Parametric Investigation of a Trigeneration System with an Organic Rankine Cycle and Absorption Heat Pump Driven by Parabolic Trough Collectors for the Building Sector

Abstract: This article presents a simulation study which focuses on the thermodynamic analysis of a solar-driven trigeneration system for heating, cooling, and electricity production. The system uses parabolic trough collectors operating with Therminol VP-1 for feeding an organic Rankine cycle operating with toluene and an absorption heat pump operating with a LiBr–H2O working pair. The collecting area is selected at 100 m2 and the storage tank at 4 m3. The system is studied parametrically in order to examine the impact of various parameters on the system energy efficiency, system exergy efficiency, electricity production, heating production, and cooling production in the simple payback period of the investment. The examined parameters are the following: solar beam irradiation level, solar beam irradiation angle, superheating degree in the turbine inlet, pressure level in the turbine inlet, heat source temperature level, generator temperature level, and the heat input in the generator. For the nominal case of a 15 kW generator input, the electricity production is 6.3 kW, the heating production 11.5 kW, and the cooling production 10.7 kW. The system energy efficiency is 40.7%, while the system exergy efficiency is 12.7%. The financial investigation of the investment proved that it is viable with the simple payback period to be 8.1 years in the nominal case and it can be reduced to 7.8 years with an optimization procedure. Lastly, it has to be said that the examined system is found to be a viable configuration which is an ideal choice for application in the building sector. The analysis was conducted under steady-state conditions with a model developed using Engineering Equation Solver (EES).


Introduction
The exploitation of solar irradiation in solar trigeneration/polygeneration systems is a new idea that can create sustainable systems [1,2]. Usually, concentrating solar collectors are selected in these systems due to their ability to produce useful heat at high-temperature levels and consequently to manage the solar irradiation with relatively low exergy destruction [3]. Trigeneration and polygeneration systems are highly efficient units that can be used for producing many useful outputs with high-efficiency values [4]. The use of these units in the building sector has high compatibility because this sector presents various needs which are mainly translated into heating, cooling, and electricity demand. There are many options for coupling trigeneration systems which are ideal in the building sector, and thus this idea has been studied considerably in the literature [5]. Usually, solar irradiation is

Solar Field Modeling
The thermal efficiency of the PTC (ηth,col) can be found according to the following formula for the EuroTrough module [17,18] The incident angle modifier (K) of the PTC is dependent on the eth incident angle on the aperture (θ) and it is calculated as below [23]: ( ) = cos( ) − 5.25091 ⋅ 10 ⋅ − 2.859621 ⋅ 10 ⋅ (2) The useful heat that the PTC produces (Qu) is given as: The solar beam irradiation on the collector aperture (Qsol) is calculated as: Moreover, the collector thermal efficiency (ηth,col) is defined as below: The heat input in the generator (Qgen) can be written as:

Solar Field Modeling
The thermal efficiency of the PTC (η th,col ) can be found according to the following formula for the EuroTrough module [17,18] η th,col = 0.7408·K(θ) − 0.0432· The incident angle modifier (K) of the PTC is dependent on the eth incident angle on the aperture (θ) and it is calculated as below [23]: The useful heat that the PTC produces (Q u ) is given as: The solar beam irradiation on the collector aperture (Q sol ) is calculated as: Moreover, the collector thermal efficiency (η th,col ) is defined as below: η th,col = Q u Q sol (5) Energies 2020, 13, 1800

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The heat input in the generator (Q gen ) can be written as: Q g = m col ·c p · T g,in − T g,out (6) In this work, the outlet temperature of the thermal oil from the generator is equal to the inlet temperature in the solar field (T g,out = T col,in ), while the inlet oil temperature in the generator is equal to the mean storage tank temperature (T g,in = T st ). In every case, the minimum temperature difference is not smaller than 5 K in order to have a proper heat exchange.
The general energy balance in the solar field can be written as below: where (Q loss ) is the storage tank thermal losses.

Organic Rankine Cycle Modeling
The work production in the turbine shaft (W T ) can be calculated as below: The pumping work demand (W p ) is calculated as: The turbine isentropic efficiency (η is,T ) is selected to be 85% [24] and it is defined as: The net electricity production (P el ) of the ORC can be calculated as: The electrical generator efficiency (η g ) is 98%, and the shaft mechanical efficiency (η m ) is 99% which are reasonable values.
Moreover, the heat input in the heat recovery system (Q hrs ) can be written as:

Absorption Heat Pump Modeling
The examined absorption heat pump is a single-stage machine which operates with the LiBr-H 2 O working pair. Below, the main equations for the AHP modeling are given.
The cooling production (Q cool ) is calculated as below: The generator heat input energy (Q g ) is calculated as: The absorber heat rejection (Q a ) is calculated as: Q a = m r ·h j + m str ·h f − m w ·h a (15) Energies 2020, 13, 1800 6 of 26 The heating production in the condenser (Q heat ) is calculated as: The effectiveness of the solution heat exchanger (η hex ) is defined below: In this work, this efficiency is selected at 60% [19] which is a typical value. The energy balance in the solution heat exchanger is given below: The work input in the solution heat pump is practically negligible; therefore: The processes in the throttling valves are adiabatic: The total mass flow rate balance in the generator can be written as: The mass flow rate balance of the LiBr substance in the generator can be written as: Moreover, it is important that the state point "j" is assumed to be saturated vapor and the state point "h" saturated liquid.

System Evaluation Criteria
The energy efficiency of the system (η en ) is defined as: The exergy efficiency of the system (η ex ) is defined as: The exergy flow of solar beam irradiation is modeled by using the Petela model [25]. The temperature levels in the previous equation have to be in Kelvin units, the sun temperature level (T sun ) is selected at 5770 K, and the reference temperature level (T 0 ) is selected at 298.15 K.
The financial evaluation is conducted by using the simple payback period (SPP) as the proper evaluation criterion. This index is calculated as below: Energies 2020, 13, 1800 7 of 26 The system capital cost of the system (C 0 ) is calculated as below: Moreover, it has to be said that Table 1 includes the values used for the specific costs. The operating period (Time) is selected at 2500 h per year which is a reasonable value for Athens (Greece) [20].
The hourly system cash flow (CF) can be written as: The operation and maintenance cost (K O&M ) is estimated to be 1% of the capital cost (K O&M = 0.01·C 0 ). The electricity cost is selected at 0.20 €/kWh el , the heating cost at 0.10 €/kWh heat , and the cooling cost at 0.067 €/kWh cool [26]. Table 1. Data for financial analysis [26,27].

Parameters Symbols Values
Electricity cost Operation and maintenance cost (K O&M ) 1% of the capital cost

Followed Methodology
The present work investigates a solar-driven trigeneration system under steady-state conditions. Mathematical modeling was performed according to the equations of Section 2.2 in the program Engineering Equation Solver (EES). Table 1 includes the main parameters of this work which are used in all the cases. The system is studied parametrically by changing the value of one parameter every time and by keeping the other parameters constant at this time. Table 2 includes the default values and the range of the parameters that are used in the parametric analysis. These values have been selected to have reasonable values that correspond to real operating conditions and they have been tested in preliminary studies of the developed program. Among the parameters, there are two parameters which have not defined yet and they are explained below: The pressure ratio (α) is the ratio of the turbine inlet (p high ) to the critical pressure of the toluene (p crit ) which is 41.26 bar. This parameter practically is equivalent to the high-pressure level in the ORC cycle. The maximum value of the parameter (α) is selected to be 90% for safety reasons.
The other parameter is the heat source temperature difference (∆T s ) and it is defined as the temperature difference between the heat source temperature in the HRS (T s,in ) and the minimum possible heat source temperature. The minimum possible value is the lowest possible value for having a pinch point of 5 K in the evaporator start. Moreover, the saturation temperature (T sat ) is dependent on the value of the parameter (α) in every scenario.  The following pertains to the selection of the solar irradiation level, solar angle, and yearly operating hours. These data correspond to the weather data for the location of Athens (Greece). The solar beam irradiation level was selected at 700 W/m 2 because this is the mean value for the year under sunny conditions. The solar angle of 30 • gives an incident angle modifier close to the mean yearly value for PTC in Athens [28]. Moreover, a simple analysis of the effective sunny hours with a positive product (K(θ)· · · G b ) indicated about 2500 h. Therefore, these selected values can lead to representative results for the weather conditions in the examined location, in accordance with Ref. [28]. The generator heat input is selected at 15 kW in order to give heating and cooling values close to 10 kW which are suitable values for a system like the present one. The superheating is selected at 20 K in order not to be too high, which usually occurs in ORCs. The zero heat source temperature difference and the maximum pressure ratio are the optimum results for Ref. [10] and thus they are selected to be the default values. The generator temperature is selected to have a relatively high value in order to achieve an adequate coefficient of performance, and also the crystallization limitation has been taken into consideration. Another important issue regards the validation of the used models. The validation and verification procedures of the AHP and of the ORC are included in our previous work; see Ref. [10], so there is no reason for including these data again. Moreover, this work is a simulation study and not an experiment, so there is no possibility of calculating "errors" from the obtained results. Strict convergence criteria have been applied, and so the results are presented with high accuracy.
In the last part of this work, an optimization procedure has been performed in order to determine the optimum design for achieving minimum SPP. The parameters that have been studied, as optimization variables, are the generator temperature, the pressure ratio, and the superheating. The range of the optimization variables follows the limits of Table 3, while the other parameters have the default values of Table 3. The optimization procedure is supported by EES software.

Results
The results of this work are expressed in terms of energy efficiency, exergy efficiency, simple payback period, hourly cash flow rate, electricity, and cooling and heating production. Section 3.1 presents the parametric analysis for different ORC parameters, Section 3.2 the AHP parameters, and Section 3.3 the parametric studies for different solar potential cases. Section 3.4 includes results about the yearly performance as well as discussion comments. It is useful to state the main results of the default case (according to Table 3). In this case, the electricity production is 6.31 kW, the heating production 11.53 kW, the cooling production 10.67%, the energy efficiency 40.72%, the exergy efficiency 12.71%, the payback period 8.1 years, and the hourly cash flow rate 3.13 €/h. Moreover, it is interesting to state that the coefficient of performance for the absorption heat pump is 0.711 for cooling and 0.769 for heating. Figure 2 shows the variation of the useful outputs for different pressure ratio values. It is obvious that only electricity production is affected by this parameter and it is maximized for pressure ratio at 0.6 and it is 6.39 kW. The heating and cooling productions are not affected by the variation of this parameter. Moreover, Figure 3 shows that both energy and exergy efficiencies are maximized for α = 0.6. More specifically, the maximum energy efficiency is 40.84%, while the maximum exergy efficiency is 12.84%. Moreover, Figure 4 indicates that the SPP of the system is minimized for α = 0.6 and it is about 8.086 years, while the hourly cash flow is maximized at 3.146 €/h. Therefore, it can be said that the maximization of electricity production at a specific value of the pressure ratio leads to the optimization of all the other indexes. However, the deviations from the default scenario are not so high, and so this fact indicates that the use of the initial value of α = 0.90 instead of the optimum value of α = 0.60 in the parametric analysis does not have a great impact on the obtained values.

Variation of the Parameters in the Organic Rankine Cycle
Energies 2020, 13, x FOR PEER REVIEW 9 of 26 production 11.53 kW, the cooling production 10.67%, the energy efficiency 40.72%, the exergy efficiency 12.71%, the payback period 8.1 years, and the hourly cash flow rate 3.13 €/h. Moreover, it is interesting to state that the coefficient of performance for the absorption heat pump is 0.711 for cooling and 0.769 for heating. Figure 2 shows the variation of the useful outputs for different pressure ratio values. It is obvious that only electricity production is affected by this parameter and it is maximized for pressure ratio at 0.6 and it is 6.39 kW. The heating and cooling productions are not affected by the variation of this parameter. Moreover, Figure 3 shows that both energy and exergy efficiencies are maximized for α = 0.6. More specifically, the maximum energy efficiency is 40.84%, while the maximum exergy efficiency is 12.84%. Moreover, Figure 4 indicates that the SPP of the system is minimized for α = 0.6 and it is about 8.086 years, while the hourly cash flow is maximized at 3.146 €/h. Therefore, it can be said that the maximization of electricity production at a specific value of the pressure ratio leads to the optimization of all the other indexes. However, the deviations from the default scenario are not so high, and so this fact indicates that the use of the initial value of α = 0.90 instead of the optimum value of α = 0.60 in the parametric analysis does not have a great impact on the obtained values.    The next examined parameter is the superheating degree in the turbine inlet. Figure 5 shows that only electricity production is affected by this parameter and it is maximized at 25 K for the examined pressure level. This is an interesting result which indicates that there is a need for optimization of this parameter in order to have adequate electricity production. It has to be commented that in the examined ranges, the optimization of the superheating degree is more important than the optimization of the pressure ratio parameter. Figure 6 illustrates that both energy and the exergy efficiencies are maximized for 25     The next examined parameter is the superheating degree in the turbine inlet. Figure 5 shows that only electricity production is affected by this parameter and it is maximized at 25 K for the examined pressure level. This is an interesting result which indicates that there is a need for optimization of this parameter in order to have adequate electricity production. It has to be commented that in the examined ranges, the optimization of the superheating degree is more important than the optimization of the pressure ratio parameter. Figure 6 illustrates that both energy and the exergy efficiencies are maximized for 25   The next examined parameter is the superheating degree in the turbine inlet. Figure 5 shows that only electricity production is affected by this parameter and it is maximized at 25 K for the examined pressure level. This is an interesting result which indicates that there is a need for optimization of this parameter in order to have adequate electricity production. It has to be commented that in the examined ranges, the optimization of the superheating degree is more important than the optimization of the pressure ratio parameter. Figure 6 illustrates that both energy and the exergy efficiencies are maximized for 25 K superheating which is a reasonable result because this superheating value also maximizes electricity production. The maximum energy efficiency is 40.73%, and the respective maximum exergy efficiency of 12.72%. Figure 7 shows that the payback period is minimized for 25 K superheating, and the hourly cash flow is maximized for the same superheating value. The minimum SPP is 8.095 years, and the respective maximum hourly cash flow rate is 3.13 €/h. superheating value also maximizes electricity production. The maximum energy efficiency is 40.73%, and the respective maximum exergy efficiency of 12.72%. Figure 7 shows that the payback period is minimized for 25 K superheating, and the hourly cash flow is maximized for the same superheating value. The minimum SPP is 8.095 years, and the respective maximum hourly cash flow rate is 3.13 €/h.   superheating value also maximizes electricity production. The maximum energy efficiency is 40.73%, and the respective maximum exergy efficiency of 12.72%. Figure 7 shows that the payback period is minimized for 25 K superheating, and the hourly cash flow is maximized for the same superheating value. The minimum SPP is 8.095 years, and the respective maximum hourly cash flow rate is 3.13 €/h.     10 show the impacts of the heat source temperature in the ORC on the system performance. This analysis is conducted by using a special parameter, which is the increase of the source temperature, and it shows the deviation of the used source temperature from the minimum possible for proper heat transfer in the HRS. The heating and the cooling production is not affected by this parameter, as Figure 8 indicates; however, the electricity production is reduced. Practically, higher heat source temperature leads to higher operating temperatures in the solar systems, and so higher thermal losses are created. Therefore, the heat input in the ORC is reduced, and the results of Figure 8 are justified. The heating/cooling production is not affected because in all cases, the heat input in the generator is 15 kW, and the temperature levels of the hot thermal oil are higher than the generator temperature, and a proper heat transfer is achieved in an easy way (high-temperature difference between the thermal oil and the generator temperature level). The increase in the heat source temperature can reduce electricity production from 3.61 kW to 5.73 K when there is a temperature increase of 40 K. This is a significant reduction that is not desired. Figure 9 shows that the increase of the heat source temperature leads to a decrease in energy and exergy efficiencies, reasonable results according to the electricity production behavior. The energy efficiency is decreased from 40.72% to 39.89%, while the exergy efficiency from 12.71% to 11.82% for a 40 K temperature increase in the heat source temperature. Moreover, Figure 10 proves that higher heat source temperature increases the SPP from 8.095 years to 8.162 years, while the hourly cash flow is reduced from 3.13 €/h to 3.01 €/h.  Figures 8-10 show the impacts of the heat source temperature in the ORC on the system performance. This analysis is conducted by using a special parameter, which is the increase of the source temperature, and it shows the deviation of the used source temperature from the minimum possible for proper heat transfer in the HRS. The heating and the cooling production is not affected by this parameter, as Figure 8 indicates; however, the electricity production is reduced. Practically, higher heat source temperature leads to higher operating temperatures in the solar systems, and so higher thermal losses are created. Therefore, the heat input in the ORC is reduced, and the results of Figure 8 are justified. The heating/cooling production is not affected because in all cases, the heat input in the generator is 15 kW, and the temperature levels of the hot thermal oil are higher than the generator temperature, and a proper heat transfer is achieved in an easy way (high-temperature difference between the thermal oil and the generator temperature level). The increase in the heat source temperature can reduce electricity production from 3.61 kW to 5.73 K when there is a temperature increase of 40 K. This is a significant reduction that is not desired. Figure 9 shows that the increase of the heat source temperature leads to a decrease in energy and exergy efficiencies, reasonable results according to the electricity production behavior. The energy efficiency is decreased from 40.72% to 39.89%, while the exergy efficiency from 12.71% to 11.82% for a 40 K temperature increase in the heat source temperature. Moreover, Figure 10 proves that higher heat source temperature increases the SPP from 8.095 years to 8.162 years, while the hourly cash flow is reduced from 3.13 €/h to 3.01 €/h. Energies 2020, 13, x FOR PEER REVIEW 13 of 26  Heating and cooling production (kW) Electricity production -P el (kW)   Heating and cooling production (kW) Electricity production -P el (kW)

Variation of the Parameters of the Absorption Heat Pump
The next part of the parametric analysis regards studies about parameters that influence mainly the absorption heat pump. Figures 11 to 13 include results about the impact of the generator heat input on the system performance. In the default scenario, a heat rate of 15 kW has been selected, while in the parametric study, it ranges from zero to 30 kW. The heating and cooling increase linearly with the increase of the generator heat input, and they reach 23.06 kW and 21.34 kW, respectively. On the other hand, the electricity production decreases linearly with the increase of the generator temperature and it can be 1.47 kW for 30 kW of generator heat input. Practically, higher heat input amounts in the generator decrease the available heat input in the HRS, and thus the electricity production is reduced. Figure 12 shows that the increase of the generator heat input can increase energy efficiency by up to 65.53%, while it reduces the exergy efficiency by 8.33%. These results are explained by the way that the generator temperature influences on the useful products. More specifically, the exergy efficiency is influenced more by electricity production than by the other useful outputs, and thus the decrease in electricity production reduces the exergy efficiency. On the other hand, the simultaneous increases in cooling and heating production lead to an increase in energy efficiency. Figure 13 shows that higher generator temperature leads to lower SPP and a higher hourly cash flow rate, which indicates that the increase of the heat input in the generator leads to a more viable investment. The lowest SPP can be 5.74 years. However, the high generator temperature leads to low electricity production, which reduces the ability of the system to satisfy the electricity demand of the respective application. Therefore, the generator temperature has to be adjusted to meet the needs of the examined application in every case.

Variation of the Parameters of the Absorption Heat Pump
The next part of the parametric analysis regards studies about parameters that influence mainly the absorption heat pump. Figures 11-13 include results about the impact of the generator heat input on the system performance. In the default scenario, a heat rate of 15 kW has been selected, while in the parametric study, it ranges from zero to 30 kW. The heating and cooling increase linearly with the increase of the generator heat input, and they reach 23.06 kW and 21.34 kW, respectively. On the other hand, the electricity production decreases linearly with the increase of the generator temperature and it can be 1.47 kW for 30 kW of generator heat input. Practically, higher heat input amounts in the generator decrease the available heat input in the HRS, and thus the electricity production is reduced. Figure 12 shows that the increase of the generator heat input can increase energy efficiency by up to 65.53%, while it reduces the exergy efficiency by 8.33%. These results are explained by the way that the generator temperature influences on the useful products. More specifically, the exergy efficiency is influenced more by electricity production than by the other useful outputs, and thus the decrease in electricity production reduces the exergy efficiency. On the other hand, the simultaneous increases in cooling and heating production lead to an increase in energy efficiency. Figure 13 shows that higher generator temperature leads to lower SPP and a higher hourly cash flow rate, which indicates that the increase of the heat input in the generator leads to a more viable investment. The lowest SPP can be 5.74 years. However, the high generator temperature leads to low electricity production, which reduces the ability of the system to satisfy the electricity demand of the respective application. Therefore, the generator temperature has to be adjusted to meet the needs of the examined application in every case.   Heating and cooling production (kW) Electricity production -P el (kW)

Generator heat input -Q g (kW)
ηen ηex Figure 11. Electricity, heating, and cooling for different generator heat input values.
Energies 2020, 13, x FOR PEER REVIEW 15 of 26 Figure 11. Electricity, heating, and cooling for different generator heat input values.  Figure 14 indicates that higher generator temperature leads to higher electricity cooling and heating production because the higher generator temperature increases the performance of the absorption heat pump. The electricity production is kept constant with the increase of the generator temperature because the heat input in the generator is constant. Figure 15 shows that higher generator temperature leads to an increase in energy and exergy efficiencies. The energy efficiency can reach 43.18%, while the exergy efficiency 12.95%. The increase in the useful outputs leads to higher efficiencies, and so the results of Figure 15 are reasonable. Figure 16 shows that the increase of the generator temperature leads to lower SPP and a higher hourly cash flow rate. The SPP can be reduced by up to 7.82 years, while the cash flow rate can be increased by up to 3.23 €/h.  Figure 14 indicates that higher generator temperature leads to higher electricity cooling and heating production because the higher generator temperature increases the performance of the absorption heat pump. The electricity production is kept constant with the increase of the generator temperature because the heat input in the generator is constant. Figure 15 shows that higher generator temperature leads to an increase in energy and exergy efficiencies. The energy efficiency can reach 43.18%, while the exergy efficiency 12.95%. The increase in the useful outputs leads to higher efficiencies, and so the results of Figure 15 are reasonable. Figure 16 shows that the increase of the generator temperature leads to lower SPP and a higher hourly cash flow rate. The SPP can be reduced by up to 7.82 years, while the cash flow rate can be increased by up to 3.23 €/h.  Figure 14 indicates that higher generator temperature leads to higher electricity cooling and heating production because the higher generator temperature increases the performance of the absorption heat pump. The electricity production is kept constant with the increase of the generator temperature because the heat input in the generator is constant. Figure 15 shows that higher generator temperature leads to an increase in energy and exergy efficiencies. The energy efficiency can reach 43.18%, while the exergy efficiency 12.95%. The increase in the useful outputs leads to higher efficiencies, and so the results of Figure 15 are reasonable. Figure 16 shows that the increase of the generator temperature leads to lower SPP and a higher hourly cash flow rate. The SPP can be reduced by up to 7.82 years, while the cash flow rate can be increased by up to 3.23 €/h.

Variation of the Solar Irradiation Parameters
Section 3.3 includes the results of the impact of the solar irradiation level and the incident solar angle on the system performance. Figure 17 shows that higher solar irradiation leads to an approximately linear increase in electricity production, while heating and cooling productions are constant. This is a reasonable result because the higher solar irradiation increases the total useful heat

Variation of the Solar Irradiation Parameters
Section 3.3 includes the results of the impact of the solar irradiation level and the incident solar angle on the system performance. Figure 17 shows that higher solar irradiation leads to an approximately linear increase in electricity production, while heating and cooling productions are constant. This is a reasonable result because the higher solar irradiation increases the total useful heat

Variation of the Solar Irradiation Parameters
Section 3.3 includes the results of the impact of the solar irradiation level and the incident solar angle on the system performance. Figure 17 shows that higher solar irradiation leads to an approximately linear increase in electricity production, while heating and cooling productions are constant. This is a reasonable result because the higher solar irradiation increases the total useful heat production and consequently the heat input in the HRS, while the generator heat input is constant. The approximately linear increase is justified by the small deviation of the collector thermal efficiency with the solar beam irradiation in the examined range. The maximum electricity production is 12.67 kW for solar beam irradiation at 1000 W/m 2 . Figure 18 shows that the exergy efficiency increases under higher solar irradiation due to the increase in electricity production. On the other hand, the increase in solar potential does not increase energy efficiency because the cooling and heating production is constant while electricity production does not increase greatly. Figure 19 exhibits the financial behavior of the system, and it is found that higher solar irradiation leads to a more viable investment. Practically, higher solar irradiation leads to more heat input with the same installation, which leads to higher profit with the same investment cost. The minimum SPP is 7.62 years, while the maximum cash flow 4.32 €/h. Energies 2020, 13, x FOR PEER REVIEW 18 of 26 production and consequently the heat input in the HRS, while the generator heat input is constant. The approximately linear increase is justified by the small deviation of the collector thermal efficiency with the solar beam irradiation in the examined range. The maximum electricity production is 12.67 kW for solar beam irradiation at 1000 W/m 2 . Figure 18 shows that the exergy efficiency increases under higher solar irradiation due to the increase in electricity production. On the other hand, the increase in solar potential does not increase energy efficiency because the cooling and heating production is constant while electricity production does not increase greatly. Figure 19 exhibits the financial behavior of the system, and it is found that higher solar irradiation leads to a more viable investment. Practically, higher solar irradiation leads to more heat input with the same installation, which leads to higher profit with the same investment cost. The minimum SPP is 7.62 years, while the maximum cash flow 4.32 €/h.    22 show the results of the impact of the incident solar angle on the system performance. This angle regards the angle between the sun and the collector aperture which follows the sun with a single-axis tracking system. As a result of the existence of the tracking, the solar angle is not that high under the majority of the operating conditions. The tracking system greatly increases the optical efficiency and this is an important point that has to be taken into consideration in studies such as the present one. Figure 20 shows that electricity production decreases with the increase of the solar angle because there are higher optical losses in the PTC and reduced useful heat production. However, the heating and the cooling remain constant due to the constant heat input in the generator.   show the results of the impact of the incident solar angle on the system performance. This angle regards the angle between the sun and the collector aperture which follows the sun with a single-axis tracking system. As a result of the existence of the tracking, the solar angle is not that high under the majority of the operating conditions. The tracking system greatly increases the optical efficiency and this is an important point that has to be taken into consideration in studies such as the present one. Figure 20 shows that electricity production decreases with the increase of the solar angle because there are higher optical losses in the PTC and reduced useful heat production. However, the heating and the cooling remain constant due to the constant heat input in the generator. It is interesting to state that for the examined conditions with 700 W/m 2 solar irradiation, the electricity production can reach 9.27 kW for a zero-incident angle, compared with 6.31 kW for a 30 • incident angle, which is the default scenario. Figure 21 makes it clear that both energy and exergy efficiencies decrease with the increase of the solar angle. Moreover, in a system with a higher solar angle, the SPP increases and the hourly cash flow decreases, as Figure 22 indicates.
It is interesting to state that for the examined conditions with 700 W/m 2 solar irradiation, the electricity production can reach 9.27 kW for a zero-incident angle, compared with 6.31 kW for a 30 o incident angle, which is the default scenario. Figure 21 makes it clear that both energy and exergy efficiencies decrease with the increase of the solar angle. Moreover, in a system with a higher solar angle, the SPP increases and the hourly cash flow decreases, as Figure 22 indicates.  It is interesting to state that for the examined conditions with 700 W/m 2 solar irradiation, the electricity production can reach 9.27 kW for a zero-incident angle, compared with 6.31 kW for a 30 o incident angle, which is the default scenario. Figure 21 makes it clear that both energy and exergy efficiencies decrease with the increase of the solar angle. Moreover, in a system with a higher solar angle, the SPP increases and the hourly cash flow decreases, as Figure 22 indicates.

Yearly Performance and Discussion
The present work studies a solar-driven trigeneration system under steady-state conditions, and the results are extended for estimating the yearly performance. Table 4 includes the total results of the system design which minimizes the SPP. The optimization has been performed by applying the proper settings in the EES and using the optimization variables of the pressure ratio, superheating degree, and generator temperature. It is found that the SPP can be 7.82 years which is a relatively satisfactory value. A simple environmental analysis proved that the equivalent yearly mitigation of CO2 is 35.51 tones. This value was calculated based on values for Greece, i.e., a specific CO2 emission coefficient of 0.989 tones per MWhel [29]. Table 5 includes important results about the ratios of the yearly production quantity. The power-to-heating ratio is 51.48%, the power-to-cooling ratio is 55.65%, and the cooling-to-heating ratio 92.51%. These ratios indicate that the obtained useful outputs are comparable, and there is no wide range among them. This fact is in accordance with the building needs in the examined useful outputs.
The optimization procedure is found to be very important. The results of Table 4 show that the overall optimum value of the pressure ratio is 58.8%, while the analysis of the default scenario (sensitivity analysis) indicates the optimum ratio is 61.4%. On the other hand, the results of the study [10] show that the optimum ratio is 9%. The result in Ref. [10] is different because, in this work, the ORC rejected heat at a high-temperature level in order to feed the AHP. Therefore, in every case, there is a need for a proper optimization procedure.
The literature results [9][10][11][12][13][14][15] indicate that the energy efficiency of other systems ranges from 21% to 150%, while the exergy efficiency from 7% to 56%. Therefore, the obtained efficiency values of this work are inside the usual range, and thus the present system is an acceptable one. Furthermore, the examined system is a relatively easily constructed unit because the devices are all coupled to the solar field loop. Therefore, there is no need for special control of the devices. Moreover, the payback period is acceptable, and energy efficiency is satisfactory. Therefore, this system is a promising one for future systems for achieving sustainability.
In the future, there will be a need for performing a detailed dynamic analysis of this system. Moreover, an idea is to select heating and cooling in specific periods of the year and not the whole

Yearly Performance and Discussion
The present work studies a solar-driven trigeneration system under steady-state conditions, and the results are extended for estimating the yearly performance. Table 4 includes the total results of the system design which minimizes the SPP. The optimization has been performed by applying the proper settings in the EES and using the optimization variables of the pressure ratio, superheating degree, and generator temperature. It is found that the SPP can be 7.82 years which is a relatively satisfactory value. A simple environmental analysis proved that the equivalent yearly mitigation of CO 2 is 35.51 tones. This value was calculated based on values for Greece, i.e., a specific CO 2 emission coefficient of 0.989 tones per MWh el [29]. Table 5 includes important results about the ratios of the yearly production quantity. The power-to-heating ratio is 51.48%, the power-to-cooling ratio is 55.65%, and the cooling-to-heating ratio 92.51%. These ratios indicate that the obtained useful outputs are comparable, and there is no wide range among them. This fact is in accordance with the building needs in the examined useful outputs.
The optimization procedure is found to be very important. The results of Table 4 show that the overall optimum value of the pressure ratio is 58.8%, while the analysis of the default scenario (sensitivity analysis) indicates the optimum ratio is 61.4%. On the other hand, the results of the study [10] show that the optimum ratio is 9%. The result in Ref. [10] is different because, in this work, the ORC rejected heat at a high-temperature level in order to feed the AHP. Therefore, in every case, there is a need for a proper optimization procedure.
The literature results [9][10][11][12][13][14][15] indicate that the energy efficiency of other systems ranges from 21% to 150%, while the exergy efficiency from 7% to 56%. Therefore, the obtained efficiency values of this work are inside the usual range, and thus the present system is an acceptable one. Furthermore, the examined system is a relatively easily constructed unit because the devices are all coupled to the solar field loop. Therefore, there is no need for special control of the devices. Moreover, the payback period is acceptable, and energy efficiency is satisfactory. Therefore, this system is a promising one for future systems for achieving sustainability. In the future, there will be a need for performing a detailed dynamic analysis of this system. Moreover, an idea is to select heating and cooling in specific periods of the year and not the whole annual period. Another point that can be studied is the investigation of the system in other locations with higher or lower solar potential. Lastly, the thermodynamic analysis of this work can be used as the input in future studies on the present system or for similar configurations.  Table 5. Important ratio values of the yearly energy amounts.

Parameter Value
Power-to-heating ratio 0.5148 Power-to-cooling ratio 0.5565 Cooling-to-heating ratio 0.9251 Power-to-solar ratio 0.0913 Heating-to-solar ratio 0.1774 Cooling-to-solar ratio 0.1641

Conclusions
The objective of the present study is the examination of a solar-driven trigeneration system for electricity, heating, and cooling production. This system uses parabolic trough collectors operating with Therminol VP-1 and includes an organic Rankine cycle, an absorption heat pump, and a storage tank. The analysis is performed with a model developed by Engineering Equation Solver (EES). The main conclusions of this work are given below: -In the default scenario, the electricity production is 6.31 kW, the heating production 11.53 kW, the cooling production 10.67%, the energy efficiency 40.72%, the exergy efficiency 12.71%, the payback period 8.1 years, and the hourly cash flow rate 3.13 €/h.
-In the optimized scenario for the minimum payback period, the electricity production is 6.39 kW, the heating production 12.42 kW, the cooling production 11.49%, the energy efficiency 43.30%, the exergy efficiency 13.08%, the payback period 7.82 years, and the hourly cash flow rate 3.29 €/h.
-It is found that there are optimum values for the turbine inlet pressure and the superheating degree in the turbine inlet, which maximize the electricity production, the exergy efficiency, and the energy efficiency, but minimize the simple payback period.
-The increase of the generator temperature increases both the energy and exergy efficiencies. On the other hand, the increase of the generator heat input increases energy efficiency and decreases exergy efficiency.
Energies 2020, 13, 1800 23 of 26 -The increase in solar irradiation values leads to higher electricity production, higher exergy efficiency, and lower energy efficiency. The increase in the solar angle leads to lower electricity production, energy efficiency, and exergy efficiency.
-Generally, it can be said that the examined system has satisfactory performance, with similar values among the useful outputs. The system is financially viable and it can be installed easily by combining well-established technologies.
Author Contributions: Conceptualization, methodology, investigation, writing-review and editing, writing-original draft preparation, E.B.; supervision, writing-review and editing, writing-original draft preparation, C.T. All authors have read and agreed to the published version of the manuscript. -The increase in solar irradiation values leads to higher electricity production, higher exergy efficiency, and lower energy efficiency. The increase in the solar angle leads to lower electricity production, energy efficiency, and exergy efficiency.
-Generally, it can be said that the examined system has satisfactory performance, with similar values among the useful outputs. The system is financially viable and it can be installed easily by combining well-established technologies.