Multi-objective Optimization and Exergo-economic Assessment of a Multi-generation Energy System

Multi-objective optimization and exergo-economic assessment of a multi-generation energy system based on geothermal and solar energy

Nomenclature
		Subscripts

1. Introduction

Design and optimization of co-generation energy-producing systems based on renewable energies have gained significant importance recently due to the adverse environmental repercussions pertinent to fossil fuels. Considering the world bank’s statistics, fossil fuels are responsible for approximately 81.2% of used energy throughout the globe [1]. Needless to say, excessive reliance on fossil fuels is not only not sustainable, but can also have pernicious consequences for the environment [2]. In order to halt this trend, it seems vital to develop CO₂-free power generation methods. Solar energy, as an easy to access and clean resource, has some drawbacks which make it difficult to harness electricity incessantly, as it fluctuates with regards to several factors. Fortunately, this predicament can be surmounted by combining solar methods with storage systems and diverse energy sources [3]. According to literature, 140 MJ/kg of energy can be stored by hydrogen, which makes it an efficacious material compared to representative fuels with the average energy density of 50 MJ/kg. Not to mention that the byproduct of burning hydrogen is water, hence it is an environmentally friendly energy-storing procedure [4]. Additionally, geothermal as clean and sustainable energy sources with minimum pollutant emissions, are being used prevalently.

Undoubtedly, apart from environmental issues, the unprecedented surge of demand for drinkable water is one of the most paramount challenges nowadays. Statistically speaking, 3.5 million people lose their lives yearly as a consequence of the shortage of clean water, and associated problems with sanitation. Thus, desalination technologies, such as reverse osmosis (RO), seem feasible approaches to address this problem [5]. However, RO systems require a substantial amount of electrical energy supply to provide the needed pressure on feed water. As a result, it is more cost-efficient to satisfy the RO system’s electrical demand by photovoltaic technologies [6]. All in all, merging of combined cooling, heating and power (CCHP) systems with novel renewable energy sources and storing technologies bears numerous benefits to the resulted system, including diminishing CO₂ emission and higher energy efficiency [7].

In this regard, Ahmadi et al. [8] proposed a co-generation where the ocean’s energy is harnessed by an energy conversion system; additionally, the system was equipped with solar collectors, a polymer electrolysis membrane (PEM) electrolyzer, a single effect absorption chiller, and an RO water desalination system. It is pointed out that the total cost rate of the system and exergy efficiency as a result of multi-objective optimization are 154 $/h and 60%, respectively. Ahmadi et al. [9] also studied the thermodynamic simulation of a flat plate solar collector attached to an ocean thermal energy conversion (OTEC) cycle and a PEM electrolysis. They concluded that the very integrated OTEC cycle can reach an exergy efficiency of 22%. Furthermore, they demonstrated that by an increase in solar radiation, the cycle’s total exergy destruction decreases. As a result, exergy efficiency and the rate of hydrogen production in the electrolyzer. Kianfard et al. [6] obtained a net cost of 4.257 $/kg and 32.73 cents/m³ for production of hydrogen and water desalination in a combined system which employs an organic rankine cycle (ORC) with dual fluid, a RO water desalination section, and a PEM electrolyzer unit. Yari [10] investigated exergy destruction, first and second-law efficiency in an assortment of ORC cycles such as an organic cycle with an internal heat exchanger (IHE), regenerative ORC, and combined flash binary cycle. The highest first-law efficiency is calculated to be 15.35% based on the input energy to an ORC cycle in the regenerative binary cycle equipped with an IHE and the operating fluid of R123. Moreover, flash-binary cycle with R123 has been estimated to have the maximum first-law efficiency of 11.81%. Also, it is showed that an ORC with an IHE and R123 as the working fluid can reach its zenith first-law efficiency which is 7.65%. Keshavarzzadeh et al. [11] proposed a novel CCHP system encompassing an ORC cycle, a proton exchange membrane electrolyzer (PEME) section, an absorption chiller, and a thermal-storage section. They drew a comparison between the indicator-based evolutionary algorithm (IBEA) optimization algorithm and non-dominated sorting genetic algorithm (NSGA-II), and they concluded that despite the fact that exergy efficiency increased by 2.5%, the overall cost rate declined by 7% in the IBEA method. Atiz et al. [12] proposed a geothermal system for low-temperature resource and solar energy. Using n-butane as the cyclic fluid, they calculated 6.92% and 21.06% as the total energy and exergy efficiencies of the system, respectively. Akrami et al. [13] modeled a multi-generation system comprised of an ORC, an absorption chiller, a PEM electrolyzer, and a water heater. Under certain conditions, they monitored 34.98% and 49.17% for the energy and exergy efficiencies, respectively. Hashemian et al. [14] studied thermodynamic, exergoeconomic, and exergoenvironmental analysis of a multi-generation system, operation with the energy of solar and biomass. Using genetic algorithm and finding optimum working points, they concluded that 0.84 $/s, 14%, and 82.4% are attainable for the proposed system for overall product cost rate, exergy and energy efficiency, respectively.

In the present paper, a multi-generation system is developed, simulated, and analyzed in terms of energy, exergy and exergoeconomy. The proposed system consists of a geothermal pit, linear parabolic solar planes, a steam cycle, a regenerative organic rankine cycle with an IHE, an absorption chiller, PEM electrolyzer, and a reverse osmosis unit. According to previous works and present study, a heat exchanger is used in hybrid systems of PTC and geothermal energy. However, multi-objective optimization for a multi-generation system wherein the geothermal fluid enters the PTC directly has never been addressed to this day.

The following is a summary of the primary objectives and innovations of this paper:

• Tailoring a heat exchanger between the steam cycle and the ORC for increasing the productivity of the system and confining energy loss.
• Considering various geothermal working fluids for the solar and geothermal cycles.
• Producing fresh water and hydrogen from the novel integrated energy system.
• Applying multi-objective optimization to determine the optimal design parameters.

2. System description

Fig. 1 shows the schematic diagram of an integrated multi-generative system, presented in this paper, based on geothermal and solar energy, which comprises of a PEM electrolyzer, a RO desalination unit, an absorption cooler system, a steam cycle, and an ORC cycle. The operating fluid in the steam cycle absorbs the required heat from a flow of hot steam to run a turbine, using a steam generator at point 2. The mentioned hot steam is obtained from production wells, and absorbs further heat in solar collectors (the thermodynamic properties of terminal 59 and organic fluid are listed in Table 1). Then, the exited hot water from Steam generator, at point 3, is used in order to exchange its remaining thermal energy to preheat the feed water of a PEM electrolyzer at point 37 via a domestic water heater (DWH), and to drive the generator of an absorption cooling system at point 4. Also, the ORC cycle consists of an open feed-organic heater (OFOH) and IHE to enhance the efficiency of the system. This cycle acquires the necessary heat through a heat exchanger at point 11. In the other part of the system, the generated electric energy from both the Rankine cycle and the steam cycle is collected to be used in a reverse osmosis desalination system, and a PEM electrolyzer to produce hydrogen for later uses. At point 46, a small turbine is placed to harvest the electricity from the RO unit’s brine water, which is going to be discharged back to the sea. Fig. 2 represents S-T diagrams of aforementioned processes.

Fig. 1. Schematic diagram of the multi-generation energy system based on geothermal and solar.

Fig. 2. S-T diagrams of processes in (a) the steam cycle and (b) the ORC.

3. Thermodynamic Analysis

In order to model the system, some inputs are needed. Input values for different parameters are listed in Table 1.

Table 1. Input parameters for the system modeling.

Parameters	Value	Unit
PTC [21], [22];
Specific heat of the working fluid (CP,C)	2314	J/kg˚C
Receiver outside diameter (Do,r)	0.07	m
Receiver inside diameter (Di,r)	0.066	m
Collector heat loss coefficient (UL)	3.82	W/m2 ˚C
Receiver inlet temperature (Tri)	180	˚C
Heat transfer coefficient inside the receiver (hfi)	300	W/m2 ˚C
Thermal conductivity of the receiver (k)	16	W/m˚C
Total solar radiation	850	W/m2
Transmissivity of the cover glazing	0.96	–
Effective transmissivity of PTC	0.94	–
Absorptivity of receiver	0.96	–
Correction factor for diffuse radiation	0.95	–
Single collector width	5.76	–
Single collector length	12.27	–
Steam & organic rankine cycle
P7	1500	kPa
Pinch point temperature of the Steam generator/HE	5	˚C
P12[extraction]	501.2	kPa
Tc	35	˚C
εIHE	0.8	–
Reverse osmosis[24],[25];
Salinity43	45	g/kg
Number of elements	7	–
Fouling factor	0.85	–
Recovery ratio	0.3	–
Number of pressure vessels	42	–
PEM electrolysis [6],[20];
Po2	101.325	kPa
PH2	101.325	kPa
TPEM	80	˚C
Eact,a	76	kJ/mol
Eact,c	18	kJ/mol
${\mathrm{\lambda }}_{\mathrm{a}}$	14	–
${\mathrm{\lambda }}_{\mathrm{c}}$	10	–
D	100	μm
	1.7 $\times$ 105	A/m2
	4.6 $\times$ 103	A/m2
F	96.486	C/mol

3.1 Steam cycle and organic Rankine cycle

In this paper, 4 different geothermal fluids namely Therminol 59, Therminol VP1, Syltherm 800, and Marlotherm SH, are compared to determine which one has better performance. This system uses a binary geothermal cycle where the geothermal fluid from production wells with initial temperature of roughly 180 C (state 1) gain extra heat from a parabolic trough collector (PTC), and reaches the temperature of approximately 380 ℃ (state 2). Then, this fluid transfers its thermal energy to the operating fluid of the steam cycle, which is water in this case, in order to drive the steam turbine. Steam enters a heat exchanger after the turbine to transfer its heat to an organic fluid. A heat exchanger, a turbine, a pump, a condenser, an OFOH, and an IHE are constituents of the ORC. IHE unit recovers heat from the low-pressure steam after turbine (state 13). The saturated vapor enters the turbine (state 11), and is expanded isentropically in an ideal ORC cycle (state 12). An OFOH mixes organic fluid in pump’s discharge with the portion of steam extracted from the turbine in intermediate pressure (state 18). The rest of the vapor expands in the turbine to reach the condenser pressure (state 13) [15]. The equation that presents energy balance in steam generator is as follows:

(1)

The following equation describes the energy balance in heat exchanger, between the steam cycle and the ORC:

(2)

The proposed cycle is designed based on mass balance, energy, and isentropic efficiency. Also, Engineering Equation Solver (EES) is used to solve equations, conduct exergy and exergoeconomic analysis, and to determine thermodynamic properties at all points [16]. The subsequent assumptions are made in this paper:

• This system operates under the steady-state conditions.
• Isentropic efficiency is proposed for pumps and turbines.
• Pressure drop in pipelines and heat exchangers are neglected.
• The fluid enters the turbine as saturated vapor (x=1), and as saturated liquid (x=0) in the pump inlet.
• The isentropic efficiency of the pump and the turbine, are assumed to be 90% and 80%, respectively.

3.2 Absorption chiller

Considering each component of the absorption chiller system as a control volume, mass balance, mass conservation, momentum, and the first and the second law of thermodynamics equations are employed in order to analyze the single-effect absorption chiller. Mass balance in steady-state conditions and constant flow are as follows [17]:

	(3)
	(4)
	(5)

The cooling capacity of the absorption chiller is obtained by:

(6)

Further information for analyzing each element of the absorption chiller is available in sources [17] and [18].

3.3 PEM electrolysis

As can be seen in Fig. 1, an electrical generator provides power for reactions in the electrolyzer. Having preheated in the domestic water heater, water enters the electrolyzer to produce hydrogen. The resulted hydrogen exits the cathode and loses its heat to reach the ambient temperature. Subsequently, the mixture of oxygen and water exits anode in order to separate oxygen, and the remaining water is used again in the electrolyzer. The required energy for the electrolysis process can be determined by:

(7)

where the properties of oxygen, hydrogen, and water are presented in thermodynamic tables [15].

Hydrogen’s outlet flow rate can be calculated by [19]:

(8)

The electrolyzer rate of electrical energy input can be obtained by [9]:

(9)

also, ref. [19] expresses V as:

(10)

where is calculated by Nernst equation:

(11)

When hydrogen ions move across the membrane, the membrane’s resistance brings about ohmic over-potential in the proton exchange membrane. Different factors are responsible for the ionic resistance of the membrane, such as humidification degree, thickness, and temperature of the membrane. The membrane’s local ionic conductivity can be calculated by experimental equation [19]:

	(12)
	(13)

As a result, the total ohmic resistance can be described by [19]:

(14)

Also, can be defined using the following equation:

(15)

An electrode’s activation over-potential and exchange current density equation can be written as follows [19]:

	(16)
	(17)

For supplementary information for PEM electrolysis, visit ref. [9], [19] and [20].

3.4 Parabolic trough collector

Geothermal fluid gains more heat passing through the PTCs, as shown in Fig. 1. The useful energy-producing rate by collectors can be calculated as [21]:

(18)

where S can be written as [23]:

	(19)
	(20)

The following equations can be used to determine and :

	(21)
	(22)

Surface of aperture is [23]:

(23)

3.5 Reverse osmosis desalination

An RO system usually takes in seawater at the first stage of the process, then the water goes through a pre-treatment procedure, and finally, the water enters the main RO system [3]. Using the mass flow rate of distillate m₄₅ and the recovery ratio (RR), the feed flow rate m₄₃ can be calculated:

(24)

Also, the volume flow rate of brine water is expressed by:

(25)

The salt concentration of distilled water and rejected water and the average salt concentration are as follows, respectively [25]:

	(26)
	(27)
	(28)

The equation for the factor of temperature correction is [25]:

(29)

The following equation determines water permeability of membrane:

(30)

Three equations below calculate the average osmosis pressure on the feed side, net osmosis pressure across the membrane, and the net pressure difference through the membrane, respectively [25]:

	(31)
	(32)
	(33)

The high pressure pump’s required power is expressed by:

(34)

Finally, the multi-generation system’s efficiency of energy and exergy can be expressed by:

	(35)
	(36)

4. Exergoeconomic analysis

In energy conversion systems, the precise magnitude and the kind of irreversibility of each point can be defined by exergy analysis in order to utilize existing energy sources in the most productive means. To be more specific, a system exergy is defined as keeping equilibrium of environment and the highest usable power of a control volume in a certain process. In this regard, having considered every element as a control volume, exergy balance equations are presented as follows [15]:

(37)

wherein, subscripts D and out, are the control volume’s inlet and outlet flow, and exergy destruction rate, respectively.

Equations determining the first law of thermodynamics and exergy destruction rate of all of the multi-generation system’s components are presented in Table 2.

Table 2. Energy balance and Exergy destruction rate equations for system’s elements.

Component	Energy balance equations	Exergy destruction rate equations
Parabolic trough collector
Steam generator
Domestic water heater
Steam turbine
ORC turbine
Heat exchanger
Pump 1
Pump 2
Pump 3
Open feed organic heater
Internal heat exchanger
Condenser
LiBr generator
LiBr absorber
LiBr condenser
LiBr evaporator
LiBr pump
LiBr valve 1
LiBr valve 2
LiBr HEX
PEM electrolyzer
RO pump
RO turbine

Simultaneous evaluation of economic and exergy issues in complicated energy systems can prove to be problematic. Hence, exergoeconomics, as a new area of engineering, has been introduced to address these concerns by combining information about exergy based on price analysis, which can assist project designers and managers to select the most cost-efficient method to enhance the system’s performance [13]. In this regard, equations for cost balance, which are applied to each system element, are listed as follows [6]:

	(38)
	(39)

Some essential parameters to evaluate the system performance from an exergoeconomic perspective, such as unit cost rate, product unit cost, and exergy destruction cost rate, can be expressed as follows [27,28]:

	(38)
	(39)
	(40)

Table 3 consists of supplementary equations and applied cost balance equations. In order to calculate the Z_k of components in table 3, references [29-31] are used.

Table 3. Formulation of cost balance and auxiliary equations for each component.

Auxiliary equation	Cost balance	Component
		PTC field
		Steam generator
		Steam turbine
		ORC turbine
		Heat exchanger
		Pump 1
		Pump 2
		Pump 3
		Condenser
		Domestic water heater
		PEM electrolyzer
		RO desalination unit
		Generator
		Condenser
		Evaporator
		Absorber
		Pump
		HEX

5. Validation

Since the proposed multi-generation system has not been studied in the preceding literature, the calculated results for subsystems have been validated individually, using experimental and theoretical data in the pertinent literature. Accordingly, the results for PEM electrolysis have been compared with the results of Ioroi et al. [26], Fig. 3, and the RO unit’s results with the work of Nafey et al. [25], Table 4. Considering the negligible errors for each part, the model and the results are acceptable.

Fig. 3. Comparison of the present model with experimental data.

Table 4. Validation of the results obtained from the present work with data reported by Nafey [25].

Error (%)	Unit	Nafy [19]	Present study	Variable
0.97	kW	1131	1120	${\dot{\mathrm{W}}}_{\mathrm{pump}.\mathrm{RO}}$
0	m3/h	485.9	485.9	Mf
0	–	0.9944	0.9944	SR
0	ppm	64,180	64,180	Xb
0.8	ppm	250	252	Xd
0.1	kPa	6850	6843	ΔP

6. Results and discussion

Different refrigerants exist in the market, each of which possesses a variety of distinct features compared to others, such as being environmentally friendly, lower cost, and so forth. Having examined energy and exergy efficiencies of a variety of working fluids for the proposed ORC in this paper, the details of resulted data, shown in Fig. 4, are listed in Table 5. According to this information, R123 yields the best efficiency of energy and exergy under the conditions of this study, in comparison to the other refrigerants which are assessed.

Fig. 4. Energy and exergy efficiencies of different operating fluids in the ORC.

Table 5. Energy and exergy efficiencies of different operating fluids in the ORC.

	Isobutene	Neopentane	n-Pentane	R11	R114	R123	R141b	R142b	R245fa	R600
Second law efficiency [%]	28.68	29.3	28.89	29.3	28.99	29.35	29.09	28.43	29.33	28.98
Thermal efficiency [%]	22.94	23.78	23.22	23.7	23.36	23.84	23.49	22.59	23.82	23.34

Geothermal fluid as the main input of the entire system has a profound impact on the overall outcome of the system. Thus, the results of using different fluids on the net overall power output have been determined and depicted in Fig. 5. As it can be seen, the fluid Marlotherm SH provides better results by producing a superior power output compared to others. As a result, Marlotherm SH is chosen to be used in the present study. Furthermore, the geothermal source’s initial temperature can significantly affect the power produced by this multi-generation system. According to Fig. 5, the more the geothermal fluid temperature increases, the more the power production capacity of the whole system increases. The underlying reason for this result is that when a geothermal fluid with a higher temperature enters the solar collector, the fluid at the outlet of the collectors, which is the inlet of the steam generator, has a higher temperature. With respect to the parametric study principles, all variations in Eq.1 are assumed to be constant, except the flow rate of the steam cycle. Therefore, according to Eq.1, the increase of inlet geothermal fluid temperature at point 2 will result in an increase in the flow rate of the steam cycle; correspondingly, since the ORC and the steam cycle are linked together by a heat exchanger, ORC flow rate will increase as well. As stated in table 2, by equations of work done by steam and working fluid of the ORC, higher flow rate in  both the ORC and the steam cycle will mean a higher power production rate, as demonstrated in Fig. 5.

Fig. 5. Effect of temperature of geothermal fluid on produced power.

Apart from the geothermal fluid’s initial temperature, the flow rate of the geothermal fluid is also a decisive variable. Although it is conceivable that the power production of the system may rise by increasing the amount of the inlet geothermal fluid, calculations suggest otherwise. Since the number and capacity of solar collectors are assumed to be constant despite the flow rate, increasing the amount of the geothermal fluid passing collectors results in lower temperature at the outlet of collectors and lower power production as well. As Fig. 6 demonstrates, raising the flow rate can drastically reduce the power output.

Fig. 6. Effect of geothermal mass flow rate on produced power.

Cooling capacity is substantially important for this research because of the reason that it is one of the key purposes of this system. As mentioned previously, an increase in the flow rate of the geothermal fluid has a negative impact on the output power. In contrast, the corresponding impact on the cooling capacity of the absorption chiller is completely the opposite. Fig. 7 indicates that the Therminol 59 has a higher performance than other fluids, but also an increase in flow rate can enhance the cooling capacity of the chiller because by doing so, the amount of hot flow in the generator of the absorption chiller increases, which culminates in an improvement in cooling capacity.

Fig. 7. Effect of the mass flow rate of geothermal fluid on cooling capacity.

According to the early mentioned paragraphs, the system exergy evaluation is of great prominence because of economic considerations. Another parameter which can challenge system performance is the correlation of steam turbine inlet pressure with exergy efficiency. Fig. 8 represents how the exergy efficiency increases by raising steam turbine inlet pressure to a peak. Nonetheless, after a critical point, this relation between the parameters is reversed, such that the exergy efficiency diminishes by further increasing the inlet pressure. This varying behavior can be explained by the association of steam turbine inlet pressure with enthalpy and flow rate of the steam cycle. Enthalpy is a parameter that depends on temperature and pressure of flow at any point, which can be obtained from thermodynamic properties tables. Hence, a lower steam turbine inlet pressure means a lower enthalpy and power production, according to the steam turbine work equations in table 2. On the other hand, temperature and pressure of the geothermal fluid are assumed to be constant, so, considering Eq.1, an increase in steam turbine inlet pressure and the consequential increase of enthalpy, results in a decline in the flow rate of the steam cycle, as well as the ORC. As it can be seen in Eq. 2, a reduction in mass flow rate can reduce the power production of the cycle. Due to this transition, the steam turbine inlet pressure needs to be optimized to reach an acceptable number, which is presented in the optimization section.

Fig. 8. Effect of inlet presuure of the steam turbine on the system exergy efficiency.

Moreover, steam turbine inlet pressure can influence the exergy destruction rate in the system. Fig. 9 suggests that regardless of the type of geothermal fluid, an increase in the inlet pressure results in an increase in the exergy destruction rate of the system. This is due to the reason that, as elaborated upon in preceding paragraphs, temperature and pressure of the geothermal fluid are assumed to be constant, and the raise in inlet pressure of the steam turbine is equal to the temperature increase of the working fluid in the steam cycle. Thus, a more significant temperature gradient will be present in the steam generator between the working fluid of the steam cycle and the geothermal fluid, which brings about a higher exergy destruction rate at higher inlet pressures.

Fig. 9. Effect of inlet pressure of steam turbine on the exergy destruction.

Solar energy, as a supplementary energy source for geothermal fluid in the proposed system, can produce a higher efficiency for the system. As demonstrated in Fig. 5, an increase in the temperature of the geothermal fluid has a positive correlation with power production. Fig. 10 explains two important features of Therminol 59; first, higher initial temperature of geothermal fluid means better exergy efficiency for the same fluid; second, greater solar radiation intensity can culminate in improved exergy efficiency. This is due to the fact that intensifying solar radiation will increase the outlet temperature of the geothermal fluid from collectors, and consequently, the flow rate of the steam cycle and the ORC, according to Eq.1 and Eq.2. Furthermore, equations of work in table2 suggest that a rise in the flow rate of the cycles, augments the power production, which means better exergy efficiency, considering  Eq. 36.

Fig. 10. Effect of solar intensity on the exergy efficiency for different temperatures of geothermal fluid.

Another indirect impact of solar radiation intensity is on the hydrogen production of the PEM electrolyzer. As monitored in Fig. 11, even though for solar intensities lower than 300 W/m², the amount of hydrogen production is approximately equal for different types of geothermal fluids,  as the solar intensity increases, the outcome of hydrogen production unit varies considerably for each fluid. This association is applicable to the RO unit and water production as well, as can be seen in Fig. 11. This is because of the inextricable connection of production rate of both the PEM electrolyzer and the RO unit with the power produced by the ORC. Since the electricity from the ORC is utilized to run these units, the increase of electricity production as a result of higher solar intensities, as elaborated on in the previous paragraph, can positively affect the production rate of hydrogen and fresh water. According to the conducted calculations in this paper, the electricity production of the ORC can vary from 52.93 kW to 399.4 kW, for solar intensities 300 W/m² and 900 W/m² respectively.

Fig. 11. Effect of solar intensity on the hydrogen production and water desalination unit.

The coefficient of performance (COP) is one of the most prevalent terms to measure the efficiency of cooling systems. Several factors can affect the COP of a system, where the evaporator temperature plays more crucial role due to its direct impact on the performance of the cooling system. Fig. 12 demonstrates the energetic and exergetic COPs of the absorption chiller, simultaneously. On one hand, the energy COP of the cooling system increases subtly by augmenting the evaporator temperature. The underlying reason is that a higher evaporator temperature can raise its heat input, which in turn can enhance the energy COP of the system. On the other hand, the exergy COP of the system falls at higher temperatures of the evaporator, since this temperature is a decisive factor in calculating the exergy COP. is the numerator of the COP exergy equation, where an increase in  evaporator temperature, raises the heat output of the evaporator, and reduces the exergy COP of the system.

Fig. 12. Effect of temperature of the absorption chiller on COP.

7.1 Results of exergy and economic analysis

Fig. 13 is represented to unify all calculated exergy destruction data in a single chart, and determine which parts of the system are responsible for the highest exergy destruction. This figure reveals that the PTC unit alone, brings about nearly 39% of the total exergy destruction rate of the proposed system, followed by DWH, absorption chiller, and the steam turbine account for 15%, 14%, and 9%, respectively.

Fig. 13. Energy destruction of system per unit.

Fig. 14 shows the correlation of different geothermal fluid temperatures with both the exergy efficiency and the total cost rate. According to this figure, regardless of the fluid type, an increase in the temperature of the fluid, reduces the cost rate of power production of the entire system. As elucidated formerly in this paper, this is because a higher geothermal temperature not only leads to a higher flow rate in both the steam cycle and the ORC, but also rises the power production of the entire system. Since the geothermal energy is considered a cost-free energy source, if more power is produced by the same system, just by increasing geothermal fluid temperature, the cost rate of power production declines. Furthermore, as clarified earlier in this paper, this temperature increase enhances the exergy efficiency of the system. In this respect, it can be concluded that Therminol 59 and Marlotherm SH yields the lowest cost rate, and Syltherm 800 produces the best exergy efficiency.

Fig. 14. Effect of temperature of geothermal fluid on both the cost rate and the exergy efficiency.

Fig. 15 focuses on Therminol 59’s cost rate, as the selected fluid of the proposed system, based on solar radiation intensity and the fluid’s initial temperature. According to this figure, for solar intensities lower that 300 W/m², there is a surge of cost rate for colder geothermal fluids. As a result, higher geothermal temperature is required for areas with weak solar intensity in order to avoid excessive cost rates. On the contrary, the cost rates decrease in higher solar intensities, and reach almost a constant value for solar intensities above 700 W/m², despite the initial temperature of the geothermal fluid. To shed more light on this issue, this reduction of cost rate stems from the fact that solar energy is a cost-free source, thus if the solar intensity rises, the total power production increases. Consequently, the total cost rate of the whole system dwindles. The constraint of solar collectors’ technology, however, restrains the capacity of solar collectors to harness the wholly available solar radiation. Therefore, for higher solar intensities, the efficacy of solar collectors, for different initial temperatures of the geothermal fluid, happens to be same.

Fig. 15. Effect of solar intensity on the cost rate for different temperatures of geothermal fluid.

7. Optimization

Different factors affect the performance of a multi-generation system, since many different variables are involved in each system. Thus, optimization is considered as a pivotal stage in the design of cogeneration systems in order to keep a balance between said factors. Exergy efficiency and cost rate are two of the most important parameters in the proposed system in this paper. In order to apply multi-optimization, the EES and MATLAB software have linked together by Dynamic Data Exchange (DDE) method. NSGA-II, as one of the well-known evolutionary algorithms (EA), has some merits such as strategy of fast crowded distance estimation [11]. Using a genetic algorithm, Pareto frontier, which is a well-converged diagram solution, can be obtained to determine the optimum values. This diagram comprises of points that draw a correlation between cost rate and exergy efficiency to find out the best working condition. Subsequently, the outcome of different parts of the system can be calculated using the obtained data. This paper considers 6 variables as follows:

1. Inlet temperature of the geothermal fluid
2. Flow rate of the geothermal fluid
3. Length of the solar collector
4. Steam generator pinch point temperature
5. Steam turbine inlet pressure
6. Temperature of the ORC’s condenser

Constraints for the abovementioned variables are presented in Table 5. This optimization aims to maximize the exergy efficiency, and to minimize the cost rate, as two objective functions.

Table 5. Optimization variables and constraints.

Upper bound	Lower bound	Parameter
180	150	Tgeo (℃)
20	15	${\dot{m}}_{\mathit{geo}}$ (kg)
12.27	9	Collector Length (m)
10	3	PPSteam generator
2000	500	P7 (kPa)
40	30	T15 (℃)

The Pareto frontier of the optimum points is presented in Fig. 16. Also, the scattered distribution of the decision variables is depicted in Fig. 17. By Contemplating data on Pareto frontier, the importance of multi-objective optimization can be realized, since if only cost rate is considered, point C would be the best solution. Conversely, if exergy efficiency is prioritized, the best result would be point A. All points on Fig. 16 are optimum points, so that each of them has the best performance in its scope. Detailed information of the points A, B, and C are listed in Table 6.

Fig. 16. Pareto frontier (optimum points obtained for the multi-generation system).

Fig. 17. Scatter distribution of the effective parameters.

Table 6. Exergy efficiency and cost rate for points A, B, and C.

${\dot{m}}_{H2}\left(\frac{\mathit{kg}}{h}\right)$	Wnet(kW)	Ctot($/GJ)	${\eta }_{\mathit{exergy}}(\%)$	T15	P7	PPSteam generator	Collector Length	${\dot{m}}_{\mathit{geo}}$	Tgeo	Point
2.648	860.3	464.2	31.99	37.48	1095.67	4	11.44	19.85	177.77	A
2.322	786.6	149.9	30.21	32.56	1599.11	6.66	12.17	19.42	176.92	B
0.3926	129.3	58.66	19.47	31.48	1925.47	9.18	9.89	18.28	151.76	C

7. Conclusion

In the present paper, a multi-generation system has been the subject of energy, exergy, and exergoeconomic analysis, and it has been optimized. Products of the proposed system include cooling by absorption refrigeration cycle, warm water generated by the domestic water heater, hydrogen generation, as well as clean water and electricity generation. The performance of the system is highly dependent on geothermal fluid initial temperature, flow rate, solar intensity, steam turbine inlet pressure, Steam generator pinch point temperature, and the number of solar panels. Judging by the acquired results, PTCs cause the most exergy destruction, thereby meaning it is of high importance to improve the performance of this part. The proposed system has been optimized using an NSGA-II algorithm. For optimization results, three points have been considered, and at the point corresponding to the best efficiency, exergy efficiency was 30.78% and the energy efficiency was 18.69%. The cost was 289.6 $/GJ for Therminol 59 as the geothermal fluid, as well as the R123 as organic fluid. The products of the system were hydrogen at 2.44 kg/h, clean water at 31.12 m3/h, as well as a cooling load of 245.2 kJ/sec, and warm domestic water at 13.57 kg/sec. Other results of the study are as follows:

• Among the fluids tried for the organic Rankine cycle, R123 boasts the highest energy and exergy efficiencies.
• While assuming constant number of solar panels, when inlet flow rate increases, outlet work of the system decreases, and the cooling load increases.
• One of the prominent parameters is the solar intensity, which affects the exergy efficiency up to 9%, when Therminol 59 is used as the geothermal fluid at the temperature of 160 degrees Celsius.
• An increase in the geothermal fluid temperature causes an increase in the exergy efficiency. Marlotherm SH has the highest exergy efficiency, and Therminol 59 has the lowest cost.
• An increase in the turbine inlet pressure increases exergy destruction.
• PTC, DWH, absorption chiller, and steam turbine are responsible for a considerable portion of exergy destruction. Hence, enhancing their performance is of great importance in order to promote the over-all efficiency of the multi-generation system.

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