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S1359-4311(17)30573-2 http://dx.doi.org/10.1016/j.applthermaleng.2017.08.005 ATE 10887

To appear in:

Applied Thermal Engineering

Received Date: Revised Date: Accepted Date:

25 January 2017 14 July 2017 2 August 2017

Please cite this article as: E. Bellos, C. Tzivanidis, Energetic and financial analysis of solar cooling systems with single effect absorption chiller in various climates, Applied Thermal Engineering (2017), doi: http://dx.doi.org/ 10.1016/j.applthermaleng.2017.08.005

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Energetic and financial analysis of solar cooling systems with single effect absorption chiller in various climates

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Evangelos Bellos, Christos Tzivanidis

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Thermal Department, School of Mechanical Engineering, National Technical University of Athens, Zografou, Heroon Polytechniou 9, 15780 Athens, Greece.

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Abstract The objective of this work is to investigate the solar cooling viability in various locations worldwide. A single stage absorption chiller operating with the LiBr-H2O working pair is coupled with evacuated tube collectors and this system produces the demanded cooling load for a typical building of 100 m2 floor area. Ten cities are examined and the analysis is performed with the commercial software TRNSYS. For every city, different combinations of collecting areas and storage tank volumes are investigated in order to determine the optimum combination which leads to the minimum levelized cost of cooling (LCOC). According to the final results, Abu Dhabi and Phoenix are the most suitable locations with LCOC equal to 0.0575 €/kWh and 0.0590 €/kWh respectively, while Rome, Madrid and Thessaloniki are the less suitable locations with 0.2125 €/kWh and 0.1792 €/kWh and 0.1771 €/kWh respectively. Moreover, it is found that the locations with high cooling loads and high solar potential are the most suitable locations for installing solar cooling. Furthermore, it is proved that higher collecting is associated with a greater optimum storage tank. Finally, the conclusions of this work can be used as guidelines for designing solar cooling system and determining the suitable locations and climate conditions for installing solar cooling systems.

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Keywords Absorption chiller, financial evaluation, solar cooling, ETC, TRNSYS

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1. Introduction The rapid development of our society is conjugated with a high amount of energy consumption [1] in order the new lifestyle trends to be satisfied [2]. However, the environmental problems as global warming [3] and the climate change [4] create constraints in the use of fossil fuels [5]. Moreover, the consequent increase in the electricity price and the depletion of fossil fuels make inevitable the use of alternative and renewable energy sources [6].

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The building sector is responsible for the 30-40% [7-8] of the worldwide energy consumption and with the industrial sector are the most energetically intense sectors. Solar energy is the most suitable renewable energy source which can be utilized in the building sector for heating, cooling and electricity production. Solar cooling is one of the most promising technologies because they lead to the decrease of high peaks of

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Corresponding author: Evangelos Bellos ([email protected])

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electricity consumption in summer and it has great compatibility between source supply and load demand [9-11].

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Many solar cooling technologies have been studied and are available commercially, as absorption, adsorption, ejector systems and desiccant wheels. Among them, absorption chiller is the mature and developed technology which is able to produce cooling and refrigeration in a high range of temperature levels [12]. In solar cooling applications, the chillers with the LiBr-H2O working pair are the most suitable solutions because of their higher performance compared to the H2O-NH3 [13].

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In the literature, there are many studies which have examined the energetic performance and the viability of these systems. Angrisani et al. [7] examined the use of flat plate collectors (FPC) and evacuated tube collectors (ETC) coupled with a single effect absorption chiller for the climate of southern Italy and they finally proved that ETCs lead to a higher yearly solar fraction. Al-Alili et al. [14] investigated a solar absorption cooling system with ETC in Abu Dhabi climate. They proved that the electricity consumption can be reduced to the half with this technology and they highlighted that the electricity cost increase in the future is a key factor for the financial viability of these systems. In another comparative study, Muye et al. [15] examined the use of a solar cooling system with ETC for Spain and Indian climate. According to their results, the system presented a higher performance in Spanish climate due to lower ambient temperature levels compared to the Indian climate. In another study, Bellos et al. [16] examined a solar cooling system with absorption chiller operating with LiBr-H2O with various collector types. Flat plate collectors, evacuated tube collectors, compound parabolic collectors and parabolic trough collectors were studied and finally, ETCs were proved to be the most suitable solution financially. In another interesting study [17] for Athens climate (Greece), the use of ETCs with a single stage absorption chiller was proved to be a financially feasible choice with a payback period close to 15 years.

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As it is obvious, there are many studies which have examined the use of ETC with solar cooling systems and also this collector type has found to be a more suitable solution than the other types. This result is based on the lower investment and maintenance cost, compared to concentrating technologies. Also, it is essential to state that ETC is a better choice than flat plate collectors because of the small thermal efficiency of FPC in relatively high-temperature levels.

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Another interesting category of studies examines the sustainability of solar cooling systems in different climates. Shirazi et al. [18] investigated the use of many different solar cooling technologies in ten different locations worldwide. They performed a detailed study which was focused on the energetic evaluation of the examined solar cooling technologies. According to their results, the use of ETC is the most reliable solution for the majority of the climates. Also, they stated that the concentrating technologies are more efficient in climates with high solar potential and they have to be coupled with multi-staged absorption machines. Palomba et al. [19] examined the 2

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energetic sustainability of a solar cooling system with ETC and flat plate collectors in various cities worldwide, and they proved that in regions with higher cooling demand, greater collecting area has to be installed. Calise [20] investigated a solar cooling system for Mediterranean climate and he proved that the auxiliary energy cost is one of the most important factors for evaluating the system sustainability in these regions. Moreover, he stated that the solar cooling system is financially beneficial in Cairo and in Almeria, while for Istanbul and Trieste it has not been applied.

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In this paper, the financial viability of a solar cooling system with ETC and single stage absorption chiller operating with LiBr-H2 O is investigated for various cities worldwide. The selected solar cooling system is the most representative candidate among the usual systems and this is used for covering the space cooling loads of the same building in ten different locations. The innovative part of this study is that the system in every city is optimized in order the optimum cases to be compared. The collecting area and the storage tank volume are the optimization parameters, while the minimization of the levelized cost of cooling is the objective function. Different combinations of the two examined parameters are tested and for every city, different designs are found as optimal. The main objective of this study is to determine the impact of the climate conditions and of the cooling needs of the system design and on its viability in every city. Thus, the same commercial building has been examined in all the cases and many parameters are the same among the examined cities. The comparison of the optimum cases is the final outcome of this study and general conclusions are extracted which can be used as guidelines for the design of the solar cooling system in different climate conditions. The difference with the other usual literature studies is that the optimization is performed financially with two optimization parameters and not only the collecting area. Thus, for every location, a suitable design for its climate is selected as the optimum one. Also, it is important to state that the use of levelized cost of cooling is used for the evaluation of the systems which is a proper financial index for comparing these systems in different climates because it takes into account the installation cost and the cooling demand.

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2. Methods 2.1 Mathematical background The basic mathematical equations which describe the present analysis are given in this section. These equations are related to the definitions of energetic and financial indexes for the evaluation of the examined heating systems.

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The mean thermal efficiency (ηth) of the solar collectors is defined as the ratio of the useful energy (Eu) to the available solar irradiation (Es), as equation 1 indicates.

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th

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In the present study, evacuated tube collectors (ETC) are selected as the most appropriate solar collectors for producing heat in low-temperature levels [17]. For this

Eu , Es

(1)

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collector type, the most usual way to express the thermal efficiency is by using the efficiency curve equation. Equation 2 is taken from literature and it corresponds to Apricus 30 [18].

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T Tam T fm Tam 0.011 fm , th 0.687 1.505 GT GT

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A useful parameter of the present study is the total incident solar irradiation in the horizontal surface during the year (H). This parameter is calculated by integrating all the incident solar irradiation for all the year, as equation 3 presents:

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H

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G

hor

dt ,

(2)

(3)

year

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The most important parameter for evaluating the absorption chiller is the coefficient of performance (COP) which is the ratio of the produced cooling (Qcool) to the heat rate input (Qhs). This heat input is provided by the solar collectors and the auxiliary electrical heater. Equation 4 shows the COP definition:

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COP

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The solar fraction is a critical parameter in the design of solar thermal systems and it indicates the fraction of the solar energy utilization in the system. In the present case, the best method for calculating this parameter is by the indirect way, using the axillary energy (Eaux) and the energy of the heat source (Ehs) which is given to the absorption chiller. Equation 5 shows the calculation way of this parameter:

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f 1

Qcool , Qhs

E aux , E hs

(4)

(5)

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The financial evaluation of the examined system is performed by using the net present cost of the investment (Ktot) and the levelized cost of cooling (LCOC). The total net present cost of the investment includes the capital cost of every system (C0) and the cost of the auxiliary electricity consumption for all of the life of the project (25 years). The investment with the lower total cost is the more beneficial financially. Equation 5 shows the analytical definition of this parameter when the yearly cash flow is the same among the years.

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K tot C0 Eaux K el R ,

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The parameter R is effective years of the project (N) and it takes into account the discount factor (r), as equation 6 shows:

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N 1 r 1 , R N r 1 r

(5)

(6) 4

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The initial cost of the investment is defined according to equation 7:

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C0 K ch Qnom Ac K c V K tan k ,

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The levelized cost of cooling is defined as the ratio of the net present cost of the investment (Ktot) to the total cooling production for the project lifetime (N), as equation 8 presents:

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LCOC

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It is important to state that the project lifetime had been taken the same for all the components.

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2.2 The examined system 2.2.1 The examined building A building of 100 m2 floor area (10 m x 10 m) is the examined for all the cities. Its characteristics are typical in order to extract general conclusions and they are included in tables 1 and 2 with details. The four external walls of the building envelope have the following composition: 1.5 cm plaster, 12 cm brick, 6 cm insulation, 12 cm brick and 1.5 cm plaster. The roof consists of 24 cm cement, 10 cm insulation and 1.5 cm plaster. The thermal transmittance (U-value) of the wall is 0.510 W/m2K, of the roof is 0.358 W/m2 K and of the window 1.4 W/m2 K. The thermal properties of the utilized structural material are given in table 1 and they are taken from TRNSYS libraries. The desired temperature of the thermostat was set at 26oC in TRNSYS for all the examined period which starts from May and ends in October, in the majority of the cases. It is essential to state for the cities with high cooling loads as Abu Dhabi, Teheran, Cairo and Phoenix, this period has been extended properly in order to cover all the possible days with cooling load demand.

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K tot , N Ecool

(7)

(8)

Table 1. Thermal properties of the building materials Material k (W/mK) cp (J/kgK) ρ (kg/m3) 0.90 1000 1800 Brick 1.40 1000 2000 Plaster 0.04 800 40 Insulation 2.10 800 2400 Concrete Table 2 includes the main parameters of the building’s envelope with all the internal loads. The examined building consists of four same external walls which are orientated in the four directions, while there is no internal wall. More specifically, the floor of the building is a square (10 m x 10 m) and the height is 3 m. There are double windows in east, south and west directions which are 60% shaded. Moreover, the internal equipment loads are about 1.5 kW, the lighting load is 1 kW, while 10 persons are assumed to be seated inside the building during the operation hours. The building is assumed to be a commercial building and its operating hours are between 8:00 am and 18:00 pm for all the examined period. Moreover, it is important to state 5

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that the infiltration and ventilation of the building are selected to be together equal to 2 air changes per hour.

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Table 2. Main parameters of the building envelope Parameter Value Parameter Area 100 m2 Specific gains (equipment) Height 3m Persons 2 East double window 3m Lighting load West double window 3 m2 Shading coefficient South double window 6 m2 Infiltration and ventilation rate Window U-value 1.4 W/m2K Roof U-value Window type Double Wall U-value

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Value 1.5 kW 10 1.0 kW 60 % 2 air changes/h 0.358 W/m2 K 0.510 W/m2 K

2.2.2 The examined solar cooling system This section is devoted to the solar cooling system description. Figure 1 depicts the examined system with the used devices and the streams. Evacuated tube collectors are used in order the solar energy to be utilized. The working fluid in their circuit is pressurized water at 8 bar for safety reasons in order to have a liquid phase in all the points of the system. The cut of temperature in the system is selected to be at 130 oC, lower than the saturation temperature at 8 bar for safety reasons. The hot water from the solar collector field is stored in the storage tank which feeds the absorption chiller. An auxiliary electrical heater is located between the storage tank and the absorption chiller in order to heat the pressurized water when its temperature is lower than the desired temperature (Tset). This temperature level is selected to be equal to 100 oC, a realistic value for the heat source of single effect absorption chillers operating with the LiBr-H2O working pair. The absorption chiller produces chilled water and this water is used in the cooling coils inside the building for covering the cooling demand.

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Figure 1. The examined solar cooling system

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Table 3 includes the main parameters of the examined system which have been inserted in the simulation tool, TRNSYS. This tool is ideal for conducting dynamic studies which include solar collector and buildings, by having validated components in its libraries. Typical values have been selected in order to perform a realistic study 6

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with general results. The solar collectors are evacuated tube collectors and their characteristics are taken from literature [18]. The slope of the collectors is selected to be 15o lower than the location latitude for maximizing the incident solar irradiation during the summer, according to Duffie and Beckman [21]. Moreover, the collector field is directed to the south and it operates from early morning up to afternoon and when the solar irradiation is over 80 W/m2. The collecting area is variable and it is ranged from 5 m2 to 60 m2 in the examined cases.

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Table 3. Parameters of the examined devices Collector field Collecting area 5 - 60 m2 Zero order heat loss coefficient 0.687 First order heat loss coefficient 1.505 W/m2 K Second order heat loss coefficient 0.011 W/m2 K2 Specific water mass flow rate 0.02 kg/sm2 Slope angle 15o lower than latitude Azimuth angle 0o Operation period 8:00-18:00 Storage tank Volume 0.5 - 3.0 m3 Thermal loss coefficient 0.8 W/m2 K Mixing zones 10 Auxiliary heater Rated capacity 10 kW Set point temperature 100 oC Efficiency 95% Absorption chiller Nominal cooling capacity 10 kW Rated COP 0.7 Cooling water inlet temperature 35 oC Cooling water mass flow rate 0.5 kg/s Chilled water outlet temperature 10 oC Heat source mass flow rate 0.5 kg/s Cooling coils Number of rows 15 Number of tubes 20 Tube spacing 0.35 m Inner tube diameter 0.020 m Outer tube diameter 0.025 m Cold air mass flow rate 1 kg/s Cold water mass flow rate 0.5 kg/s Thermostat control Set temperature level 26 oC Dead band 0.5 oC Number of oscillations per time step 5

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Moreover, the storage tank volume is variable from 0.5 m3 to 3.0 m3, as table 3 indicates. The storage tank is selected to be insulated with thermal loss coefficient 7

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equal to 0.8 W/m2K [2]. This device is modeled with the mixing zone methodology which is usually selected in similar studies [2, 22]. The auxiliary heater consumes electrical energy and its capacity is 10kW. The absorption chiller is a single-effect machine operating with LiBr-H2O. Its rated COP is selected to be equal to 0.7 [18]; a typical value according to the literature. The set point temperature was selected to be 100oC [18], while the other parameters are given in table 3. Furthermore, the selected parameters for the design of the cooling coil are included in this table. The thermostat is set to 26oC which is the maximum temperature level for indoor thermal comfort. Finally, it is important to state that the mass flow rates in various circuits are given in table 3 and they have been selected by conducting sensitivities analysis for minimizing the auxiliary energy consumption.

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2.3 Simulation methodology As it has been stated, the simulation tool is TRNSYS (Transient System Simulation Tool). This software solves differential equations with the modified Euler method while the non-linear equations are solved with the successive method. In this environment, a solar cooling system is developed by using specific types which are given in table 4. The examined system is depicted in figure 1 and the characteristics of the separate components are included in table 3. For the examined building envelope, tables 1 and 2 give the most important data which describe it properly. The same building envelope is examined in 10 different cities which present interest for solar cooling applications. More specifically, the following cities are examined: Abu Dhabi (U.A.E.), Almeria (Spain), Athens (Greece), Cairo (Egypt), Istanbul (Turkey), Madrid (Spain), Phoenix (U.S.A), Rome (Italy), Teheran (Iran) and Thessaloniki (Greece).

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The reason for examining the same building envelope is for conducting a suitable comparative study in order to correlate the system viability with the climate characteristics. For this reasoning, the data for the financial analysis are the same for all the cases. These data are included in table 5 and they are typical according to the literature. The discount factor has been selected to have a low value (3%) because of the financially unstable conditions the last years worldwide. The electricity cost for every city is given in table 6.

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Table 4. The used types in TRNSYS Device Type in TRNSYS Building 56 Solar collector 71 Storage tank 4c Pump 3b Absorption chiller 107 Auxiliary heater 6 Cooling coils 529 Weather data 109 Controller – Thermostat 672 Controller for solar collector field 14h 8

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Table 5. Financial data of the study Parameter Value Specific cost of solar collectors (Kc) 250 €/m2 Specific cost of storage tank (Ktank) 500 €/m3 Specific cost of absorption chiller (Κch) 300 €/kW Discount factor (r) 3% Investment lifetime (N) 25 years

Reference [23] [24] [25-26] [27] [28]

Table 6. Electricity prices for various cities City Abu Dhabi Phoenix Teheran Cairo Athens Almeria Thessaloniki Madrid Rome Istanbul

Kel (€/kWh) 0.08 0.13 0.04 0.16 0.20 0.24 0.20 0.24 0.30 0.13

Reference [29] [30] [31] [32] [33] [33] [33] [33] [29] [33]

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The simulation period includes the month which presents cooling demand and for this reason, a specific analysis has been performed for every city separately. The time step selected to be 0.05 hours (= 3 minutes), a low value which is selected after a simple sensitivity analysis and it leads to independent results (for temperature profiles, heating loads, etc).

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For every city, different combinations of collecting areas and storage tank volumes are tested in order to determine the combination which leads to the lowest net present cost and consequently to the lowest LCOC. The results of this procedure are described with details for Athens in section 3.1, while all the optimum cases (for the 10 cities) are given in section 3.2. Section 3.3 is devoted to presenting general guidelines for the design of solar cooling systems, using the cooling load of every location (Er) for a usual building of 100 m2 floor area, as the examined.

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3. Results 3.1 The case study of Athens In this section, the results of the parametric analysis for the system in Athens are presented in figures 2 to 7. These figures show the energetic and financial results for all the examined design cases. For Athens, the storage tank volume is examined from 0.5 m3 to 3 m3, while the collecting area from 5 m2 to 50 m2. Examining greater values of these parameters has no interest, according to the given curves in figures 2 to 7, because the auxiliary energy consumption tends towards to zero for high collecting areas and for great storage tank volumes.

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Figure 2 illustrates the auxiliary energy consumption in the electrical heater for all the examined period in Athens. This parameter is presented as a function of the collecting area and for six different storage tanks. It is obvious that higher collecting area leads to lower auxiliary consumption, the fact that is explained by the higher useful energy from the sun in cases with higher collecting area. The influence of the storage tank volume is critical on the results. In low collecting areas, lower storage tanks are most suitable solutions, while in higher collecting areas greater storage tanks have to be selected. Furthermore, greater storage tank leads to zero auxiliary energy consumption in high collecting areas, while the small tanks of 0.5 m3 and 1.0 m3 leads to minimum auxiliary energy consumption 1003 kWh and 375 kWh respectively.

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Another interesting result is that every curve presents a critical point which leads to auxiliary energy minimization. This point is observed in greater collecting areas when the storage tank is getting greater. For the storage tank of 0.5 m3, the critical collecting area is equal to 20 m2, for the tank of 1.0 m3 is 30 m2 and for the other storage tanks is about 35 m3. This observation is important for the financial analysis because the cases with higher collecting areas than the respective critical are not a financially feasible solution due to the extra cost of the useless collecting area.

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Figure 3 exhibits the useful energy production from the collector field for all the examined combination of collecting areas and storage tanks. The curves of figure 3 show that the useful energy production increases for higher collecting areas and also for greater storage tanks. Moreover, it is observed that there is a different critical collecting area, higher for greater storage tank volumes, as it has been stated in figure 2. This critical collecting area is approximately the lower collecting area which leads to the useful energy production maximization. Higher collecting areas make the water temperature in the collector loop (close to the cutoff temperature) and the pump in the collector loop stops operating. Figure 4 presents the solar fraction of the system and it is practically the “inverse” of figure 2. The solar fraction is higher for higher collecting areas. Higher storage tanks lead to a higher solar fraction in great collecting areas, while in low collecting areas cases, smaller tanks have to be selected.

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Figure 2. Auxiliary energy consumption for various collecting areas and storage tanks for Athens case

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Figure 3. Useful heat production from the collector field for various collecting areas and storage tanks for Athens case

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Figure 4. Solar fraction for various collecting areas and storage tanks for Athens case

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Figure 5 illustrates the mean thermal efficiency of the solar field for all the examined cases. It is obvious that higher collecting area leads to lower mean thermal efficiency because the mean system temperature is getting higher with the more collectors (see equation 2). On the other hand, greater storage tank volume leads to lower mean temperature and consequently to higher mean thermal efficiency in the system (see equation 2). The lower mean thermal efficiency has a significant influence on the system evaluation because this fact leads to the existence of critical temperature, as it has been presented in figures 2 to 4.

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Figure 5. Mean thermal efficiency of the solar collectors for various collecting areas and storage tanks for Athens case

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Figures 6 and 7 are devoted to the financial evaluation of the examined system in Athens. Figure 6 includes the net present cost of the system and figure 7 the levelized cost of cooling. Lower values of these parameters lead to more viability solutions financially. Observing these figures, for every storage tank volume, there is an optimum collecting area which leads to minimum net present cost (figure 6) and also to the minimum levelized cost of cooling (figure 7). The optimum collecting area, which leads to the lowest financial indexes, is greater for higher storage tank volumes; a result which indicates the direct relationship between the collecting area and the storage tank volume.

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Studying figures 6 and 7 together, the combination of 25 m2 collecting area and 1m3 storage tank is the optimum one. This combination leads to minimum net present cost and levelized cost or cooling simultaneously. In this case, the net present cost is 10280 € and the levelized cost of r cooling 0.1301 €/kWh, while the solar fraction is 86.6% and the mean thermal efficiency is 18.9%. For the optimum case with financial criteria, the solar fraction is high and so this solution is viable financially and energetically. It is important to compare the optimum collecting area which is 25 m2, with the critical collecting area which is 30 m2 according to figures 2, 3 and 4 for the same storage tank volume (1 m3). The optimum collecting area is the one which leads to minimum net present cost (and consequently to the minimum Levelized cost of cooling), while the critical collecting area is the one which leads to an approximately maximum solar fraction. The critical collecting area is found to be greater than the optimum, but with a small difference and for this reason the solar fraction in the optimum financial case is also high. This result is explained by the decrease of the mean thermal efficiency (figure 5) of the collector field for higher collecting areas, something that decreases the slope of the solar fraction close to the critical collecting area point (figure). In other words, it is not financial optimum to work on the critical collecting area which means a maximum solar fraction, but to lower collecting area because after a point the extra collecting area is not profitable.

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Lastly, figure 8 shows the temperature profile of the indoor air for all the examined period, for the optimum case for Athens climate. It is obvious that the temperature level does not exceed the limit of 26oC. This result proves that the system is designed properly and it operates with the desired way. Moreover, it is shown that the cooling loads are mainly observed the months from June to September because this period the temperature distribution is closer to the upper thermal comfort limit.

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Figure 6. Net present cost for various collecting areas and storage tanks for Athens case

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Figure 7. Levelized cost of cooling for various collecting areas and storage tanks for Athens case

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Figure 8. Indoor temperature distribution for the examined period in Athens ad for the optimum design case

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3.2 Solar cooling in various cities In this section, the optimum financially cases for ten different cities are presented. The methodology that followed for Athens in section 3.1 has been applied for also nine other cities and the final results are summarized in figures 9 to 15, as well as in table 7. Figure 9 shows the cooling loads for the ten examined cities for all the yearly period. It is obvious that there is a great variation in the results with the building in Istanbul to have 1229 kWh cooling demand and in Abu Dhabi 14007 kWh.

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A critical parameter in solar cooling systems is the solar potential of the examined location. For this reason, the yearly incident solar energy on a horizontal surface for the examined cities is given in figure 10. The minimum value is observed at Thessaloniki with 1229 kWh/m2, while the highest at Phoenix with 2117 kWh/m2. Higher solar potential means greater available solar energy for utilization in the system and consequently higher cooling demand due to higher cooling loads. However, many factors influence on the cooling loads as the building envelope structure, the mean ambient temperature, the fluctuations of ambient temperature, the internal loads (equipment, lighting, and infiltration), etc.

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Figures 11 and 12 present the optimum collecting area and storage tank volume respectively. The optimum collecting area is ranged from 10 m2 to 60 m2, while the storage tank volume varies from 0.5 m3 to 3 m3. It is obvious that lower collecting areas correspond to the cities with lower cooling demand, according to figure 9. This is an accepted result which proved a direct correlation between these parameters. Also, it is again proved that higher collecting areas need greater storage tanks in order to work properly.

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Figure 9. Yearly cooling loads for the examined cities

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Figure 10. Yearly solar potential on horizontal plane for the examined cities

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Figure 11. Optimum collecting area for the examined cities

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Figure 12. Optimum storage tank for the examined cities

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Figure 13 depicts the solar fraction for the examined cities. Generally, this quantity is close to 0.8 for the majority of the cities. For the city with the lowest solar potential (Thessaloniki), the solar fraction is only 0.548, while for the city with the highest solar potential (Phoenix) solar fraction is 0.968. This result proves that higher solar potential leads to a higher solar fraction. For the rest cities, solar fractions from 0.716 to 0.92 are found.

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Figure 13. Solar fraction of the optimum design for the examined cities

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Figures 14 and 15 show the financial indexes for the ten examined cities. Figure 14 proves that the total cost of the system is lower for the cities with lower cooling load, because of the lower installed collecting area; a factor which directly decreases the investment cost. Thessaloniki seems to have greater net present cost than the cities with similar cooling loads because of its low solar fraction, according to figure 13. The results of figure 14 are not suitable for comparing all the cities because every city presents different cooling demand. Thus, the levelized cost of cooling is given in figure 15. This financial index takes into account the net present cost and also the cooling need. It is obvious that this parameter is generally lower in the cities with higher cooling demand. Also, the solar potential plays a significant role in this analysis and it makes the Phoenix and the Abu Dhabi to be the cities with the lowest LCOC with 0.0590 €/kWh and 0.0575 €/kWh respectively. These cities present the highest solar potentials and thus it is proved that the higher solar potential is a critical parameter in the financial viability of the solar cooling system. Moreover, it is noticeable that Cairo has great solar potential but the LCOC is high (0.1045 €/kWh) because of its low cooling demand. These observations prove that solar cooling technologies have to be applied in locations with both high solar potential and cooling demand.

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Table 7 includes all the results for the optimum systems in the examined cities. As it has been said, the lowest LCOC is observed at Abu Dhabi with 0.0575 €/kWh when the collecting area is 60 m2 and the storage tank volume is 3 m3. The next city with high financial viability for this system is Phoenix with a design of 45 m2 collecting area and 3 m3 storage tank to lead to LCOC equal to 0.0590 €/kWh. The higher collecting area in Abu Dhabi is a result of the higher cooling demand in the region compared to the Phoenix. After these cities, Teheran, Cairo, Athens, Almeria, Istanbul, Thessaloniki, Madrid and Rome and are following with levelized costs of 18

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cooling 0.0712 €/kWh, 0.1045 €/kWh, 0.1301 €/kWh, 0.1514 €/kWh, 0.1652 €/kWh, 0.1771 €/kWh, 0.1792 €/kWh and 0.2125 €/kWh. It is important to state that the electricity cost plays an important role in this sequence because there is a great variation in this parameter, as it is obvious by table 6. The high electricity cost in Rome makes this city to be the less suitable location for solar cooling.

432 433 434 435 436 437

By comparing the correlation between cooling demand and LCOC, it easily can be said that these parameters are connected and higher cooling demand leads to lower LCOC. Moreover, higher solar potential leads usually to lower LCOC and thus Thessaloniki is a city with relatively high LCOC. Higher electricity cost leads also to higher LCOC and so the solar cooling technology is not financially sustainable in Rome and in Madrid.

438 439

Figure 14. Net present cost of the optimum design for the examined cities

440 441

Figure 15. Levelized cost of cooling of the optimum design for the examined cities 19

442

Table 7. Final results of the financial optimum cases for the ten cities φ H Ecool Ac V Ktot LCOC f City o 2 2 3 () (kWh/m ) (kWh) (m ) (m ) (€) (€/kWh) (%) 1957 14007 60 3.0 20144 0.0575 0.920 Abu Dhabi 24.47 33.43 2117 10356 45 3.0 15278 0.0590 0.968 Phoenix 35.70 1794 5796 25 1.5 10321 0.0712 0.738 Teheran 30.03 2026 5580 25 1.5 14582 0.1045 0.716 Cairo 37.97 1562 3160 25 1.0 10280 0.1301 0.866 Athens 36.83 1733 2529 20 1.0 9591 0.1517 0.822 Almeria 1259 2434 15 0.5 10776 0.1771 0.548 Thessaloniki 40.63 40.42 1662 1579 15 0.5 7076 0.1792 0.825 Madrid 41.90 1562 1526 15 0.5 8107 0.2125 0.763 Rome 41.00 1627 1229 10 0.5 5076 0.1652 0.784 Istanbul

443 444 445 446 447 448 449 450

3.3 Guidelines for system design This section is devoted to evaluating the results for the optimum operation of section 3.2. These results correspond to optimum design and all of them can be used for creating useful conclusions for optimum design. Figure 16 shows the optimum collecting area financially as a function of the cooling demand for the examined building of 100 m2 floor area. The relationship between these parameters is linear with R2 equal to 96.33% and it is presented by equation 9. This result proves that higher cooling demand needs collecting area for designing a sustainable system.

451

Ac m 2 8.314 0.0036 Ecool kWh,

(9)

452 453 454

Figure 16. Optimum collecting area as a function of the yearly cooling demand of the building of 100 m2 floor area

20

ηth (%) 0.195 0.194 0.255 0.198 0.189 0.192 0.202 0.159 0.154 0.188

455 456 457

Figure 17 shows that the optimum storage tank volume is linearly connected with the collecting area for optimum design financially. Equation 10 is the exact mathematical correlation between them with R2 equal to 91.85%.

458

V m 3 0.0603 Ac m 2 0.2376 ,

(10)

459 460 461

Figure 17. Optimum storage tank volume as a function of collecting area of the building of 100 m2 floor area

462 463 464 465 466 467 468 469 470 471 472 473 474 475 476 477 478 479

4. Discussion In this work, a typical solar cooling system is examined for ten characteristic locations in the world. In every place, the system is optimized financially by determining the optimum combination of collecting area and storage tank volume which leads to the lowest levelized cost of cooling. The final results lead to useful conclusions which can be used for the future design of solar cooling systems. Moreover, these conclusions can also be used as guidelines for determining the ideal locations of applying solar cooling technologies. Compared to the other literature studies, this work presents results which correspond to the financial optimum system, while the other comparative studies face this problem with energetic criteria only as the solar fraction and the installed specific collecting area. For this reason, this work is able to give more accurate results and conclusions about the viability of solar cooling in different locations. Moreover, the small number of studies which compare the solar cooling system financially, they do not include optimization of the design in every location, as it is done in the present study. Moreover, it is important to state that the same building has been examined in all the cities in order the emphasis to be given to the impact of different climate conditions on the system performance. Furthermore, different electricity costs have been used in the cities in order to perform a realistic analysis.

21

480 481 482 483 484 485

First of all, it is useful to be commented that the financial optimum collecting area is slightly lower than the critical collecting area which leads to a maximum solar fraction. This result proves that after the limit of the optimum collecting area, the extra solar collectors are not lead to extra profit because either the solar demand has been covered either the thermal efficiency is getting lower with the extra collecting area.

486 487 488 489 490

In the analysis of the results of section 3.2, it is essential to state that the levelized cost of cooling is found to be the most useful financial index for evaluating the system viability among the cities because this takes into account the net present cost of the system and simultaneously the demanded cooling load. In the optimization of the system for a specific city, these two indexes lead to equivalent optimum solutions.

491 492 493 494 495

The evaluation of the final results proved the relationship of the system viability with the yearly cooling load with a direct way; higher cooling loads leads to lower LCOC and to for feasible investments. Moreover, the higher solar potential in a location is a positive factor which leads to improved results, while the relatively low solar potential is a discouraging factor for selecting solar cooling technologies.

496 497 498 499 500

In the last part of the results section, useful correlations are suggested. More specifically it is proved that the optimum collecting area is approximately a linear function of the cooling demand and the optimum storage tank is also a linear function of the optimum collecting area. These results can be used in the design of solar cooling systems and they are useful guidelines.

501 502 503 504

In future studies, it would be interesting to examine the impact of different electricity process on the financial viability of the solar cooling system among the various locations. Also, different building envelopes can be tested in order to examine a greater range of cases and the results to be more general.

505 506 507 508 509 510 511

5. Conclusions This paper examines a solar cooling system with evacuated tube collectors with a single stage absorption chiller operating with the LiBr-H2O working pair. This system is examined for ten different cities worldwide in order general and useful results to be extracted. In every location, the system is optimized financially by the criterion of minimum levelized cost of cooling. The collecting area and the storage tank volume are the optimization parameters which are examined in specific ranges.

512 513 514 515 516 517

The optimum collecting area with financial criteria is found to be slightly lower than the collecting area which leads to maximum solar coverage. This result indicates the need for conducting financial analysis and not only energetic in order to design sustainable systems. Moreover, it is found that the LCOC is lower when the cooling demand is higher. Thus, it is found that the high solar potential is beneficial for the financial viability of the system.

22

518 519 520 521 522 523 524 525

The most appropriate locations for installing solar cooling system are Abu Dhabi and Phoenix with levelized costs of cooling equal to 0.0575 and 0.0590 €/kWh respectively. The optimum collecting areas were found 60 m2 and 45 m2, while the optimum storage tanks 3 m3 and 1.5 m3, respectively for Abu Dhabi and Phoenix. These cities present the highest cooling needs and the highest solar potentials. On the other hand, Rome, Madrid and Thessaloniki are the less suitable location for installing solar cooling applications due to the low cooling demands, the low solar potential and the high electricity cost.

526 527 528 529

Lastly, it is important to be stated that the optimum collecting area is found to be directly influenced by the cooling load and their relationship is approximately linear. Moreover, higher collecting areas have to be coupled with greater storage tank volumes and there is a linear relationship between these parameters.

530 531

Nomenclature Ac Collecting area, m2

532

cp

Specific heat capacity, J/kgK

533

C0

Capital cost, €

534

E

Energy, kWh

535

f

Solar fraction, -

536

Ghor

Incident solar irradiation on horizontal surface, W/m2

537

GT

Incident solar irradiation on titled surface, W/m2

538

H

Yearly solar energy on horizontal plane, kWh/m2

539

Kc

Collectors specific cost, €/m2

540

Kch

Chiller specific cost, €/kW

541

Kel

Cost of electricity, €/kWhel

542

Ktank

Storage tank Specific cost, €/m3

543

Ktot

Net present cost, €

544

k

Thermal conductivity, W/mK

545

N

Investment lifetime, years

546

Q

Heat, kW

547

R

Effective investment years, years

548

r

Discount factor, % 23

549

T

Temperature, oC

550

U

Thermal transmittance, W/m2K

551

V

Storage tank volume, m3

552 553

Greek Symbols ηth Solar collector thermal efficiency, -

554

ρ

Density, kg/m3

555

φ

City latitude, o

556 557

Subscripts and superscripts am ambient

558

aux

auxiliary

559

cool

cooling

560

fm

fluid mean

561

in

indoor

562

hs

heat source

563

nom

nominal cooling

564

s

solar

565

set

set point

566

u

useful

567 568

Abbreviations COP Coefficient of performance

569

ETC

Evacuated tube collector

570

FPC

Flat plate collectors

571

LCOC Levelized cost of cooling

572 573

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656 657 658

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659

27

660

Highlights

661

A single stage absorption chiller coupled with ETCs is the examined system.

662

This configuration is optimized financially in ten different cities.

663

The final results proved sustainability in Abu Dhabi and in Phoenix.

664

Thessaloniki, Madrid, and Rome are not ideal locations for this system.

665

General guidelines for the design of solar cooling systems are presented.

666

28

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