power, voltage, current density, fuel utilization, average cell temperature, combusted gas flowrate, combusted gas temperature, combusted gas pressure, and combusted gas composition, were computed. These outlet variables, as well as the variables shown in boxes A1, B1, and C1 in Fig. 2, were recorded for every 0.8 h sampling interval within the week-long pseudo-steady-state time-step. The data for the fifth hour of the pseudo-steady-state time-step were selected to represent the slow dynamics of the system as a pseudo-steady-state, and were used for the balance-of-plant model simulations. These steps were completed by a matlab script with a function that called matlab simulink for the dynamic simulation. The pseudo-steady-state data, which were recorded as .csv files by the matlab script, were then used by a python script that called aspen plus for the balance-of-plant model simulation. The outlet variables from the simulink model (such as combusted gas flowrate, combusted gas temperature, combusted gas pressure, and combusted gas composition as stream 4 in Fig. 1) were taken as inlet variables for the aspen plus balance-of-plant model. The GT isentropic efficiency in the Aspen model was specified using a reduced model that correlated the GT isentropic efficiency with the GT efficiency predicted in the dynamic model simulation. The inlet natural gas flowrate was also estimated using a reduced model that predicted the natural gas flowrate based on the SOFC cathode inlet fuel flowrate in the dynamic model. The steady-state simulation of the balance-of-plant model returned results as blocks A2, B2, and C2 (see Fig. 2), which were compared to blocks A1, B1, and C1 on the dynamic model side, respectively. If the relative error between these variable sets was less than 0.005%, the week-long pseudo-steady-state time-step was completed. If the error was not acceptable, the algorithm was iterated with new estimated values for certain variables (such as GT efficiency and inlet natural gas flowrate) until the relative error fell within the acceptable range. By using the discussed reduced models to give very good initial guesses, only one or two iterations were required for a pseudo-steady-state time-step. Pseudo-steady-state simulations were performed using the week-long time-step over the lifetime of the SOFC stack in each base case (SOFC lifetime varied from case to case), with this cycle being repeated for a plant lifetime of 30 years.

### 2.4 Eco-Technoeconomic Analyses.

The natural gas combined cycle (NGCC) base case without CO_{2} capture presented in Ref. [50] was selected as the baseline reference point for the eTEA in this study. The selected reference case had a levelized cost of electricity (LCOE_{base}) of $US 48.4/MWh and CO_{2} emission_{base} of 373.0 kg CO_{2}e/MWh (note CO_{2}e is short for CO_{2} equivalents). In the present work, the price of the SOFC was assumed to be $ 2000/kW of nameplate power capacity, and the cost of the gas turbine used in Base Cases 3 and 4 was estimated based on the data provided in Refs. [51,52] (additional details are shown in Appendix B available in the Supplemental Materials). All dollar amounts in this work are expressed in 2016 USD. The capital cost of the SOFC stacks in each base case was calculated for each year in the plant’s 30-year lifetime based on the number of stacks needed in each year. The capital costs of the upstream NG reformer and the water-gas shift reactor were estimated based on the units used in Case 1-1 (an NG-powered hydrogen production plant equipped with a reformer and water-gas shift reactor) of a baseline report by NETL [53] and adjusted according to the NG flowrate. Details regarding the capital costs of other small units can be found in Appendix B available in the Supplemental Materials. The operating costs were mainly estimated based on Case B31A of a different baseline report from NETL. This case consisted of an NGCC plant without CO_{2} capture [44], only with the addition of 21% (estimated based on the portion of capital costs) of the operating cost of Case 1-1 (adjusted with NG flowrate) to account for the reformer and water-gas shift reactor [53]. The NG price we used was $3.37/GJ (or $3.55/MMBtu both in HHV), which is the same price as the reference case [50].

_{2}avoided (CCA) of each case were calculated using Eqs. (2) and (3) as follows:

_{2e}emission refers to direct CO

_{2}e greenhouse gas potential of the plant over the lifetime, which equals the CO

_{2}emission in all cases since CH

_{4}was assumed to be completely combusted in the post-combustor and NOx was not considered. The CCA expresses the cost of CO

_{2}e emissions avoided by constructing and using one of the four base case plants instead of the baseline NGCC plant. An extensive discussion on why this formulation is the most appropriate choice for CCA can be found in Ref. [50]. Finally, the SOFC stack efficiency is defined as the stack’s DC power output divided by the LHV of the syngas fuel it consumes, and the overall plant efficiency is defined as the SOFC stack’s DC power output plus the balance-of-plant AC power output, divided by the LHV of the natural gas entering the plant. Both the efficiencies are calculated over the 30-year plant lifetime.

## 3 Results and Discussion

The dynamic SOFC model simulation results for the four base cases are shown in Fig. 3, and the corresponding results for the entire plants are shown in Fig. 4. In Base Case 1 (Figs. 3(a)–4(a)), the SOFC power output was controlled to follow a declining trajectory (a second-order polynomial trajectory) in order to maintain a net plant power (including the balance-of-plant) of 550 MW. The FU was also controlled at a constant level of 80%. As the SOFC stack degraded over time, the current density increased from its initial value of 0.5 A/cm^{2}, while the voltage dropped below 0.8 V. Under these operating conditions, the standalone SOFC stack in Base Case 1 was predicted to have a lifetime of around 20 weeks before catastrophic breakage would occur. Figure 4(a) shows the periodic replacement of the SOFC stack every 20 weeks over the plant’s 30-year lifetime. Within each replacement cycle, the stack and plant efficiency decreased as the SOFC degraded due to the system requiring greater amounts of fuel to produce the same amount of power.

The SOFC performance curves for Base Case 2 followed similar trends to those observed in Base Case 1, except the stack power was allowed to drop further down (also following a second-order decreasing trajectory). In Base Case 2, not only did the amount of power produced by the upstream turbine continually increase due to the increase in the fuel flowrate over time, but the power produced by the steam bottoming cycle similarly increased as the heating value of the SOFC anode exhaust stream also increased over time. By offsetting the decreasing stack power with the increase in balance-of-plant power (including the upstream turbine and the steam bottoming cycle), the net power was maintained at around 550 MW. Compared to Base Case 1, the decrease in stack power output in Base Case 2 indicated a slower increase in current density, which resulted in a slower degradation rate. Consequently, the lifetime of the SOFC stack in Base Case 2 increased to around 25 weeks. Furthermore, the net plant efficiency in Base Case 2 was also significantly higher compared to Base Case 1, as the steam bottoming cycle was able to capture and reuse the waste heat in the SOFC anode exhaust.

The SOFC stack in Base Case 3 (SOFC/GT hybrid plant) was operated in constant voltage mode with decreasing current density and power output, which can markedly increase the SOFC’s lifetime. Although the simulation predicted that the SOFC’s lifetime could exceed 14 years, a practical regular replacement lifetime of 375 weeks (around 7.2 years) was chosen, as the FU dropped to 25% at this point. At this replacement point, the SOFC stack’s power output decreased to 157.5 MW (about 38.5% of its initial capacity) and its current density dropped from the initial value of 0.5–0.19 A/cm^{2}. As can be seen in Fig. 4(c), the plant gradually shifted the power load from the SOFC stack to the GT as the SOFC degraded, thus maintaining a net power output of 550 MW. The GT was designed to operate at its maximum power capacity (405 MW) and maximum efficiency (42.6%) at the end of the 375-week-cycle; as shown in the turbine characteristic curve, the GT’s power and efficiency gradually increased throughout each cycle. However, the net plant efficiency decreased throughout each cycle, as the NG fuel flowrate needed to be continually increased to maintain a constant net power output. This decline in net efficiency was also due to the shift in power load from the more efficient SOFC stack to the less efficient GT over the course of each cycle.

The SOFC stack performance curves and plant performance curves in Base Case 4 were very similar to those in Base Case 3, except Base Case 4 also included the addition of curves for the steam bottoming cycle. In Base Case 4, the SOFC stack was operated with constant voltage, along with decreasing current density and power output. Following the same rule as Base Case 3, a lifetime of 427 weeks (around 8.2 years) was selected for the SOFC stack in Base Case 4, as this is the point where the FU dropped to 25%. Compared to Base Case 2, the steam cycle in Base Case 4 produced much less power due to the much lower heating value of the exhaust stream (can be seen in stream 5, Fig. 1). However, the addition of the steam cycle resulted in a higher net plant efficiency compared to Base Case 3.

The short stack lifetime in Base Cases 1 and 2 indicates that these two SOFC plants might not be applicable in practice under the current operating conditions (80% fuel utilization and 0.5 A/cm^{2} initial current density). In fact, running the SOFC with lower fuel utilization or lower current density could reduce the degradation rate and thus increase the stack lifetime [2]. It should be noted that, with lower initial fuel utilization or current density, the degradation rates in Base Cases 3 and 4 are expected to be slower too. In this study, the main focus is the comparison between two different operating modes of SOFC: nearly constant power mode (Base Cases 1 and 2) and constant voltage mode (Base Cases 3 and 4), with all other operating conditions remain the same (such as initial fuel utilization, initial current density, and average cell temperature). The values of these operating conditions were selected according to the experimental conditions which the model was developed based on Ref. [37], and changing these operating conditions would be out of the scope of this study.

The results of key parameters of the eTEA for the four base cases are summarized in Table 4, including efficiencies, costs, LCOE, and CCA. While the hybrid plants (Base Cases 3 and 4) were generally more efficient than the SOFC standalone plants (Base Cases 1 and 2), Base Case 2 had the highest overall plant efficiency, mainly due to the highly-efficient SOFC power production enabled by the steam bottoming cycle’s reuse of waste heat. The hybrid plants sacrificed efficiency by shifting the power load to the less efficient GT as the SOFC replacement cycle progressed in order to prolong the SOFC stack’s lifetime. Figure 5 shows the number of times the SOFC stacks in each base case needed to be replaced each year over the plant’s 30-year lifetime. For instance, Base Cases 1 and 2 each used three stacks in the first year of the plant’s life, as the lifetimes of the stacks in these cases were 20 and 25 weeks, respectively. In contrast, Base Cases 3 and 4 only required one stack each in the first year, as their SOFC stacks had lifetimes of 375 weeks and 427 weeks, respectively. The total number of SOFC stacks required over the 30-year plant lifetime for Base Cases 1–4 were 79, 63, 5, and 4, respectively. As mentioned in the methodology section, the cost of the SOFC stacks was calculated for each year in the plant’s 30-year lifetime based on the number of stacks needed in each base case. Predictably, the first-year capital costs for Base Cases 1 and 2 were much higher compared to Base Cases 3 and 4, as Base Cases 1 and 2 each required the use of three stacks in the first year, while Base Cases 3 and 4 only required one. In addition to the SOFC stacks purchased in the first year, this first-year capital costs for each base case accounted for all other units in each plant. The average annual SOFC replacement cost was calculated as the annual average of the sum of the cost of SOFC stacks accounting for time-value-of-money and the inflation rate over the plant’s 30-year lifetime. This cost decreased from Base Case 1 to Base Case 4 because the frequency of SOFC stack replacement correspondingly decreased. Notably, Base Case 2 had the lowest annual material, operating, and maintenance costs, mainly due to having the highest overall plant efficiency. In particular, Base Case 2 achieved significant cost savings on fuel, as it used the least amount of NG out of the four base cases.

Base Case 1 SOFC standalone | Base Case 2 SOFC with steam cycle | Base Case 3 SOFC/GT hybrid | Base Case 4 SOFC/GT with steam cycle | |
---|---|---|---|---|

SOFC stack efficiency (LHV) | 58.3% | 57.4% | 65.3% | 65.3% |

Overall plant efficiency (LHV) | 46.8% | 65.0% | 50.8% | 53.0% |

First-year capital cost ($ Million) | $3558 | $2636 | $1464 | $1445 |

Average annual SOFC replacement cost ($ Million) | $2642 | $1515 | $120 | $90 |

Annual material, operating and maintenance cost ($ Million) | $161 | $116 | $148 | $141 |

LCOE ($/MWh) | $327 | $194 | $38.5 | $35.1 |

CO_{2} emission (kg/MWh) | 275 | 198 | 252 | 240 |

CCA ($/ton CO_{2}e) | $2833 | $831 | −$81.4 | −$99.9 |

Base Case 1 SOFC standalone | Base Case 2 SOFC with steam cycle | Base Case 3 SOFC/GT hybrid | Base Case 4 SOFC/GT with steam cycle | |
---|---|---|---|---|

SOFC stack efficiency (LHV) | 58.3% | 57.4% | 65.3% | 65.3% |

Overall plant efficiency (LHV) | 46.8% | 65.0% | 50.8% | 53.0% |

First-year capital cost ($ Million) | $3558 | $2636 | $1464 | $1445 |

Average annual SOFC replacement cost ($ Million) | $2642 | $1515 | $120 | $90 |

Annual material, operating and maintenance cost ($ Million) | $161 | $116 | $148 | $141 |

LCOE ($/MWh) | $327 | $194 | $38.5 | $35.1 |

CO_{2} emission (kg/MWh) | 275 | 198 | 252 | 240 |

CCA ($/ton CO_{2}e) | $2833 | $831 | −$81.4 | −$99.9 |

The LCOE decreased sequentially from Base Case 1 to Base Case 4 due to the corresponding decrease in the number of SOFC stacks (which contributed the largest portion of the total costs) required over the plant’s 30-year lifetime. The findings showed that the hybrid plants (Base Cases 3 and 4) had lower LCOEs compared to the baseline NGCC plant (baseline = $48.4/MWh), as determined based on the assumed SOFC price in the four base cases. In addition, all four base cases had lower direct CO_{2} emissions compared to the baseline NGCC plant (373.0 kg/MWh), mainly due to their higher efficiency. Predictably, the lowest CO_{2} emissions were observed in Base Case 2, as it was the most efficient of the four base cases. However, Base Case 2 had high costs associated with SOFC stack replacement, as the SOFC stack in this case had a fairly short lifetime. As a result, Base Case 2 had a CCA of $831/ton CO_{2}e. This CCA figure indicates that, although Base Case 2 emitted less CO_{2} than the baseline NGCC plant, the high cost per ton of emitted CO_{2} undermines its viability. The CCA results for Base Cases 3 and 4 are negative because these cases had both lower costs and lower CO_{2} emissions compared to the baseline NGCC plant. The lower LCOEs and negative CCAs recorded for Base Cases 3 and 4 established them as better alternatives than the baseline NGCC plant and Base Cases 1 and 2 from an eco-technoeconomic perspective. Ultimately, the eTEA results revealed that Base Case 4 (SOFC/GT hybrid plant with a steam bottoming cycle) had the lowest LCOE ($35.1/MWh) and lowest CCA (−$99.9/ton CO_{2}e) of the four base cases, thus establishing it as the best design. To see if there are significant changes when considering more recent price scenarios, we re-ran the analysis for Base Case 4 following the same procedure (as in Appendix B available in the Supplemental Materials) but with an updated capital cost using the 2022 cost index and an updated fuel price using the average for 2022. Prices are reported in 2022 USD. The LCOE and CCA of Base Case 4 were $51.5/MWh and −$257/ton CO_{2}e, respectively. Note that the LCOE of the baseline reference case NGCC [50], LCOE_{base}, was also converted to 2022 USD as $85.6/MWh for the CCA calculation.

## 4 Sensitivity Analyses

Since the lifetimes of the SOFC stacks in the SOFC/GT hybrid plants (Base Cases 3 and 4) were chosen arbitrarily, the first sensitivity analysis investigated how the use of different SOFC lifetimes in these plants impacted the eTEA results. Instead of replacing the SOFC stack when FU reached 25%, as we did in the base cases, we replaced the SOFC stack when FU reached 20% and 30% (henceforth referred to as the “20% FU case” and “30% FU case”) in the sensitivity analyses. In Base Cases 3 and 4, the GT was designed to provide peak performance (maximum power output and maximum efficiency) at the end of the SOFC replacement cycle (when FU reached 25%). However, it was necessary to redesign and re-simulate the systems, as changing the replacement point of the SOFC stack also changed the required power capacity of the GT. Compared to the base cases, 20% FU cases required a larger GT, while 30% FU cases needed a smaller GT. First, we scaled the GT (model SGT6-9000HL) used in the base cases to the desired power capacities for the 20% FU and 30% FU cases by assuming the scaled GT retained the same maximum efficiency when it was operated at its full power capacity. Second, two real GT models were selected for the 20% FU (model SGT5-8000H) and 30% FU (model SGT5-2000E) cases for comparison with the scaled GTs [51]. Table 5 summarizes the GT models, as well as the power capacities and max efficiencies used in all the sensitivity analysis cases. The models of Base Cases 3 and 4 were modified by substituting in the GT models for the 20% FU and 30% FU cases (Table 5), generating eight new cases covering the combinations of the plant models in Base Case 3 or 4, along with the 20% FU or 30% FU cases and the scaled GT or real GT.

SOFC stack replaced at | 25% FU (base cases) | 20% FU | 30% FU | ||
---|---|---|---|---|---|

GT model | SGT6-9000HL | Scaled SGT6-9000HL | SGT5-8000H | Scaled SGT6-9000HL | SGT5-2000E × 2 |

Power capacity | 405 MW | 435 MW | 450 MW | 350 MW | 187 MW × 2 |

Max efficiency | 42.6% | 42.6% | 42.6% | 42.6% | 36.5% |

SOFC stack replaced at | 25% FU (base cases) | 20% FU | 30% FU | ||
---|---|---|---|---|---|

GT model | SGT6-9000HL | Scaled SGT6-9000HL | SGT5-8000H | Scaled SGT6-9000HL | SGT5-2000E × 2 |

Power capacity | 405 MW | 435 MW | 450 MW | 350 MW | 187 MW × 2 |

Max efficiency | 42.6% | 42.6% | 42.6% | 42.6% | 36.5% |

The eTEA results of the eight cases used in the sensitivity analysis, as well as the results for the base cases, are shown in Fig. 6. With the exception of the 30% FU cases with real GTs, the results followed the trends observed in the base case studies, namely: longer SOFC stack lifetime (replaced at lower FU) was associated with lower net plant efficiency, lower LCOE, and lower CCA. Replacing the SOFC stack at lower FU further shifted the power load to the less efficient GT, thus resulting in lower net efficiency. On the other hand, as the SOFC stack lifetime increased, the frequency of replacement decreased, thus reducing the costs associated with SOFC stack replacement and, consequently, the LCOE and CCA. The 30% FU cases with real GTs had lower efficiencies, higher LCOEs, and higher CCAs than the 30% FU cases with scaled GTs. This result is due to two small GTs (SGT5-2000E) with lower maximum efficiency being used to satisfy the desired power capacity in the real GT cases. This result implies that replacing the SOFC stack at lower FU (i.e., prolonging the SOFC stack lifetime) in the SOFC/GT hybrid plant design generally results in worse (lower) net efficiency, a better (lower) LCOE, and a better (lower) CCA; however, this approach is also limited by factors such as the availability of practical GT models and SOFC price.

The second sensitivity analysis built upon the first by investigating how SOFC price affected the eTEA of each base case. In addition to the SOFC price used in the base cases ($2000/kW), we selected a lower price of $1000/kW and two higher prices of $4000/kW and $8000/kW (all figures in 2016 USD). The results of the SOFC price sensitivity analysis reveal that Base Case 1 (the standalone SOFC plant) was the most sensitive to SOFC price, as the SOFC stack was replaced most frequently in this case (Fig. 7). When the base case SOFC price was doubled to $4000/kW, Base Case 4 (the SOFC/GT hybrid plant with a steam bottoming cycle) remained a potential alternative to the baseline NGCC plant, as its LCOE ($50.1/MWh) was close to the baseline and its CCA ($12.7/ton CO_{2}e) was close to 0.

Since the NG price has been fluctuating greatly in recent years, we performed a sensitivity analysis to investigate how natural gas prices affect the eTEA results of the four base cases. The LCOE and CCA of the base cases were calculated for a range of NG prices from 30% to 500% of the base price $3.55/MMBtu, as shown in Fig. 8. We also selected three typical historical prices in June 2020, Feb. 2021, and April 2022 [54] as interesting points of reference as shown in Fig. 8 (expressed in $US2016 using the consumer price index) [55]. Note that the LCOE of the baseline NGCC plant was also recalculated for the range of NG prices, which were used to compute the CCA for the base cases. As can be seen in Fig. 8, the CCA decreased as the NG price increased for all the base cases, mainly due to the higher net efficiency and lower CO_{2} emissions of the base cases over the baseline NGCC plant. In other words, the higher the price of natural gas, the more advantageous it is to use an SOFC-based system. However, the CCA of Base Cases 1 and 2 were always very high, even when the NG price increased to five times of the base price. This implies that the SOFC replacement costs were still the most contribution of the total costs in Base Cases 1 and 2. The CCAs of Base Cases 3 and 4 were always negative; and as the NG price increased, these two cases were increasingly better from an eco-technoeconomic perspective. This is because Base Cases 3 and 4 have lower LCOEs and lower lifecycle greenhouse gas emissions than NGCC.

Besides the NG prices (or fuel costs), the last sensitivity analysis was on the non-fuel costs. We varied the total non-fuel costs of the four base cases over the plant lifetime from 30% to 500% of their original non-fuel costs, while keeping the fuel price at the base level. The LCOE and CCA were re-computed and plotted against each other in Fig. 9. The CCA of Base Cases 1 and 2 were still positive even when the non-fuel costs were reduced to 30% of their original costs. When the non-fuel costs became double, Base Cases 3 and 4 had higher LCOEs than the baseline NGCC plant, with CCAs of $133/ton CO_{2}e and $75.3/ton CO_{2}e, respectively. Even with double-than-expected non-fuel costs, Base Cases 3 and 4 have low enough CCA’s to be commercially relevant CO_{2}-mitigation technology options, noting that the carbon tax floor in Canada will be 110 $CA/ton CO_{2}e (85 $US/ton CO_{2}e) in 2026 and 170 $CA/ton CO_{2}e (132 $US/ton CO_{2}e) in 2030 [56]. Note that the LCOE of the baseline NGCC plant remained the same for the CCA calculations throughout this sensitivity analysis.

## 5 Conclusion and Future Work

The simulation results showed that operating the SOFC stack in the SOFC/GT hybrid plants (Base Cases 3 and 4) at constant voltage greatly slowed degradation and increased the stack lifetime. As a result, the SOFC/GT hybrid plants had lower stack replacement costs over their 30-year lifetime compared to the standalone SOFC plants (Base Cases 1 and 2), wherein the SOFCs were operated in near-constant power mode. The eTEA results further showed that the SOFC/GT hybrid plants (Base Cases 3 and 4) had much lower LCOEs and CCAs compared to the standalone SOFC plants (Base Cases 1 and 2), implying that the SOFC/GT hybrid design is preferable to the standalone SOFC design from an eco-technoeconomic perspective. The addition of steam bottoming cycles in Base Cases 2 and 4 resulted in higher efficiency, lower LCOEs, and lower CCAs compared to Base Cases 1 and 3, respectively. Although the findings revealed that Base Case 2 (standalone SOFC plant with a steam bottoming cycle) had the highest overall plant efficiency (65.0% LHV), the near-constant power mode of SOFC stack operation led to faster degradation and shorter SOFC stack lifetimes, resulting in high stack replacement costs over the 30-year plant lifetime. As a result, Base Case 2 is likely economically infeasible, as the high stack replacement costs contributed to an unacceptably high LCOE ($194/MWh) and CCA ($831/ton CO_{2}e). In contrast, Base Case 4 had the lowest LCOE ($35.1/MWh) and CCA (−$99.9/ton CO_{2}e) of the four base cases, which established it as the most economically and environmentally feasible design.

Sensitivity analyses were also conducted to examine how SOFC stack lifetime and SOFC cost in the SOFC/GT hybrid plants influenced the eTEA results. The findings of these analyses revealed that prolonging the lifetime of the SOFC stack (i.e., replacing it at lower FU) resulted in lower net efficiency due to the power load being gradually shifted to the less efficient GT; however, the results also indicated that prolonging the SOFC’s lifetime led to a lower LCOE and CCA due to the reduced costs associated with SOFC replacement. By altering the SOFC stack’s lifetime, the hybrid plants can be re-designed according to the required size of GT, though this may be limited by the existing commercial GT models in practice. The sensitivity analysis of SOFC price showed that the standalone SOFC plants (Base Cases 1 and 2) were more sensitive to changes in SOFC price, mainly due to the need to replace the SOFC stack more frequently in these designs. Ultimately, the sensitivity analysis of SOFC price and NG price revealed that Base Case 4 remained a competitive alternative to the baseline NGCC plant when the SOFC price or the NG price was doubled from the price used in the base cases, respectively.

Besides the factors investigated in this work, the eTEA results of SOFC systems might also be strongly affected by long-term degradation. If the degradation occurred much slower in reality than predicted by the model, the standalone SOFC plants (Bases 1 and 2) could be economically feasible. The degradation model used in this work was limited to one specific SOFC type (in terms of materials) and certain operating windows (where the cases in this work were designed). As such, different degradation models should be incorporated into future eTEA studies to cross-validate the proposed degradation model and to explore different SOFC operations.

In this work, we conducted an eTEA of four large-scale NG-powered baseload SOFC power plants that accounted for long-term degradation. Future research could examine SOFC/GT hybrid designs and standalone SOFC designs in peaking power or load-following applications at large or small scales. Such research could include household, building, and community power systems, and consider how these systems might be integrated with other applications such as combined heat and power, energy storage, and wind and solar systems.

## Footnote

## Acknowledgment

This work was funded by a Natural Sciences and Engineering Research Council (NSERC) Postgraduate Graduate Scholarship for Doctoral Students (PGS-D), an NSERC Discovery Grant (RGPIN 2016-06310), and the U.S. Department of Energy (DE-FE0031512).

## Conflict of Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

## Data Availability Statement

Models and codes related to this work have been released to the public in LAPSE.^{2}

## Nomenclature

- AC =
alternating current

- CCA =
cost of CO

_{2}avoided- DC =
direct current

- EOS =
equation of state

- eTEA =
eco-technoeconomic analysis

- FU =
fuel utilization

- GT =
gas turbine

- HHV =
higher heating value

- LCOE =
levelized cost of electricity

- LHV =
lower heating value

- PID =
proportional-integral-derivative (controller)

- SOFC =
solid oxide fuel cell

- YSZ =
Yttria-stabilized zirconia

## References

_{2}Recycle

_{2}-Capture

_{2}Cycle

_{2}Capture by Integration of Solid Oxide Fuel Cells With Compressed Air Energy Storage

_{2}Capture Approaches for Fossil-Based Power Generation: Review and Meta-Study