Introduction

A combined cooling, heating, and power generation system shows higher capability in energy and cost-saving, as well as its flexibility and reliability in generating power, and thus becomes one of the most promising methods of energy conversion [1]. Also, the total efficiency of thermal power plants in Iran and in general is between 30 and 50% while considering 20% transmission losses; the distributed energy generation seems more perspective [2].

One of the main concerns of designing the CCHP system for residential applications is the selection of high-efficiency prime movers. Different models of integration of the CCHP system have been studied with different prime movers in the literature [3, 4], as many of them either studied single PMs in energetic or economic points of view. In this regard, Kaldehi et al. [5] studied a micro-Stirling engine as a prime mover of a CCHP system in the residential sector for different climates. They found out that the integration of the Stirling engine with heating and cooling cycles results in a significant amount of emission reduction. Their results revealed that maximum CO2 reduction in every climate is more than 40%. Also, Mojaver et al. [6] investigated an SOFC-based power generation system and found out that at optimum conditions, the efficiency and emission are 48.03% and 281.4 kg/MW.h, respectively. Abbasi et al. [7] studied ICE and GT as prime movers of a CCHP and considered the economic and exergetic factors of the system. They found out that energy efficiency will increase up to 10% if both prime movers are selected in one order. Also, the best scenario was combining the ICE and GT as prime movers and 87% energy efficiency, 62.8% exergy efficiency, and operating cost reduction of about 80% are obtained. Optimal design and operation strategy for integrated evaluation of CCHP (combined cooling heating and power) system is studied by Cai et al. [8]. Mehrpouya et al. [9] studied technical performance analysis of a (CCHP) system based on (SOFC) technology for educational building applications. The SOFC efficiency of 120 kW was about 45% while the hybrid system electrical cooling efficiency reached 58%, and the total CCHP system was 60% efficient. Also, they found out that the capital recovery factor is 8.3 years. Moreover, using SOFC and gas turbines as prime movers of CCHP systems has been of great interest to the researchers. Wang et al. [10] investigated the CCHP system integrating gas turbine and heat-driven cooling/power cogeneration. The main result of their research was that the CCHP system could consume 31% less natural gas than stand-alone power generation systems. Optimization and analysis of the CCHP system based on energy load coupling of residential and office buildings were carried out by Li et al. [11]. They found out that increasing gas prices will result in increased air-conditioning cooling load. Also, using SOFC-based CCHP system in residential buildings in China is studied by Jing et al. [12]. Their study included a comparison between SOFC-based CCHP and combustion-based ones, which resulted in that SOFC-CCHP systems demonstrate outstanding performance on energy efficiency as well as reducing carbon emission. Abbasi et al. [13] proposed a methodology to size the CCHP systems prime movers for large-scale residential buildings. Their results show that ICE-based trigeneration system is beneficial in all climates of the study. But the more important finding was that determining the right CCHP system is a far better solution for every environment. Many researchers have put their best effort in gas turbine and fuel cell analysis and optimization [14, 15]. Farahnak et al. [16] used ICE as the prime mover of the CCHP system and found out that using the CCHP system in small buildings results in 17.24% energy saving, but in large buildings, it causes 5.1% energy saving. Also, according to their study, the optimal payback period for large residential buildings is found to be 5.08 years. Feng et al. studied the performance analysis of a CCHP system with different cooling supply modes [17]. Moghimi et al. [18] studied GT-based CCHP systems, and a 4E analysis is performed to show that the CCHP system has7% higher exergy efficiency and 12% higher energy efficiency instead than stand-alone Brayton cycle. Exergy analysis is identified as a very powerful and cutting-edge tool in analyzing the power plants, which helps the scientists define the inefficiencies in the systems and improve the effectiveness of these power plants [9, 19]. In this regard, Ansarinasab et al. [20] developed an exergy-based investigation (exergy, exergoeconomic, etc.) of hydrogen liquefaction plant. Moreover, in a review study, Ahmadi et al. [21], investigated the thermodynamic and economic analysis of performance evaluation of all the thermal power plants and they found out that exergy analysis enables designers to make intricate thermodynamic systems operate more efficiently. Al Moussavi et al. [22] studied optimal management of SOFC-based CCHP systems for residential applications. Two strategies for the operation were employed: off-grid following electrical load and on-grid baseload operations. Their optimized results show that the CCHP system performs better from energetic and economic points of view. The maximum energy and exergy efficiencies (65.2% and 45.77%) and minimum system cost rate (22.2 cents kWh−1) are obtained under on-grid baseload operation for the CCHP system. Yousefi et al. [23] studied the component sizing of a hybrid ICE + PV/T-driven CCHP microgrid system and optimized the system multi-objectively. The results discovered that, regardless of slight growth in the average rate of net present cost, the combined cooling, heating, and power system integrated with solar energy has a substantially better performance in energy saving and emissions than the ICE-driven system. Rey et al. [24] analyzed the performance of an ICE-based CCHP and compared it with experimental data. Results revealed that maximum electrical efficiency is 7.63%, and it is obtained when the heat pump is off, and the engine is operating at a low speed. Also, they reported that the higher performance of the gas engine-driven heat pump is 10.79% when the engine is running at high speed. Luo et al. [25] studied a multisupply multidemand control strategy for combined cooling, heating, and power system primed with SOFC and gas turbine. Also, Chen et al. [26] investigated the Multi-criteria assessment and optimization study on a 5 kW PEMFC-based residential CCHP system. The optimized results show that exergy efficiency, cost, and GHG emission are 39.9%, 29337.3$, and \(1.8 \times 10^{7}\) gr, respectively, at optimal points. Chitgar et al. [27] proposed an integrated energy system based on SOFC. The optimization results in their works showed that an optimal point exergy efficiency and total cost rate are 54% and 36.8 $ h−1, respectively. Behzadi et al. [28] studied a hybrid renewable system and found out that in case of considering cooling set for absorption chiller, it has the highest exergy destruction rate. Jokar et al. [29] carried out a multi-objective optimization of hybrid fuel cell systems and figured out that in optimum case the exergy destruction becomes 1.314 and rate density meets 0.3864 kW m−2. Safari and Dincer [30] developed a novel biomass fired multigeneration system with hydrogen production. They found out that the energy and exergy efficiency of hybrid system reaches 40% and 63.6%, respectively. Beigzadeh et al. [31] modeled a SOFC and absorption chiller using nanofluids as heat transporters. They found out that nanofluid would result in an improve about 6&in efficiency.

There is a growing attention to the importance of prime movers of CCHP systems to reach maximum efficiency and the techno-economic and environmental analysis of these systems. However, little work is done on the comprehensive analysis and a complete multi-objective optimization of 3 counterparts of the simulation. To summarize the literature survey from the perspective of the present study, the research background is gathered in Table 1, which indicates the authors’ motivations to carry out the study.

Table 1 Summary of the literature survey highlighting the research gap
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Some latest research on economic and environmental analysis of building-integrated CCHP systems reveals the importance of techno-economic and environmental analysis of these systems.

In this paper, the trigeneration system is proposed to supply the heating and cooling, along with the power demand in a residential building. A comparison is made to find the best prime mover for the CCHP system between SOFC, GT, and ICE, considering the efficiency, emission, and economic factors. The parametric study of key design variables like (stack temperature difference, fuel utilization factor, compressor pressure ratio and pinch point temperature difference, etc.) defines the domain of optimization. The scenario analysis helps us select the best prime mover based on the needs of the building, for example, power, heating, or cooling. Also, each study in the literature has focused on certain area and objective like optimizing energy, exergy, cost, or emission. Considering the literature survey (as illustrated in Table 1), there is a knowledge gap of a comprehensive analysis of the optimized prime mover’s selection in microsize following main objectives and novelties as below:

  • Comprehensive exergy, exergoeconomic, and environmental analysis of four CCHP systems and multi-objective optimization of the best prime mover case.

  • Considering the low price of fuel for Tehran (instead of biomass or solar power), to result in an excellent payback period.

  • Evolutionary-based, 3-dimensional multi-objective optimization of the best-case scenario, to find the higher exergetic efficiency and lower emission and unit product cost.

  • Using a hybrid renewable energy system with considering heat recovery options for HRSG and refrigeration system.

  • Comparison of SOFC, ICE, and MGT for residential application power production

System description and assumptions

Figure 1 shows the schematic diagram of the different scenarios proposed in this study. The prime mover of the CCHP system for power production might be stand-alone, SOFC (scenario 1), ICE (scenario 2), MGT (scenario 3), or hybrid SOFC-GT (scenario 4). The systems are considered in a way that the power generation is different in 4 scenarios, and the exiting streams play the same role in the generation of heating and cooling. The exciting high-temperature combustion products are used in a heat recovery system to produce hot water for domestic use and in a double effect Li/Br system for production of refrigeration, respectively. In the first case, a fuel cell is considered for power generation, and HRSG and chiller are used to generate heating and cooling, respectively. The fuel is blown into the fuel mixer in state 7. In the fuel mixer, it is mixed up with the return stream from the fuel cell at 8b and exits to go through the fuel cell at state 8. On the other hand, the air is brought to the cathode to be reacted with fuel after being mixed in the mixer and passed through an air heat exchanger to raise the fluid temperature to the temperature of the cathode. After electrochemical reaction occurs in the fuel cell stack, the exiting streams mix and burn in the afterburner to ensure there is not any unreacted gas to be wasted and raise the temperature to higher levels. The existing gas at state 10 heats the air at AHX and then goes through the HRSG and double effect lithium bromide cycle to produce hot water and cooling. If the hot gases are warm enough, it will pass through a single turbine (scenario 4) to provide extra power. The description of the double effect refrigeration cycle can be found in the literature [32]. An MGT and ICE are other unsophisticated and straightforward method to be used as the chief mover of a residential-scale CCHP system (scenarios 3 and 2, respectively). At the combustion chamber of MGT, the fuel is mixed up with incoming air of the compressor before being expanded in the turbine. The hot gases are then used in an HRSG to create heating as in scenario 1.

Fig. 1
figure 1figure 1

Schematic diagrams of the proposed CCHP systems for a scenario 1, b scenario 2, c scenario 3, d scenario 4

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Nevertheless, the ICE can create less power; it can generate more heating by the cooling water used to cool the engine to lower temperatures in scenario 2. There are some assumptions made in the modeling of the CCHP system, in which the main premises considered to model the proposed system are as follows [33, 34]:

  • There is negligible heat loss from the components

  • Steady-state conditions are applied

  • Air and gas mixtures are modeled via ideal gas models

  • Contact resistance in SOFC is neglected

  • Kinetic and potential energy changes are small to consider

  • Unburned gasses are fully oxidized at the exit of afterburner and combustion chambers (scenarios 2 and 3)

Modeling and analysis

In order to render the analysis of the proposed systems, thermodynamic equations (energy and exergy balance equations as well as mass balance) are solved for each component of the order (considering a control volume around the elements) in the package of engineering equation solver EES. Also, to find the final cost and CO2 emission of the system, the environmental assessment, along with cost balance equations, is considered. The efficiency and the unit product cost of each scenario are regarded as the objective functions of genetic algorithms optimization code, which is developed in MATLAB.

Thermodynamic modeling

Energy and exergy balance is solved for each component to find the corresponding energy flow and exergy destruction via [35, 36]:

$$\sum \dot{m}_{\text{in}} = \sum \dot{m}_{\text{out}}$$
(1)
$$\dot{Q} - \dot{W} = \sum \dot{m}_{\text{out}} h_{\text{out}} - \sum \dot{m}_{\text{in}} h_{\text{in}}$$
(2)
$$\dot{E}x_{\text{Q}} - \dot{E}x_{\text{W}} = \sum \dot{m}_{\text{out}} ex_{\text{out}} - \sum \dot{m}_{\text{in}} ex_{\text{in}} + \dot{E}x_{\text{D}}$$
(3)

in which \(\dot{E}x\) is the rate of exergy and \(\dot{Q}\) and \(\dot{W}\), respectively, define the rate of heat transfer and power of the control volume. There are different subsystems in the proposed CCHP system which will be discussed through the following:

SOFC system

In the SOFC system, the fuel will be reformed, so the H2 content becomes higher in the SOFC system and so the global reaction as equation four is taken place [37]:

$${\text{H}}_{2} + \frac{1}{2}{\text{O}}_{2} \to {\text{H}}_{2} {\text{O}}$$
(4)

For the reforming purposes, the internal reformer is a better choice since it will charge no additional cost to the system [33].

The two equations occurring in each cell of the stack are reforming and shifting equations, the equilibrium constant of which is [33, 38]:

$$lnK_{\text{R}} = - \frac{{\Delta \bar{g}_{\text{R}}^{0} }}{{\bar{R}T_{\text{FC,e}} }} = ln\left[ {\frac{{\left( {\dot{n}_{\text{CO}} + x_{\text{r}} - y_{r} } \right) \times \left( {\dot{n}_{{{\text{H}}_{ 2} }} + 3x_{r} + y_{r} - z_{r} } \right)}}{{\left( {\dot{n}_{{{\text{CH}}_{ 4} }} + x_{\text{r}} } \right) \times \left( {\dot{n}_{{{\text{H}}_{ 2} {\text{O}}}} - x_{r} - y_{r} + z_{r} } \right)}} \times \frac{{P^{2} }}{{n_{\text{tot,in}}^{2} + 2x_{r} }}} \right]$$
(5)
$$lnK_{\text{S}} = - \frac{{\Delta \bar{g}_{\text{s}}^{0} }}{{\bar{R}T_{\text{FC,e}} }} = ln\left[ {\frac{{\left( {\dot{n}_{{{\text{CO}}_{ 2} }} + y_{\text{r}} } \right) \times \left( {\dot{n}_{{{\text{H}}_{ 2} }} + 3x_{\text{r}} + y_{\text{r}} - z_{\text{r}} } \right)}}{{\left( {\dot{n}_{\text{CO}} + x_{\text{r}} - y_{\text{r}} } \right) \times \left( {\dot{n}_{{{\text{H}}_{ 2} {\text{O}}}} - x_{\text{r}} - y_{\text{r}} + z_{\text{r}} } \right)}}} \right]$$
(6)

where \(x_{\text{r}}\,{\text{and}}\,y_{\text{r}}\), respectively, are the reaction rate of reforming and shifting equations. Moreover, Faraday’s law is used to determine the amount of hydrogen reacted according to equation four as:

$$j = \frac{{n_{\text{e}} Fz_{\text{r}} }}{{N_{\text{c}} A_{\text{c}} }}$$
(7)

in which Nc, Ac, and ne refer to the number of cells, area of cells, and the number of electrons transferred in the global reaction, respectively.

Furthermore, to find the reacted hydrogen, the fuel utilization factor will be written in the system of equations as [39]:

$$U_{\text{f}} = \frac{{z_{\text{r}} }}{{\dot{n}_{{{\text{H}}_{ 2} }} + 3x_{\text{r}} + y_{\text{r}} }}$$
(8)

Also, to find the net power output to the SOFC stack, the energy balance can be written as follows to find the gas properties at the exit of the stack:

$$\dot{W}_{\text{SOFC,stack,DC}} = mh_{8} + \dot{m}h_{4} - \dot{m}h_{3} - \dot{m}h_{7}$$
(9)

Also, from the electrochemical reaction, the fuel cell power is:

$$\dot{W}_{\text{SOFC,stack,DC}} = N_{\text{c}} A_{\text{c}} jV_{\text{c}}$$
(10)
$$\dot{W}_{\text{SOFC,stack,AC}} = \dot{W}_{\text{SOFC,stack,DC}} \times \eta_{\text{inv}}$$
(11)

in which j is the current density and Vc is the voltage of the cell and is calculated from the nominal voltage minus the losses which occur in the cell as:

$$\varvec{V}_{\text{c}} = \varvec{V}_{\text{N}} - \varvec{V}_{\text{loss}}$$
(12)
$$V_{\text{loss}} = V_{\text{ohm}} + V_{\text{act}} + V_{\text{conc}}$$
(13)
$$\varvec{V}_{\text{N}} = - \frac{{\Delta \varvec{G}^{0} }}{{\varvec{n}_{\text{e}} \varvec{F}}} - \frac{{\bar{\varvec{R}}\varvec{T}_{\text{C}} }}{{\varvec{n}_{\text{e}} \varvec{F}}}\varvec{ln}\left( {\frac{{\varvec{p}_{{{\text{H}}_{ 2} {\text{O}}}} }}{{\varvec{p}_{{{\text{H}}_{ 2} }} \sqrt {\varvec{p}_{{{\text{O}}_{ 2} }} } }}} \right)$$
(14)

in which \(V_{\text{ohm}}\), \(V_{\text{act}}\), \(V_{\text{conc}}\) is Ohmic over potential, activation overpotential, and concentration overpotential, respectively [33, 40].

Other system components

Energy and exergy balance equations for SOFC and other components like heat exchangers, compressors, pumps, and turbine, as well as expansion valves, are tabulated in Table 2 based on Eqs. 1–3.

Table 2 Energy and exergy rate balances for the system components in different scenarios [41, 42]
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Exergoeconomic analysis

To find a suitable option between different scenarios from an economic point of view, an exergoeconomic analysis seems necessary. Between various methods that have been proposed (SPECO), specific costing theory is used expansively to figure out the economic aspects of energy systems.

In this method, the exergy cost of the component is determined via writing exergy balance equations and solving them simultaneously with cost balances. In order to find the exergy, the cost of each stream, auxiliary equations are applied to each component. Cost balance equations are applied to each system component as follows [43]:

$$\sum \dot{C}_{\text{out,k}} + \dot{C}_{\text{w,k}} = \sum \dot{C}_{\text{in,k}} + \dot{C}_{\text{q,k}} + \dot{Z}_{\text{k}}$$
(15)
$$\dot{Z}_{\text{k}} = \dot{Z}_{\text{k}}^{\text{CI}} + \dot{Z}_{\text{k}}^{\text{OM}}$$
(16)
$$\dot{C} = c\dot{E}X$$
(17)
$$\dot{C}_{\text{out}} = c_{\text{out}} \dot{E}X_{\text{out}}$$
(18)
$$\dot{C}_{\text{q}} = c_{\text{q}} \dot{E}X_{\text{q}}$$
(19)
$$\dot{C}_{\text{w}} = c_{\text{w}} \dot{E}X_{\text{w}}$$
(20)

in which \(\dot{Z}_{\text{k}}^{\text{OM}}\) is the price of operation and maintenance of each component, c represents specific exergy cost, and Ċ stands for the cost rate.

Besides, annual Levelized capital investment for the kth component is determined [44]:

$$\dot{Z}_{\text{k}}^{\text{CI}} = \left( {\frac{\text{CRF}}{\tau }} \right)Z_{\text{k}}$$
(21)

where τ is the total operation time of the energy system in one year, which is assumed 8000 h in this research and CRF is the capital recovery factor that can be defined as [45]:

$${\text{CRF}} = \frac{{i_{\text{r}} \left( {1 + i_{\text{r}} } \right)^{\text{n}} }}{{\left( {1 + i_{\text{r}} } \right)^{n} - 1}}$$
(22)

Table 3 summarizes the cost equations(Zk)of the system components at the base year. Subsequently, Zk for the present year (2018) is premeditated [46]:

$${\text{Cost}}\;{\text{at}}\;{\text{present}}\;{\text{year}} = {\text{Original}}\;{\text{cost}} \times \frac{{{\text{CEPCI}}\;{\text{of}}\;{\text{the}}\;{\text{present}}\;{\text{year}}}}{{{\text{CEPCI}}\;{\text{of}}\;{\text{the}}\;{\text{base}}\;{\text{year}}}}$$
(23)

where ir is the interest rate and n is the number of operating years.

Table 3 Cost equations for components of the proposed systems [47,48,49]
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In order to evaluate the system from exergoeconomic point of view, cF, k, cP, k, ĊD, k, ĊL, k, and fk are illustrated as [50]:

$$c_{\text{F,k}} = \frac{{\dot{C}_{\text{F,k}} }}{{\dot{E}X_{\text{F,k}} }}$$
(24)
$$c_{\text{P,k}} = \frac{{\dot{C}_{\text{P,k}} }}{{\dot{E}X_{\text{P,k}} }}$$
(25)
$$\dot{C}_{\text{D,k}} = c_{\text{F,k}} \dot{E}X_{\text{D,k}}$$
(26)
$$f_{k} = \frac{{\dot{Z}_{k} }}{{\dot{Z}_{k} + \dot{C}_{D,k + } \dot{C}_{L,k} }}$$
(27)
$$r_{\text{k}} = \frac{{c_{\text{P,k}} - c_{\text{F,k}} }}{{c_{\text{F,k}} }}$$
(28)

which are defined as the unit cost of fuel, the unit cost of the product, the cost rate of exergy destruction, the cost rate of exergy loss, and the exergoeconomic factor, respectively. The exergoeconomic factor, as shown in Eq. (27), demonstrates the importance of capital and operating and maintenance costs against exergy inefficiency costs.

Cost balances for the components and auxiliary equations are tabulated in Table 4.

Table 4 Cost balances and auxiliary equations for the components [28, 38, 51]
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Performance evaluation

In order to evaluate the performance of the system, the energy efficiency from the first law of thermodynamics, for different scenarios in the proposed CCHP system, can be defined as [43, 52]:

$$\eta_{\text{I,a}} = \frac{{\dot{W}_{\text{SOFC}} - \dot{W}_{\text{Compressors}} - \dot{W}_{\text{Pump}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{Cooling}} }}{{\dot{m}_{\text{F}} LHV_{\text{F}} }}$$
(29)
$$\eta_{\text{I,b}} = \frac{{\dot{W}_{\text{ICE}} - \dot{W}_{\text{Pump}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{Cooling}} }}{{\dot{m}_{\text{F}} LHV_{\text{F}} }}$$
(30)
$$\eta_{\text{I,c}} = \frac{{\dot{W}_{\text{MGT}} - \dot{W}_{\text{Pump}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{Cooling}} }}{{\dot{m}_{\text{F}} LHV_{\text{F}} }}$$
(31)
$$\eta_{\text{I,d}} = \frac{{\dot{W}_{\text{SOFC}} - \dot{W}_{\text{Compressors}} - \dot{W}_{\text{Pump}} + \dot{W}_{\text{MGT}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{Cooling}} }}{{\dot{m}_{\text{F}} LHV_{\text{F}} }}$$
(32)

where \(\eta_{\text{I,a - d}}\) defines the first law efficiencies for the scenarios 1–4, respectively. Also \(\dot{m}_{\text{F}}\) and \({\text{LHV}}_{\text{F}}\) are the flow rate and lower heating value of the fuel (which is considered natural gas since its price in Iran is very low). \(\dot{Q}_{\text{heating}}\) is the generated heating for domestic use by HRSG and \(\dot{Q}_{\text{cooling}}\) is the amount of generated cooling via absorption chiller.

Also, to find out how the proposed system in different scenarios operates in terms of the second law of thermodynamics, the exergetic efficiency of the system for scenarios 1–4 is defined as follows, respectively [42, 53]:

$$\eta_{\text{II,a}} = \frac{{\dot{W}_{\text{net,SOFC}} + \dot{E}X_{\text{heating}} + \dot{E}X_{\text{cooling}} }}{{\dot{E}X_{F} }}$$
(33)
$$\eta_{\text{II,b}} = \frac{{\dot{W}_{\text{net,ICE}} + \dot{E}X_{\text{heating}} + \dot{E}X_{\text{cooling}} }}{{\dot{E}X_{\text{F}} }}$$
(34)
$$\eta_{\text{II,c}} = \frac{{\dot{W}_{\text{net,MGT}} + \dot{E}_{\text{heating}} + \dot{E}_{\text{cooling}} }}{{\dot{E}X_{\text{F}} }}$$
(35)
$$\eta_{\text{II,d}} = \frac{{\dot{W}_{\text{net,SOFC,MGT}} + \dot{E}X_{\text{heating}} + \dot{E}X_{\text{cooling}} }}{{\dot{E}X_{\text{F}} }}$$
(36)

in which \(\dot{E}_{\text{F}}\) is the exergy of the fuel, which is equal to the chemical exergy of the fuel [43]. And \(\dot{E}X_{\text{heating}} = \dot{E}X_{33} - \dot{E}X_{34}\) and \(\dot{E}X_{\text{cooling}} = \dot{E}X_{22} - \dot{E}X_{23}\).

The total unit product cost can be achieved for the system by writing an overall cost balance to the proposed method in different scenarios as [39]:

$$c_{\text{p,tot}} = \frac{{\mathop \sum \nolimits_{i = 1}^{{n_{k} }} \dot{Z}_{\text{k}} + \mathop \sum \nolimits_{i = 1}^{{n_{F} }} \dot{C}_{{{\text{F}}_{\text{i}} }} }}{{\mathop \sum \nolimits_{i = 1}^{k} \dot{E}X_{{{\text{P}}_{\text{i}} }} }}$$
(37)

in which cF is considered to be 0.04 cent m−3 in Iran. Furthermore, the payback period can be defined as [47]:

$$c_{\text{p,tot}} = \frac{{\mathop \sum \nolimits_{i = 1}^{{n_{k} }} \dot{Z}_{\text{k}} }}{{\dot{W}_{\text{net}} \times \tau \times EC}}$$
(38)

in which EC is assumed to be the electricity cost and equals to 0.1 $ kWh−1 in this study.

Environmental impact assessment

Using CCHP systems and efficient design of the energy systems, along with the utilization of renewable technology with low GHG emissions, results in environmental sustainability. In this manner, a sustainability index is defined in the literature, and the amount of emitted CO2 is of prime importance in this index [54, 55]. The emitted CO2 for different scenarios is defined via Eqs. 38–41. Also, for showing the motivation of the use of CCHP systems, the emitted CO2 for the best case from efficiency and economic viewpoints is put to a comparison. The three considered cases for the best-case scenario are: (1) single prime mover is the sole objective of the system, and the exhaust gases are discharged to the atmosphere; (2) prime mover and HRSG for hot water production are used; (3) a CCHP system based on prime mover and HRSG along with absorption chiller is used.

$$\varepsilon_{\text{em,1}} = \frac{{\dot{m}_{{{\text{CO}}_{ 2} , {\text{emitted}}}} }}{{\dot{W}_{\text{SOFC}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{cooling}} }}$$
(39)
$$\varepsilon_{\text{em,2}} = \frac{{\dot{m}_{{{\text{CO}}_{ 2} , {\text{emitted}}}} }}{{\dot{W}_{\text{ICE}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{cooling}} }}$$
(40)
$$\varepsilon_{\text{em,3}} = \frac{{\dot{m}_{{{\text{CO}}_{ 2} , {\text{emitted}}}} }}{{\dot{W}_{\text{MGT}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{cooling}} }}$$
(41)
$$\varepsilon_{\text{em,4}} = \frac{{\dot{m}_{{{\text{CO}}_{ 2} , {\text{emitted}}}} }}{{\dot{W}_{\text{SOFC,MGT}} + \dot{Q}_{\text{heating}} + \dot{Q}_{\text{cooling}} }}$$
(42)

3D optimization procedure

In designing thermal systems, many contradictory objectives need to be satisfied concurrently. When considering single-objective optimization, it is evident that to reach higher efficiency, the equipment with higher price suits well to the system performance. Also, when the price is the sole objective to be minimized, the efficiency will be sacrificed. In this study, a 3D multi-objective optimization is carried out considering to maximize exergy efficiency and minimize both the unit product cost and emissions simultaneously. Neural fuzzy network code is developed in MATLAB software to get the advantage of a genetic algorithm to optimize Eqs. 33–36 (to be maximized) along with Eq. 37 and 42 (to be minimized). An optimal point is selected among a set of the optimized solution which will be given by MATLAB known as Pareto frontier [56]. The parameters and their domain in the optimization method are gathered in  3D Multi-objective optimization results section for the best-case scenario. Figure 2 indicates the flowchart of optimization carried out to reach the best solution point. Also, the genetic algorithm is an iterative method to find the ideal solution imitating the attitude of the natural evolutionary process [57]. Using a genetic algorithm, abundant populations are generated in a random manner, among which the ones having the greatest compatibility with the objective functions are selected and the less compatible ones are crossed out. In the genetic algorithm method, the two important factors are crossover and mutation. The crossover operative mixes chromosomes as parents to produce new chromosomes called offspring. The new generations in the genetic algorithm have higher correspondence to the objective functions since in each step, genes with higher compatibility are chosen as parents. The mutation operator, however, causes chaotic variations in the structures of the genes and thus makes the optimization process away from the confined optimal.

Fig. 2
figure 2

Flowchart of optimization based on genetic algorithm

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Moreover, the tuning decision variables for multi-objective method are listed in Table 5.

Table 5 Tuning parameters in the genetic algorithm optimization method
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Results and discussion

To find the effective critical parameters on the system performance, a parametric study is carried out in the proposed CCHP system. Also, an environmental analysis result, along with exergoeconomic results proposing exergoeconomic factors and variables, is reported. Finally, the results of Multi-objective optimization point out the best solution and the best prime mover for us.

Verification of developed models

To verify the developed thermodynamic models for each of the subsystems of the proposed CCHP system, the available data in the scientific literature are used. Validation of the SOFC and verification of the ICE are presented in Fig. 3 by comparing to the available experimental results reported by Tao et al. [58] and Hosseinpour et al. [59]. As the figure shows, the outcomes of the present study fit well on available experimental and numerical results.

Fig. 3
figure 3

a Validation of modeling of the SOFC modeling and b verification of the modeling of the ICE

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Moreover, to show the accuracy of the results obtained for the double effect absorption refrigeration system in the present work, the reported data by Gomri and Hakimi are used [60]. The comparison is shown in Table 6, indicating an excellent agreement between the two sets of results.

Table 6 Comparison of the results obtained from the present work with experimental data for double effect absorption cycle
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Comparative study results

In order to evaluate the best proposed CCHP system, the efficiencies of each scenario for the power production system, the CHP system, and the CCHP system are, respectively, demonstrated in Fig. 4. Also, the generated power, heating, and cooling, as well as unit product cost of different scenarios, are presented in Fig. 5. Taking Fig. 4 into consideration, it is evident that considering only the power production system, scenario 4 has the most energetic and exergetic efficiency, namely 66.67% and 64.73%, respectively. Scenario 4 is capable of producing 441.9 kW net power output, and the scenarios 1, 3, and 2 are in the next positions with 346.5 kW, 311 kW, and 210.5 kW, respectively. According to Fig. 5, the power production in different cases is all the more reason that scenario 4 indicates more energetic and exergetic efficiency. Another essential aspect of Fig. 5 is the energetic and exergetic efficiencies of different cases when the CHP system is considered. Since the energetic efficiency considers the quantity of energies and not the qualities, the energetic efficiency of scenario 2 is the highest efficiency among the cases with 86.7%, which is because it can generate 719.5 kW heating capacity. Moreover, the MGT system produces 271 kW heating, which is more than 174 kW in scenario 1 and 78.69 kW in scenario 4. Besides, the exergetic efficiency in scenario 4 is 68.65%, which is more than in other cases, since the power generation, in this case, is higher. The last but not the least important aspect of Fig. 5 is energetic and exergetic efficiency of the CCHP system in 4 cases. Considering the energetic efficiency, scenario 2 is the most efficient system with an efficiency of 91.87%. The hybrid SOFC/GT system operates better in terms of exegetic efficiency, with an efficiency of 69.06%.

Fig. 4
figure 4

Comparison of efficiencies for power production, CHP system and CCHP system in four different scenarios

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Fig. 5
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Comparison of the unit product cost, generated power, heating, and cooling in different scenarios

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The conclusion from Figs. 3 and 4 is that hybrid SOFC/GT system operates better in terms of power generation, and considering the second law efficiency, it has the highest efficiency. It is noteworthy that scenario 2 generates more heating than other cases, and it is the best case when more steam is required. Another important aspect of Fig. 4 is the unit product cost in different cases. According to Eq. (37), the more exergy of products is, the cheaper the unit product of the system becomes. Also, more equipment in the system causes the nominator of Eq. (37) to become larger. The unit product cost in scenarios 1–4 is 38.88 ($ GJ−1), 18.91($ GJ−1), 30.98($ GJ−1), and 37.78($ GJ−1), respectively.

Figure 6 indicates the comparison of emission in power generation system, CHP, and CCHP system along with the payback period in four different scenarios. According to Eqs. (39–42), emission in the CCHP system becomes less than the power generation system and CHP system, which is an excellent motivation to use the CCHP system. Scenario 4 indicates the fastest payback period among the other cases with 1.49 years, while scenario 2 has the longest payback period of 5.33. Additionally, the power generation, CHP and CCHP emissions for hybrid SOFC/GT are 0.30 (ton/MWh), 0.25 (ton/MWh), and 0.23 (ton/MWh), respectively.

Fig. 6
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Comparison of payback period and emission reduction in different scenarios

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To investigate the systems from exergy and exergoeconomic points of view, the exergy indicator parameters like exergy destruction, the exergy of fuel, exergy of product, and lost exergy are presented as exergy indicators. Besides, the cost of components, cost of fuel, and cost of product along with destructed cost and lost cost are illustrated as exergoeconomic indicators in Tables 78, 9, 10 for different cases, respectively. According to tables, in scenario 1, AHE, SOFC, and AB with exergy destruction of 120 kW, 52.16 kW, and 42.62 kW, respectively, have the highest exergy destruction rate. These values are the same for scenario 4. This is due to the fact that in SOFC and A.B, there is all three primary source of irreversibility in the system, which is chemical reaction, mixing, and temperature difference. Moreover, because of the very high temperature difference in AHE, the exergy destruction in this component is higher than the others. In the case of ICE and MGT, the engine and combustion chamber have the highest exergy destruction rate, which is 132.4 kW and 198.8 kW, respectively. Additionally, it is noteworthy that the last column of Tables 5–8 is the exergoeconomic factor (f). A low value of this factor calculated for a significant component suggests that cost-saving in the entire system might be achieved by improving the component efficiency (reducing exergy destruction) even if the capital investment for the component will increase. So, it is evident that in the system, FHE and AHE have very low exergoeconomic factors, which are 2.92% and 10.26% for scenarios 1 and 4. These values are 1.34% for cooling set in scenario 2 and 10.26 for the combustion chamber in scenario 3. On the other hand, a high value of this factor suggests a decrease in the investment cost of this component at the expense of its exergetic efficiency (like fuel compressor in cases 1 and 4).

Table 7 Exergy and exergoeconomic parameters of scenario 1
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Table 8 Exergy and exergoeconomic parameters of scenario 2
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Table 9 Exergy and exergoeconomic parameters of scenario 3
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Table 10 Exergy and exergoeconomic parameters of scenario 4
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Parametric study results

The effect of crucial decision variables on the system performance indexes which are exergetic efficiency and unit product cost is indicated in this section, for the scenario number 4, which is proved to be the better case study among the other proposed cases.

Figure 7 depicts the effect of stack temperature difference on exergy efficiency and unit product cost. Increasing stack temperature difference has a positive effect on unit product cost and reduces the cost from 40.43 (S/GJ) to 34.38 (S/GJ). However, the change in exergetic efficiency is not much, and after reaching a maximum of 69.07% at 102 °C, it reduces to 68.46%. This is mainly due to the fact that increasing stack temperature difference results in a reduction in power output and an increase in heating capacity since the outlet enthalpy of the SOFC is higher.

Fig. 7
figure 7

Effect of stack temperature difference on exergy efficiency and unit product cost of the system in scenario 4

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Fuel utilization factor is another crucial design parameter, the effect of which on exergetic efficiency and unit product cost is shown in Fig. 8. Increasing fuel utilization factor from 0.65 to 0.9 causes a maximum in exergy efficiency in Uf = 0.83, corresponding to a value of 69.2%. Also, a minimum of 23.6 ($ GJ−1) is reached for unit product cost at the fuel utilization factor of 0.68, which makes this parameter more critical form the multi-objective optimization viewpoint.

Fig. 8
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Effect of fuel utilization factor on exergy efficiency and unit product cost of the system in scenario 4

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The effect of the current density of SOFC on exergy efficiency and unit product cost is indicated in Fig. 9. Increasing current density from 2500 (A m−2) to 6100 (A m−2) results in a decrease in exergy efficiency from 73.4 to 67.1%. This is mainly because cell voltage decreases, and therefore, power output from the SOFC decreases as a result of an increase in the current density. Also, this increase causes a reduction in unit product cost from 55.08 ($ GJ−1) to 35.01 ($ GJ−1).

Fig. 9
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Effect of current density on exergy efficiency and unit product cost of the system in scenario 4

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One of the crucial decision variables on system performance is the pressure ratio of air compressor, which is also equal to the value of the fuel compressor, pressure ratio, the effect of which is indicated in Fig. 10. According to this figure, when the value of PRac is raised from 1.1 to 2.1, the exergy efficiency decreases, and unit product cost increases from 69.4 to 66.3% and 27.1($ GJ−1) to 98.02 ($ GJ−1), respectively. This trend is primarily because increasing the pressure ratio of the compressors requires more power input to the compressors.

Fig. 10
figure 10

Effect of air compressor pressure ratio on exergy efficiency and unit product cost of the system in scenario 4

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The last but not the least important parameter to study is the effect of pinch point temperature difference in the variation in unit product cost and exergy efficiency, which is presented in Fig. 11. As was anticipated, rising pinch point temperature difference has a negative effect on heating capacity and, thus, on overall exergy efficiency and unit product cost. Furthermore, increasing pinch point temperature difference about 50 °C causes a reduction in exergy efficiency, about 2.1%, and an increase in unit product cost about 0.5%.

Fig. 11
figure 11

Effect of pinch point temperature difference in exergy efficiency and unit product cost of the system in scenario 4

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3D Multi-objective optimization results

By considering the overall exergy efficiency, CO2 emission, and the total unit product cost as the objective parameters, a multi-objective optimization is applied by using MATLAB software. Five decision parameters, along with their ranges, are listed in Table 11.

Table 11 Domain of major decision parameters
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The optimal solution points of the system are illustrated in Fig. 12 as a Pareto frontier solution. As a result of multi-objective optimization to maximize exergy efficiency and minimize unit product cost and CO2 emission, a 3-dimensional Pareto Frontier is presented in Fig. 12, which is a fitted surface to the optimum results of optimization. The ideal point of the Pareto Frontier is specified in the figure, and it has an exergy efficiency of 73.15%, unit product cost of 25.08 ($ GJ−1), and CO2 emission of 58.10 g MWh−1. To investigate the behavior of each decision variable on the optimization process, 4 points of the Pareto Frontier are selected, and their results, such as the value of decision variables and objective functions, are listed in Table 10. The first 3 points are called single-objective optimum points in which only the value of one objective is considered as criteria to be minimized or maximized. The fourth point is the closest to the ideal point, which is called the best solution point. As illustrated in Table 11, point 1, possessing the maximum exergy efficiency of 73.15%, has the minimum stack temperature difference (85.09 K), pressure ratio of (1.20), current density of 2570.23 A m−2, and fuel utilization factor of 0.87, which shows that the lower amount of these parameters leads the system to a higher amount of exergy efficiency. However, the fuel utilization factor (Uf) has a reverse effect on the efficiency, and the higher amount of Uf = 0.87 results in maximum efficiency. If the unit product cost is selected as the only objective to be minimized, point 2 is the optimum point of the total cost rate of 25.08 ($ GJ−1). According to Table 12, the higher values of pinch point temperature difference cause lower values of the unit product cost. Point 3 is the point with the lowest CO2 emission of 58.10 (g/MWh). Stack temperature difference has a reverse effect on the emission in the way that increasing the Stack temperature difference reduces the emission.

Fig. 12
figure 12

Distribution of the 3D Pareto optimal solutions for exergy efficiency, CO2 emission, and unit product cost of the system

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Table 12 Pareto frontier selected points with decision variables and objective functions value
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To have a better overview of the decision variables, the scattered distribution of these parameters is depicted in Fig. 13. From data in Fig. 13a, it can be seen that all the optimal points of stack temperature difference are located nearly between 120 and 140. This means that if stack temperature difference is around 130 °C, the optimum solution can be reached. Figure 13b shows the distribution of the pressure ratio of air compressors and reveals that keeping this parameter at its lowest value results in better optimization outcomes. These results also are shown in Fig. 8 in the parametric study section, which shows that increasing the pressure ratio of air compressor leads to the exergy efficiency decreasing and unit product cost increasing. Figure 13c, d and e reveals that current density, fuel utilization factor, and pinch point temperature difference have scattered distributions in their allowable domain. Current density tends to have lower values around 3000 A m−2, and fuel utilization factor shall be above 0.75 to get an optimal solution. Moreover the selected optimal range for pinch point temperature difference is around 165 °C.

Fig. 13
figure 13figure 13

Scatter distribution of decision variables with Pareto frontier: a stack temperature difference, b pressure ratio of air compressor, c current density, d fuel utilization factor, e pinch point temperature difference

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Conclusions

In this research paper, four different scenarios are proposed for producing, heating, cooling, and power in a small residential scale. The proposed systems are studied from viewpoints of energy, exergy, exergoeconomic, and environmental impact. The superior prime mover for the integrated system is selected to be optimized, considering exergetic efficiency and unit product cost as two main objectives. Three-objective optimization is carried out to find the maximum of exergy efficiency and a minimum of unit product cost and CO2 emission. Main findings of the present study, as well as multi-objective optimization results, are as follows:

  • Results demonstrate that the hybrid SOFC/GT system proves to be better in terms of exergetic efficiency and payback period, which is 69.06% and 1.49 years, respectively.

  • ICE proves to be the better system in terms of heating generation and unit product cost, which is 719.50 kW and 18.91 ($ GJ−1).

  • The parametric study shows that for specific values of fuel utilization factor, the efficiency increases and unit product cost decreases, which is of great importance for optimization purposes.

  • Results show that using CCHO system demonstrates a great motivation in reducing the GHG emission.

  • Optimization results show that maximum exergy efficiency for the best case can be reached higher costs, respectively, at 73.15% and 61.1 ($ GJ-1).

  • Moreover, the minimum cost can be reached to the hybrid SOFC/GT system at 29.02 ($ GJ−1), which corresponds to the efficiency of 66.44%.

  • The best solution points based on five decision parameters are 73.15% in exergetic efficiency, 25.08 $ GJ−1 in unit product cost, and 58.10 (g MWh−1) of CO2 emission.