1. Introduction
A hybrid system refers to the combination of two or more different energy technologies to produce a more efficient, flexible, reliable, and nature-friendly system. Hence, hybrid systems are fast becoming a key technology for an alternative solution to the incessantly growing global energy demand [
1]. In fact, the vast majority of the proposed hybrid systems are mostly based on renewable energy technologies such as solar, wind, or biomass, or alternative ones such as fuel cells, in combination with conventional technologies such as steam or gas turbines. Interestingly, solid oxide fuel cells (SOFCs) are the most preferred technology because of their high energy efficiency, low polluting emissions, and their ability to use different types of fuels such as hydrogen, biogas, carbon dioxide, alcohols, or other hydrocarbons [
2]. In fact, when SOFCs are combined with other technologies to yield hybrid systems, there exists the possibility of increasing the efficiency of the entire system and decreasing the costs [
3].
Accordingly, much of the current literature on hybrid systems based on solid oxide fuel cells pays particular attention to the evaluation of their thermodynamic performance through either exergy or thermoeconomic analysis. One study by Rokni [
4], for example, evaluated the thermodynamic and thermoeconomic performance of a 120 kWe small-scale integrated gasification-solid oxide fuel cell and Stirling engine. The author estimated a system thermal efficiency of 42%, an electricity unit generation price of 0.124
$/kWh and a unit price for water of 0.0124
$/kWh. A broader analysis is proposed by Baghernejad et al. [
5] who made a comparison, based on an exergoeconomic method, between three different trigeneration systems, namely an SOFC trigeneration, a biomass trigeneration, and a solar trigeneration. Their findings suggest a maximum exergy efficiency of 64.5% achieved by the SOFC-trigeneration system, and a minimum unit electricity cost of 0.682
$/kWh achieved by the biomass-based trigeneration system. More recently, Duk Lee et al. [
6] discuss the exergy and exergoeconomic evaluation of a SOFC-engine hybrid power system. Their results showed an overall system efficiency of 26% and a levelized cost of electricity of 0.2792
$/kWh.
Likewise, Cheddie [
7] investigated the unit cost of electricity and the overall efficiency of an 18.9 MW hybrid system integrated by a solid oxide fuel cell and a gas turbine using a thermoeconomic method. He provided a unit cost of 4.54
$/kWh and 48.5% efficiency, respectively. In a previous study, Arsalis [
8] applied a thermoeconomic analysis to determine a system efficiency of up to 74% of a solid oxide fuel cell-gas turbine-steam turbine hybrid system. Another interesting contribution is the exergy evaluation conducted by Wang et al. [
9] on an integrated power system composed of a solid oxide fuel cell-gas turbine-Kaline cycle. The authors reported an overall energy efficiency of 70% and an exergy efficiency of 67%.
However, even though all together these studies provide important insights into the evaluation of SOFC systems integrated with other technologies through thermoeconomic or exergoeconomic methods, there is not much evidence of published works providing the contribution of environment and residues on the exergy costs of processes nor even the breakdown of exergy costs due to contributions of the irreversibility. In this regard, among the most representative works reported and from which some results have been considered here are, for example, the work reported by Rangel et al. [
10], in which a detailed parametric analysis of a SOFC system coupled with a VAR system using exergoeconomic techniques is carried out. However, the authors did not report any productive structure, nor do they make a difference between product and residues costs. However, the idea of coupling a VAR system to a SOFC had already been previously reported by Venkataraman et al. [
11], in which they provide only a detailed thermodynamic analysis of the hybrid system for truck applications. Torres et al. [
12] presented the fundamentals of the methodology for determining exergy cost through the theory of the exergy costs, but they did not apply it to a system such as the one presented in this work. Similarly, Torres et al. [
13] presented only the mathematical formulation of the exergy cost assignation to residues with simple applications.
Therefore, in this research, through the application of the exergy cost theory, it is intended to propose a productive structure of the hybrid system comprised of a 500 kWe SOFC stack and of a vapor-absorption refrigeration (VAR). As a result, the exergy costs of flows and processes are obtained and analyzed.
4. Results and Discussion
Among the benefits of the theory of exergetic cost is the fact that it allows a clear understanding of the cost formation process through the system. This can be better understood by means of
Figure 4, which shows the contribution of the irreversibility generated in the i-th process to the unit cost of th product of the
j-th equipment. For example, the unit product cost of the SOFC (1.74 kW/kW) is mostly comprised of the irreversibility contribution from the SOFC itself (13%), the air preheater (11%), the water preheater (7%) and the afterburner (6%), whereas the environment account for as much as 57%. Most importantly, it can be noted that the product of the fuel compressor is the most expensive, in terms of exergy consumption, because most of its contribution is due to its own inefficiency.
4.1. Integration Analysis
Consider the integrated system SOFC-VARS system depicted in
Figure 5, where each plant is considered to be a simple process. If the exhaust gases yielded in the SOFC stack are not reused in other systems, it means that all its exergy is wasted and therefore its cost is charged to the electricity.
Alternatively, as in the case of the SOFC-VAR system, if part of the exhausted gases Q = E− E are reused in the VAR process, then the cost of electricity decreases from 2.74 to 2.19 kW/kW, whereas the cost of gases is around 3 kW/kW, higher than the cost of electricity. It is important to note that this cost is inclusive higher than other heat alternatives to fuel the VARS system.
Consider that the exhaust gases are a by-product of the SOFC system, the cost for which varies from 0 (waste) to 3 (product), and so the cost of electricity and electricity produced by the integrated system varies according to the following equations:
These costs variations are graphically shown in
Figure 6. For example, if the cost of gases equals the cost of methane
the cost of electricity is 2.56 kW/kW and the cost of cold is 15.1 kW/kW. On the other hand, if the cost of gases equals electricity
kW/kW the cost of cold is 35 kW/kW.
Consequently, using exergy costs analysis it is possible to identify integration possibilities, efficiency improvement, and quantify the benefits due to system integration, as well as the determination of fair prices based on physical roots, see [
19].
4.2. Impact of Current Density
An important control parameter when it comes to operating SOFC stacks is the current density. It is interesting to study its influence on the unit exergy costs of both electricity and exhaust gases, as is shown in
Figure 7. It can be noted that a variation in the current density impacts both variables equally. Yet, the unit exergy costs of the exhaust gases are 45% higher than those of the electricity. This stems from the fact that exhaust gases have gone through a series of heat exchangers before leaving the SOFC system and, as a consequence, have assimilated the irreversibilities of each piece of equipment in accordance with the principle of the cost formation process of residues [
13]. In general, the unit exergy cost of both variables increases as current density rises too. It must be kept in mind that the stack voltage decreases because of the increased current density, which explains the reason the unit exergy cost also increases.
Conversely, the effect of the current density on the unit exergy cost of the refrigeration is more notable than on the electricity and the exhaust gases. On comparison, the generation of a refrigeration unit requires more resources than a unit of electricity. This is mainly due to the irreversibilities generated through the absorption refrigeration system, as it is composed of a steam generator and an evaporator and condenser; processes that, by nature, are highly dissipative. At a fixed current density of 8000 (A/cm2), the unit exergy cost of refrigeration is 45.8 (kW/kW), whereas for the electricity it is 2.1 (kW/kW). Thus, it can be deduced, from this point of view, that the production of refrigeration is not especially suitable with this configuration.
4.3. Impact of Fuel Use, FU
Another important parameter in the operation of a solid oxide fuel cell stack is the fuel use. However, this parameter cannot be physically manipulated but, in practice, it is calculated by Faraday’s Law using the current generated in the stack [
20]. Thus, the effect of fuel use on the unit exergy costs is explained as follows. First, the existing correlation between FU and the unit exergy costs of electricity and exhaust gases is provided in
Figure 8 at a fixed current density (8000 A/cm
) and stack temperature difference (100 K). It can be noted that the unit exergy cost of electricity is not sensitive to FU variations above 80%. Yet, a noticeable increase of up to 28% is found when FU drops below 80%. This is because at low FU ratios, less hydrogen is converted into power and higher additional air flow is required for cooling. Consequently, more power is required in the compressor, and therefore the electrical efficiency of the stack decreases, hence the high unit exergy cost at low FU ratios. In contrast, the unit exergy cost of the exhaust gases is more sensitive to FU variations. The reason for this is because, as previously mentioned, this exergy stream is accompanied by the inefficiencies of the heat exchangers located upstream. In comparison, between both costs the minimum difference is 20% at 89% of FU, whereas the maximum difference is 30% at 77% of FU.
Most interestingly, it is the remarkable impact that FU has on the unit exergy cost of the refrigeration. It falls sharply and follows the same trend as the unit costs of electricity and exhaust gases but in a greater proportion. For example, at a fixed 83% FU, each unit of refrigeration costs as much as 44 kW of resource consumption, while the unit exergy cost of electricity is around 2.2 kW/kW. As previously mentioned, the production of cooling is not viable in this configuration.
4.4. Impact of Anode Gas Recirculation
The analysis of anode gas recirculation is of particular interest, as apart from providing the heat for the steam-reforming reaction, it is used to control the stack difference temperature and hence the air for the cooling rate. Thus, in terms of costs,
Figure 9 unveils the unit exergy cost of electricity and exhaust gases as a function of the anode gas recirculation. Interestingly, two trends in the costs can be observed as the percentage of gas recirculation rises. On the one hand, the unit exergy cost of electricity slightly decreases, which is largely due to the higher fuel use as a result of the anode gas recirculation increase and hence the improvement in the stack efficiency as investigated in the work of Peters et al. [
21]. On the other hand, the unit exergy cost of the exhaust gases increases because they have lower energy availability as a result of bifurcation or by-pass and hence its unit cost increases. However, an increase in 25% in the anode gas recirculation does not have a notable effect on the unit exergy costs, this is lower than 1%.
On the contrary, the same 25% increase has a more noticeable effect on the unit exergy cost of the product of the refrigeration system of approximately 4.7%. In this case, the difference between the highest and the lowest unit exergy cost of refrigeration is at least 7.5%. Hence, the effect of the anode gas recirculation is greater in downstream equipment than in the same cell.
4.5. Impact of the Stack Temperature Difference
The control of the temperature difference across the stack is of great importance, because it can avoid causing large thermal stresses that can damage the entire SOFC stack, as well as allowing control of the amount of cooling air entering the system. However, it is valuable to discover how the temperature control measures positively or negatively affect the exergy costs of products. Therefore, the analysis of
Figure 10 allows the determination that the unit exergy costs for the exhaust gases are more sensitive to changes in the stack temperature difference than the electrical ones. As expected, increasing the temperature difference across the SOFC stack from 90 to 110
C represents a 6.5% decrease in the unit exergy costs of the exhaust gases, while in the case of electricity, it only represents a 1% decrease. The reason the unit exergy costs decrease is mainly down to the reduction of the energy consumption of the air compressor. The surplus air flow injected to the SOFC stack is inversely related to the temperature difference across the stack, and so if the surplus air is reduced, then so is the power consumption of the compressor [
20].
Likewise, the unit exergy cost of the refrigeration drops as the temperature difference across the stack increases. However, for the same case as assumed above, the impact on the unit exergy cost of the refrigeration is 10%. Apparently, if the temperature difference across the stack continues to increase, the unit exergy costs of the products would fall. Yet, for operational and safety reasons, the SOFC stack cannot be operated at high temperature difference [
20,
22].
5. Conclusions
The application of the exergy cost theory to a hybrid system based on an SOFC stack and on a VAR system has permitted to make several contributions to the current literature:
The first productive structure of a Solid Oxide Fuel Cell stack coupled to a Vapor-Absorption Refrigeration system is here reported. It depicts the integration of the different components by means of resources, products, and residues flows.
The application of this approach has shown that for a reference case, the unit exergy costs of electrical power, cooling, and waste heat are 2.192 kW/kW, 3.014 kW/kW and 45.515 kW/kW, respectively.
This approach has also permitted to know the contribution of the environment and the residues to the cost of the product. In the case of the electrical power, the contribution of the environment was 80% and the other 20% was provided by the residues. Meanwhile, for the unit exergy cost of cooling, the environment accounts for 96% and the residues for only 4%.
The analysis of the impact of current density on the exergy costs has revealed that the unit exergy cost of cooling turned out to be the more sensitive to it than the exergy cost of the electrical power and the exhaust gases.
The study of the effect of the fuel use on the unit exergy costs has shown that below 80%, the unit exergy cost of the cooling is the most sensitive of all. However, above 80%, the unit exergy cost of the electrical power has remained constant, 2.1 kW/kW.
In the case of the percentage of the anode gas recirculation, the results have revealed that its effect is greater on the unit exergy cost of the cooling and exhaust gases then on the electrical power.
The analysis of the impact of the stack temperature difference on the unit exergy costs has been of further interest. The results have revealed a steeper fall of the unit exergy cost of cooling as the temperature difference begins to increase. In thermodynamic terms, this situation would be ideal but due to operational and safety reasons, the stack temperature difference cannot reach higher values.
Altogether, the paper has provided an alternative to conventional analysis for identifying integration possibilities, efficiency improvements, quantification of benefits, and providing a physical basis for prices. Finally, the findings of this research have been limited due to the lack of information in current literature on the physical characteristics of a real solid oxide fuel cell stack.