*3.4. System Pricing and Optimization*

financing period.

*3.5. Boundary Conditions* 

Electricity and combustible price

The detailed system cost of the PVT system is defined by customizing each component, such as flat or tilted mounting structure, single-phase or three-phase inverter, material marginal rate, electrical and combustible price escalation rate, annual maintenance cost, etc.

The simulation considers the appropriate dynamic inputs and generates the report of assessment on the key economic performance indicators, i.e., lifetime cash flow with appropriate total annual savings, NPV, and payback period. This simulation tool allows collector economic performance with several financing options shown in Figure 4. For instance:


*Buildings* **2020**, *10*, x FOR PEER REVIEW 10 of 30

**Figure 4.** Cost optimization of the PVT system in the simulation tool. **Figure 4.** Cost optimization of the PVT system in the simulation tool.

This simulation tool is also flexible in customizing several real-time scenarios, i.e., the number of payments in a single year and the total number of payments in the entire financing period. The

This section pre-determines the boundary conditions for the simulation as shown in Table 3.

**Table 3.** Boundary conditions for the simulation tool.

Type of demand Electricity demand and thermal demand for DHW

Inclination Selected optimally based on a parametric study for

Annual maintenance cost Assumed that no maintenance is required for a single

increment 6% per year is assumed for all the location

Interest rate Selected appropriately for each location

maximum energy production

collector to reduce uncertainties

**Parameter Description**  Type of application Single-family house

Auxiliary system Electrical heater

No. of people in house 5 DHW temperature 60° PVT Collector model aH72SK No. of collectors 1 Specific volume capacity 80 liters/m2

Type of mounting structure Tilted

Type of inverter Single-phase inverter

System lifetime 25 years

Auxiliary system energy price This is selected individually for each location

This simulation tool is also flexible in customizing several real-time scenarios, i.e., the number of payments in a single year and the total number of payments in the entire financing period. The early cancellation interest rate can be applied when the system is to be dismantled during the financing period.

#### *3.5. Boundary Conditions*

This section pre-determines the boundary conditions for the simulation as shown in Table 3.


**Table 3.** Boundary conditions for the simulation tool.

Initially, the energy performance of the PVT system is simulated in 85 different locations using the simulation tool. In order to discover and compare the collector energy performance in different locations, the thermal demand is maintained the same in all selected locations. Therefore, the simulated system considers a single PVT collector (1.96 m<sup>2</sup> ), for a single-family house application with 5 people, for the same demand, and the same tank volume for all locations. These assumptions provide a common system boundary to understand the effect of climatic variables and financing parameters on collector performance. Two types of demands are considered as DHW and electricity use in the building. In the electricity model, no price difference in self-consumed and exported power to the grid is considered. In the thermal system configuration, the auxiliary source for the house is the electricity grid with appropriate energy prices for every location. The generated DHW by the collector is utilized for household purposes using a storage tank connected to the auxiliary system which will deliver demand at the desired temperature of 60 ◦C, as shown in Figure 5. For each location, the installed tilt and azimuth angles are taken optimally based on higher collector production. The specific volume capacity is assumed 80 L/m<sup>2</sup> for all the locations which is equivalent to total 150 L of storage tank capacity.

In the proposed simplified energy system, PVT collector is directly connected to the tank without any internal or external heat exchanger. The cold water from the tank enters the PVT module, exchanges heat from the absorber, and hot water is fed to the top of the tank. The DHW cold water enters at bottom of the tank, and hot water leaves from top of the tank for DHW supply in the building. The DHW distribution system and associated heat losses are not considered in the analysis. The maximum DHW supply temperature is set at 60 ◦C, and an electric auxiliary heater is provisioned in the tank for periods when the energy from PVT modules is not enough to meet the DHW load. Electric heater starts and stops at the determined dead band to optimize energy consumption while maintaining the fixed supply DHW temperature. During the periods when tank temperature exceeds the set limit, the energy from PVT modules is fed to a heat sink (air/water heat exchanger), and this spilled energy from the collector is not counted as part of useful energy output.

equivalent to total 150 liters of storage tank capacity.

Initially, the energy performance of the PVT system is simulated in 85 different locations using the simulation tool. In order to discover and compare the collector energy performance in different locations, the thermal demand is maintained the same in all selected locations. Therefore, the simulated system considers a single PVT collector (1.96 m2), for a single-family house application with 5 people, for the same demand, and the same tank volume for all locations. These assumptions provide a common system boundary to understand the effect of climatic variables and financing parameters on collector performance. Two types of demands are considered as DHW and electricity use in the building. In the electricity model, no price difference in self-consumed and exported power to the grid is considered. In the thermal system configuration, the auxiliary source for the house is the electricity grid with appropriate energy prices for every location. The generated DHW by the collector is utilized for household purposes using a storage tank connected to the auxiliary system which will deliver demand at the desired temperature of 60 °C, as shown in Figure 5. For each location, the installed tilt and azimuth angles are taken optimally based on higher collector

**Figure 5.** Thermal and electrical system configurations. **Figure 5.** Thermal and electrical system configurations.

In the proposed simplified energy system, PVT collector is directly connected to the tank without any internal or external heat exchanger. The cold water from the tank enters the PVT module, exchanges heat from the absorber, and hot water is fed to the top of the tank. The DHW cold water enters at bottom of the tank, and hot water leaves from top of the tank for DHW supply in the building. The DHW distribution system and associated heat losses are not considered in the analysis. The maximum DHW supply temperature is set at 60 °C, and an electric auxiliary heater is provisioned In the electrical system configuration, the generated DC power will be converted to AC power using an inverter. Then, it is utilized for household purposes and the remaining will be sent to the electricity grid, whereas the excess electricity demand is taken from the grid connection as shown in Figure 5. As the tilt angle of the PVT collector is a key parameter that will also decide the collector production, a preliminary parametric study is carried for each location to determine the optimal tilt angle for maximum annual collector production.

in the tank for periods when the energy from PVT modules is not enough to meet the DHW load. Electric heater starts and stops at the determined dead band to optimize energy consumption while maintaining the fixed supply DHW temperature. During the periods when tank temperature exceeds the set limit, the energy from PVT modules is fed to a heat sink (air/water heat exchanger), and this The total system cost is determined using variables such a module cost, system components cost, annual operation, and maintenance cost. The electricity and auxiliary energy price escalation is assumed to be 6% per year for all the locations. Various parameters considered for economic analysis are shown in Table 4.


The payback time and NPV are estimated by considering a reference system using an electric heater. The price of electricity considered for various locations is shown in Figure 6 below.


Electricity price Variable based on each location

heater. The price of electricity considered for various locations is shown in Figure 6 below.

**Table 4.** Parameters considered for economic analysis.

**Parameter Value**  Abora PVT collector 350 EUR Cost for Connection kit 128 EUR Tilted mounting structure 243 EUR

Storage tank 1553 EUR Valve (servo meter) 127 EUR Flowmeter 142 EUR Copper tubes 19 EUR Isolation tubes 14 EUR Heat sink 474 EUR Microinverter 500 EUR Legal regulations 377 EUR Electricity price increment 6% annually System lifetime 25 years

**Figure 6.** Considered electricity prices in all countries [37]. **Figure 6.** Considered electricity prices in all countries [37].

#### The economic performance of the collector in two different financial models is evaluated based **4. Results and Discussion**

discussed.

on: • Model 1: The total system cost is invested as initial capital investment in the first year; This section details the simulation results using the digital mapping approach. Table 5 shows the inputs and results of key performance indicators for all selected locations, and the results are discussed. *Buildings* **2020**, *10*, x FOR PEER REVIEW 16 of 30

#### • Model 2: 25% of total system cost is capital investment and remaining 75 % is paid within *4.1. Energy Performance Evaluation of PVT Panel 4.1. Energy Performance Evaluation of PVT Panel*

#### 4.1.1. Collector Thermal Production 4.1.1. Collector Thermal Production

estimate the collector output.

**4. Results and Discussion**  This section details the simulation results using the digital mapping approach. Table 5 shows the inputs and results of key performance indicators for all selected locations, and the results are The simulated results are visualized using geospatial maps, as they provide clear indication for understanding regional trends for thermal and electrical output even in the case of large datasets. Figure 7 shows the variation in the thermal output of the collector. The simulated results are visualized using geospatial maps, as they provide clear indication for understanding regional trends for thermal and electrical output even in the case of large datasets. Figure 7 shows the variation in the thermal output of the collector.

financial period of 7 years with a certain variable interest rate with every location.

**Figure 7.** Annual average collector thermal performance. **Figure 7.** Annual average collector thermal performance.

The general trend shows that thermal output is higher in countries with higher irradiation, such as Saudi Arabia, Algeria, Morocco, Brazil, Mexico, India, etc., with annual thermal production above 1800 kWh (area-specific output 918 kWh/m2) due to high GHI and ambient temperatures. The lower

obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m2 annual production. The collector shows better performance in countries, such as Spain, Portugal, and Australia, with collector production of above 1600 kWh (816 kWh/ m2).

Figure 8 shows the correlation of collector thermal production with GHI and ambient temperature. All the simulated data points of these parameters are considered to define the possible trend. Results show that thermal output has a strong linear correlation with GHI with R2 value close to 0.98. Thus, the location with higher GHI has higher thermal output. In addition, thermal output shows a linear trend with ambient temperature for most of the data points, however, the correlation is not as strong as with GHI. Therefore, ambient temperature cannot be used as a sole indicator to


**Table 5.** All simulated data of key performance indicators.

*Buildings* **2020**, *10*, 148


**Table 5.** *Cont.*

*Buildings* **2020**, *10*, 148


**Table 5.** *Cont.*

*Buildings* **2020**, *10*, 148

The general trend shows that thermal output is higher in countries with higher irradiation, such as Saudi Arabia, Algeria, Morocco, Brazil, Mexico, India, etc., with annual thermal production above 1800 kWh (area-specific output 918 kWh/m<sup>2</sup> ) due to high GHI and ambient temperatures. The lower band of average collector production can be seen in Reykjavik, Iceland, and for some locations in Norway, with a specific output of 475 and 500 kWh/m<sup>2</sup> , respectively. Similar thermal output is obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m<sup>2</sup> annual production. The collector shows better performance in countries, such as Spain, Portugal, and Australia, with collector production of above 1600 kWh (816 kWh/ m<sup>2</sup> ).

Figure 8 shows the correlation of collector thermal production with GHI and ambient temperature. All the simulated data points of these parameters are considered to define the possible trend. Results show that thermal output has a strong linear correlation with GHI with R<sup>2</sup> value close to 0.98. Thus, the location with higher GHI has higher thermal output. In addition, thermal output shows a linear trend with ambient temperature for most of the data points, however, the correlation is not as strong as with GHI. Therefore, ambient temperature cannot be used as a sole indicator to estimate the *Buildings*  collector output. **2020**, *10*, x FOR PEER REVIEW 17 of 30

**Figure 8.** Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature. **Figure 8.** Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature.

#### 4.1.2. Collector Electrical Production 4.1.2. Collector Electrical Production

Figure 9 represents the electrical performance of the collector, which shows similar trends as thermal output. For locations in countries with high GHI, such as Saudi Arabia, Algeria, Morocco, Brazil, India, etc., generation is above 500 kWh, and the peak value is in Saudi Arabia with 540 kWh. The electrical production is much less in Iceland with 266 kWh due to less available GHI, and the collector generation is lower than 300 kWh in Sweden, Finland, Denmark, Poland, United Kingdom, etc. The collector performed slightly better in Spain, Portugal, and Australia, with more than 400 kWh annually. However, it shows there is no significant difference in thermal and electrical production trends. Furthermore, a correlation of collector electrical production with GHI and ambient temperature is developed based on all monthly points from all chosen locations and a positive correlation is realized as shown in Figure 10. A large variation in electrical output for similar values of ambient temperature can be observed, which again shows that GHI is the critical parameter governing the electrical output of the collector. Figure 9 represents the electrical performance of the collector, which shows similar trends as thermal output. For locations in countries with high GHI, such as Saudi Arabia, Algeria, Morocco, Brazil, India, etc., generation is above 500 kWh, and the peak value is in Saudi Arabia with 540 kWh. The electrical production is much less in Iceland with 266 kWh due to less available GHI, and the collector generation is lower than 300 kWh in Sweden, Finland, Denmark, Poland, United Kingdom, etc. The collector performed slightly better in Spain, Portugal, and Australia, with more than 400 kWh annually. However, it shows there is no significant difference in thermal and electrical production trends. Furthermore, a correlation of collector electrical production with GHI and ambient temperature is developed based on all monthly points from all chosen locations and a positive correlation is realized as shown in Figure 10. A large variation in electrical output for similar values of ambient temperature can be observed, which again shows that GHI is the critical parameter governing the electrical output of the collector.

**Figure 9.** Annual average collector electrical performance.

ambient temperature.

–50

0

50

100

150

**GHI (kWh)**

200

250

300

4.1.2. Collector Electrical Production

**Figure 8.** Correlation of collector thermal production with global horizontal irradiation (GHI) and

0 50 100 150 200 250

GHI Ambient temperature

Linear (GHI) Linear (Ambient temperature)

**Monthly thermal production (kWh/m2/month)**

**Ambient temperature (°C)**

Figure 9 represents the electrical performance of the collector, which shows similar trends as thermal output. For locations in countries with high GHI, such as Saudi Arabia, Algeria, Morocco, Brazil, India, etc., generation is above 500 kWh, and the peak value is in Saudi Arabia with 540 kWh. The electrical production is much less in Iceland with 266 kWh due to less available GHI, and the collector generation is lower than 300 kWh in Sweden, Finland, Denmark, Poland, United Kingdom, etc. The collector performed slightly better in Spain, Portugal, and Australia, with more than 400 kWh annually. However, it shows there is no significant difference in thermal and electrical production trends. Furthermore, a correlation of collector electrical production with GHI and ambient temperature is developed based on all monthly points from all chosen locations and a positive correlation is realized as shown in Figure 10. A large variation in electrical output for similar values

**Figure 9.** Annual average collector electrical performance. **Figure 9.** Annual average collector electrical performance. *Buildings* **2020**, *10*, x FOR PEER REVIEW 18 of 30

**Figure 10.** Correlation of collector electrical production with global horizontal irradiation (GHI) and ambient temperature. **Figure 10.** Correlation of collector electrical production with global horizontal irradiation (GHI) and ambient temperature.

A large variation in thermal and electrical output is seen for many countries and is reflected in Figures 7 and 9. The range of collector output with a maximum and minimum value of thermal and electrical production is shown in Figure 11. A large variation in thermal and electrical output is seen for many countries and is reflected in Figures 7 and 9. The range of collector output with a maximum and minimum value of thermal and electrical production is shown in Figure 11.

The minimum thermal production in blue color represents the minimum production for analyzed location, while the maximum thermal production is indicated with an orange color that represents the highest thermal production of a city in each country. The results show likely high variation in Italy, Spain, United States, and Australia, as many cities were simulated in those countries, and less variation is recorded in countries Denmark, Iceland, United Kingdom, etc., due to the lower number of simulated cities.

In general, PVT collector monthly production is an important key factor in the sizing of a solar system to match the monthly variation of energy consumption. Figures 12 and 13 show the variation in collector monthly thermal and electrical production, respectively. The thermal performance in April and July is relatively higher and less in January and October for the locations in the northern hemisphere,

**Figure 11.** Country-wise collector thermal performance uncertainty.

the lower number of simulated cities.

The minimum thermal production in blue color represents the minimum production for analyzed location, while the maximum thermal production is indicated with an orange color that represents the highest thermal production of a city in each country. The results show likely high variation in Italy, Spain, United States, and Australia, as many cities were simulated in those countries, and less variation is recorded in countries Denmark, Iceland, United Kingdom, etc., due to

In general, PVT collector monthly production is an important key factor in the sizing of a solar system to match the monthly variation of energy consumption. Figures 12 and 13 show the variation 100

150

**GHI (kWh)**

200

250

300

0

such as Madrid, Stockholm, and Berlin. In Medina, although GHI and ambient temperatures are higher in July, the thermal production is lower compared to in October. This is because the thermal demand in July is less than in October. Therefore, in July, due to high GHI and less thermal demand, the storage tank losses will be higher as the tank temperature increases. Higher tank temperature results in lower thermal and electrical production of collector. As the GHI trend in the southern hemisphere is opposite to the northern hemisphere, the production in January and October is likely higher than the April and July months. In Stockholm, the variation between the months is significant because of seasonal variation in GHI, and the same is lower in Medina, which results in more uniform monthly production. **Figure 10.** Correlation of collector electrical production with global horizontal irradiation (GHI) and ambient temperature. A large variation in thermal and electrical output is seen for many countries and is reflected in Figures 7 and 9. The range of collector output with a maximum and minimum value of thermal and electrical production is shown in Figure 11. 0 10 20 30 40 50 60 70 **Monthly electrical production (kWh/m2/month)**

**Ambient temperature (°C)**

*Buildings* **2020**, *10*, x FOR PEER REVIEW 18 of 30

GHI Ambient temperature

**Figure 11.** Country-wise collector thermal performance uncertainty. **Figure 11.** Country-wise collector thermal performance uncertainty. months is significant because of seasonal variation in GHI, and the same is lower in Medina, which results in more uniform monthly production.

The minimum thermal production in blue color represents the minimum production for analyzed location, while the maximum thermal production is indicated with an orange color that represents the highest thermal production of a city in each country. The results show likely high variation in Italy, Spain, United States, and Australia, as many cities were simulated in those countries, and less variation is recorded in countries Denmark, Iceland, United Kingdom, etc., due to The trends for monthly electrical production are slightly different than thermal output. For example, in Medina, electrical production is higher in July than in October even though the ambient temperature is maximum in July. This is due to high GHI in July and is in line with findings that the major factor influencing the electrical production is GHI, rather than ambient temperature. The trends for monthly electrical production are slightly different than thermal output. For example, in Medina, electrical production is higher in July than in October even though the ambient temperature is maximum in July. This is due to high GHI in July and is in line with findings that the major factor influencing the electrical production is GHI, rather than ambient temperature.

**Figure 12.** Collector monthly thermal production variation. **Figure 12.** Collector monthly thermal production variation.

**Figure 13.** Collector monthly electrical production variation.

January April July October

Madrid Stockholm Berlin Medina Melbourne

0

10

20

30

40

Electrical production (kWh)

50

60

70

Thermal production (kWh)

results in more uniform monthly production.

**Figure 12.** Collector monthly thermal production variation.

January April July October

Madrid Stockholm Berlin Medina Melbourne

in collector monthly thermal and electrical production, respectively. The thermal performance in April and July is relatively higher and less in January and October for the locations in the northern hemisphere, such as Madrid, Stockholm, and Berlin. In Medina, although GHI and ambient temperatures are higher in July, the thermal production is lower compared to in October. This is because the thermal demand in July is less than in October. Therefore, in July, due to high GHI and less thermal demand, the storage tank losses will be higher as the tank temperature increases. Higher tank temperature results in lower thermal and electrical production of collector. As the GHI trend in the southern hemisphere is opposite to the northern hemisphere, the production in January and October is likely higher than the April and July months. In Stockholm, the variation between the months is significant because of seasonal variation in GHI, and the same is lower in Medina, which

The trends for monthly electrical production are slightly different than thermal output. For example, in Medina, electrical production is higher in July than in October even though the ambient temperature is maximum in July. This is due to high GHI in July and is in line with findings that the

major factor influencing the electrical production is GHI, rather than ambient temperature.

**Figure 13.** Collector monthly electrical production variation. **Figure 13.** Collector monthly electrical production variation. *Buildings* **2020**, *10*, x FOR PEER REVIEW 20 of 30

#### 4.1.3. Collector Energy Utilization Ratio 4.1.3. Collector Energy Utilization Ratio

53% 54% 55%

The energy utilization ratio of the collector for various locations is shown in Figure 14. The correlation trends between energy utilization ratio and annual average ambient temperature are shown in Figure 15 with consideration of all selected 85 geographical locations to derive a possible trend between the parameters. The energy utilization ratio of the collector for various locations is shown in Figure 14. The correlation trends between energy utilization ratio and annual average ambient temperature are shown in Figure 15 with consideration of all selected 85 geographical locations to derive a possible trend between the parameters.

**Figure 14.** Collector energy utilization ratio. **Figure 14.** Collector energy utilization ratio.

56% 57% 58% 59% 60% 61% 62% 63% 64% **Energy utilization ratio (%)** Some locations show interesting results of system boundaries on PVT collector performance. This can be realized by comparing the energy utilization ratio for Medina (high irradiation) and Davos (low irradiation location). The energy utilization for Davos (63%) is higher compared to Medina (52.5%), even though the absolute value of total energy output is higher for Medina (2506 kWh) compared to Davos (1988 kWh). This is because the load demand for Medina is comparably lower, while the other system design parameters remain the same (collector area, tank volume, etc.), which resulted in higher average tank temp and thus lower collector efficiency for Medina. Results show that the total thermal demand for every location varies depending on the ambient temperature as shown in Figure 16. This is because of the temperature difference between the annual average ambient temperature of each

Ambient temperature (°C) Energy utilization ratio

**Figure 15.** Correlation of energy utilization ratio with the annual average ambient temperature.

Rome, Italy Madrid, Spain Davos, Switzerland Stockholm, Sweden Berlin, Germany Athinai, Greece Medina, Saudi arabia

4.1.3. Collector Energy Utilization Ratio

trend between the parameters.

Chicago, USA

Cairo, Egypt New Delhi, India Brasilia, Brazil

Melbourne, Australia

location and desired water temperature (assumed 60 ◦C), which has to be covered by the collector thermal production. **Figure 14.** Collector energy utilization ratio.

Energy utilization ratio

50% 52% 54% 56% 58% 60% 62% 64%

*Buildings* **2020**, *10*, x FOR PEER REVIEW 20 of 30

The energy utilization ratio of the collector for various locations is shown in Figure 14. The correlation trends between energy utilization ratio and annual average ambient temperature are shown in Figure 15 with consideration of all selected 85 geographical locations to derive a possible

**Figure 15.** Correlation of energy utilization ratio with the annual average ambient temperature. be covered by the collector thermal production.

**Figure 16.** Total thermal demand of single-family house relation with the average ambient **Figure 16.** Total thermal demand of single-family house relation with the average ambient temperature.

#### temperature. 4.1.4. Collector Exergy Efficiency

4.1.4. Collector Exergy Efficiency From the Carnot efficiency, it can be noted that exergy efficiency is a function of inlet temperature and thermal output of the collector (assumed that the desired output temperature is From the Carnot efficiency, it can be noted that exergy efficiency is a function of inlet temperature and thermal output of the collector (assumed that the desired output temperature is fixed at 60 ◦C). Hence, it can be derived that locations with higher ambient temperature will result in less quality of exergy and, thus, lower exergetic efficiency.

fixed at 60 °C). Hence, it can be derived that locations with higher ambient temperature will result in less quality of exergy and, thus, lower exergetic efficiency. Figure 17 shows the correlation of exergetic efficiency with ambient temperature based on all selected 85 geographical locations to derive a possible trend between the parameters. Similar trends can be seen for some specific locations shown in Figure 18. It can be seen that even though the energy Figure 17 shows the correlation of exergetic efficiency with ambient temperature based on all selected 85 geographical locations to derive a possible trend between the parameters. Similar trends can be seen for some specific locations shown in Figure 18. It can be seen that even though the energy efficiency of Madrid is higher compared to Davos, the exergy efficiency of Davos is higher due to lower annual ambient temperature and, thus, higher quality of heat is delivered to the user.

efficiency of Madrid is higher compared to Davos, the exergy efficiency of Davos is higher due to

lower annual ambient temperature and, thus, higher quality of heat is delivered to the user.

**Figure 17.** Correlation of exergy efficiency with the annual average ambient temperature. **Figure 17.** Correlation of exergy efficiency with the annual average ambient temperature.

**Figure 18.** Collector exegetic efficiency. **Figure 18.** Collector exegetic efficiency.

#### **Figure 18.** Collector exegetic efficiency. *4.2. Economic Performance Evaluation of the PVT Collector 4.2. Economic Performance Evaluation of the PVT Collector*

*4.2. Economic Performance Evaluation of the PVT Collector*  Based on the above energy performance, the economic performance of such a PVT system is investigated in the 85 different locations. In this section, the NPV per unit collector area is analyzed Based on the above energy performance, the economic performance of such a PVT system is investigated in the 85 different locations. In this section, the NPV per unit collector area is analyzed and represented. Based on the above energy performance, the economic performance of such a PVT system is investigated in the 85 different locations. In this section, the NPV per unit collector area is analyzed and represented.

#### and represented. 4.2.1. Collector Economic Performance in Financing Model 1 4.2.1. Collector Economic Performance in Financing Model 1

4.2.1. Collector Economic Performance in Financing Model 1 This financing model scenario has assumed that the total cost of the system is invested in the first year of the system period. As the total system cost will be invested in the first year, the interest rate is not considered. Figure 19 is the digital representation of NPV potential per unit collector area with financial model 1 in all 85 geographical cities across the world and Figure 20 shows the NPV This financing model scenario has assumed that the total cost of the system is invested in the first year of the system period. As the total system cost will be invested in the first year, the interest rate is not considered. Figure 19 is the digital representation of NPV potential per unit collector area with financial model 1 in all 85 geographical cities across the world and Figure 20 shows the NPV potential per unit collector area in geographical cities in the European continent. This financing model scenario has assumed that the total cost of the system is invested in the first year of the system period. As the total system cost will be invested in the first year, the interest rate is not considered. Figure 19 is the digital representation of NPV potential per unit collector area with financial model 1 in all 85 geographical cities across the world and Figure 20 shows the NPV potential per unit collector area in geographical cities in the European continent.

potential per unit collector area in geographical cities in the European continent.

*Buildings* **2020**, *10*, x FOR PEER REVIEW 23 of 30

*Buildings* **2020**, *10*, x FOR PEER REVIEW 23 of 30

**Figure 19.** Net present value (NPV) potential per unit collector area for financing model 1. **Figure 19.** Net present value (NPV) potential per unit collector area for financing model 1. **Figure 19.** Net present value (NPV) potential per unit collector area for financing model 1.

**Figure 20.** NPV potential per unit collector area in Europe for financing model 1. **Figure 20.** NPV potential per unit collector area in Europe for financing model 1. **Figure 20.** NPV potential per unit collector area in Europe for financing model 1.

The cities with larger dots represent the high NPV potential and cities with smaller dots size represents the least NPV potential. The cities Catania and Munich have the highest potential of 5140 and 5348 EUR, respectively, followed by the cities Bari, Lisbon, Setubal, Sevilla, Valencia, Zaragoza, Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due to their high available GHI and electricity grid price, so the energy savings are high in these locations which is reflected in huge NPV potential for this system. Cities such as Oslo, Bergen, Reykjavik, etc., with relatively less electricity grid price resulted in having negative NPV due to lower available GHI. The cities with high collector production such as Medina, Algeria, and Cairo have shown negative NPV potential due to a much lower electricity grid price which eventually showed fewer energy savings. The cities with larger dots represent the high NPV potential and cities with smaller dots size represents the least NPV potential. The cities Catania and Munich have the highest potential of 5140 and 5348 EUR, respectively, followed by the cities Bari, Lisbon, Setubal, Sevilla, Valencia, Zaragoza, Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due to their high available GHI and electricity grid price, so the energy savings are high in these locations which is reflected in huge NPV potential for this system. Cities such as Oslo, Bergen, Reykjavik, etc., with relatively less electricity grid price resulted in having negative NPV due to lower available GHI. The cities with high collector production such as Medina, Algeria, and Cairo have shown negative NPV potential due to a much lower electricity grid price which eventually showed fewer energy savings. The cities with larger dots represent the high NPV potential and cities with smaller dots size represents the least NPV potential. The cities Catania and Munich have the highest potential of 5140 and 5348 EUR, respectively, followed by the cities Bari, Lisbon, Setubal, Sevilla, Valencia, Zaragoza, Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due to their high available GHI and electricity grid price, so the energy savings are high in these locations which is reflected in huge NPV potential for this system. Cities such as Oslo, Bergen, Reykjavik, etc., with relatively less electricity grid price resulted in having negative NPV due to lower available GHI. The cities with high collector production such as Medina, Algeria, and Cairo have shown negative NPV potential due to a much lower electricity grid price which eventually showed fewer energy savings.

The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the appropriate countries to define the NPV range per unit collector area of each country as shown in

The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the

of the key uncertainty.

The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the appropriate countries to define the NPV range per unit collector area of each country as shown in Figure 21. A large variation in NPV can be seen in a few countries, such as Italy and Portugal, due to variability in GHI for simulated locations. However, a smaller variation is identified in countries such as China, Argentina, Brazil, etc., because only one city has been simulated in this paper, which is part of the key uncertainty. *Buildings* **2020**, *10*, x FOR PEER REVIEW 24 of 30 Figure 21. A large variation in NPV can be seen in a few countries, such as Italy and Portugal, due to variability in GHI for simulated locations. However, a smaller variation is identified in countries such as China, Argentina, Brazil, etc., because only one city has been simulated in this paper, which is part of the key uncertainty. *Buildings* **2020**, *10*, x FOR PEER REVIEW 24 of 30 Figure 21. A large variation in NPV can be seen in a few countries, such as Italy and Portugal, due to variability in GHI for simulated locations. However, a smaller variation is identified in countries such as China, Argentina, Brazil, etc., because only one city has been simulated in this paper, which is part

**Figure 21.** Country-wise NPV potential per unit collector area for financial model 1. **Figure 21.** Country-wise NPV potential per unit collector area for financial model 1. **Figure 21.** Country-wise NPV potential per unit collector area for financial model 1.

Morocco

Figure 22 shows the payback period of this PVT system for a single-family house of 5 people in several countries based on financial model 1. The results show that the total system cost will be returned in the first 10 years in countries such as Australia, Belgium, Denmark, Germany, Greece, Italy, Portugal, Spain, Switzerland, etc. This is due to high collector production and high electricity grid price. Although countries such as Algeria, Saudi Arabia, and Egypt have the highest collector production, the grid price is comparatively lower, which reflects the payback period of more than 20 years. Figure 22 shows the payback period of this PVT system for a single-family house of 5 people in several countries based on financial model 1. The results show that the total system cost will be returned in the first 10 years in countries such as Australia, Belgium, Denmark, Germany, Greece, Italy, Portugal, Spain, Switzerland, etc. This is due to high collector production and high electricity grid price. Although countries such as Algeria, Saudi Arabia, and Egypt have the highest collector production, the grid price is comparatively lower, which reflects the payback period of more than 20 years. Figure 22 shows the payback period of this PVT system for a single-family house of 5 people in several countries based on financial model 1. The results show that the total system cost will be returned in the first 10 years in countries such as Australia, Belgium, Denmark, Germany, Greece, Italy, Portugal, Spain, Switzerland, etc. This is due to high collector production and high electricity grid price. Although countries such as Algeria, Saudi Arabia, and Egypt have the highest collector production, the grid price is comparatively lower, which reflects the payback period of more than 20 years.

**Figure 22.** Country-wise average payback period of the PVT collector system. **Figure 22.** Country-wise average payback period of the PVT collector system. **Figure 22.** Country-wise average payback period of the PVT collector system.

#### 4.2.2. Collector Economic Performance in Financing Model 2 *Buildings* **2020**, *10*, x FOR PEER REVIEW 25 of 30

This financing model has been analyzed by assuming that 75% of total system cost is paid within a financing period of 7 years with a certain interest rate and that the remaining 25% of total system cost is invested in the first year without any interest rate. The NPV potential per unit collector area with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV potential per unit collector area in a specific European continent is shown in Figure 24. 4.2.2. Collector Economic Performance in Financing Model 2 This financing model has been analyzed by assuming that 75% of total system cost is paid within a financing period of 7 years with a certain interest rate and that the remaining 25% of total system cost is invested in the first year without any interest rate. The NPV potential per unit collector area with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV potential per unit collector area in a specific European continent is shown in Figure 24. 4.2.2. Collector Economic Performance in Financing Model 2 This financing model has been analyzed by assuming that 75% of total system cost is paid within a financing period of 7 years with a certain interest rate and that the remaining 25% of total system cost is invested in the first year without any interest rate. The NPV potential per unit collector area with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV

potential per unit collector area in a specific European continent is shown in Figure 24.

*Buildings* **2020**, *10*, x FOR PEER REVIEW 25 of 30

**Figure 23.** NPV potential per unit collector area for financing model 2. **Figure 23.** NPV potential per unit collector area for financing model 2. **Figure 23.** NPV potential per unit collector area for financing model 2.

**Figure 24.** NPV potential per unit collector area in Europe for financing model 2. **Figure 24.** NPV potential per unit collector area in Europe for financing model 2. **Figure 24.** NPV potential per unit collector area in Europe for financing model 2.

The cities with larger dots represent the high NPV potential cities and those with smaller dots represent the lower NPV potential. The cities that showed high NPV potential in financing model 1, such as Catania and Munich, which have shown improved NPV of 5140 and 5348 EUR, respectively, were because of the almost zero interest rates in those countries. This is because if the interest rate is zero, the user needs to pay part of the system cost in later years, and the present value of this investment will be lower due to the time value of money. This will reduce the accumulated investment and thus higher NPV. However, if the interest rate is high, the extra amount paid due to high interest in later years will overweigh the advantage due to the time value of money, and it will decrease the overall NPV. Therefore, financial model 1 is recommended for countries with a high interest rate to maximize the NPV and minimize the payback. Meanwhile, financial model 2 is recommended for countries with zero or lower interest rates to maximize the NPV. The cities with larger dots represent the high NPV potential cities and those with smaller dots represent the lower NPV potential. The cities that showed high NPV potential in financing model 1, such as Catania and Munich, which have shown improved NPV of 5140 and 5348 EUR, respectively, were because of the almost zero interest rates in those countries. This is because if the interest rate is zero, the user needs to pay part of the system cost in later years, and the present value of this investment will be lower due to the time value of money. This will reduce the accumulated investment and thus higher NPV. However, if the interest rate is high, the extra amount paid due to high interest in later years will overweigh the advantage due to the time value of money, and it will decrease the overall NPV. Therefore, financial model 1 is recommended for countries with a high interest rate to maximize the NPV and minimize the payback. Meanwhile, financial model 2 is recommended for countries with zero or lower interest rates to maximize the NPV.

*Buildings* **2020**, *10*, x FOR PEER REVIEW 26 of 30

Figure 25 shows the NPV potential per unit collector area in each country for the financing model 2. As compared with financing model 1, there is slightly better performance in NPV in most of the countries. Thus, not much variation has been identified in model 2 compared with model 1. Figure 25 shows the NPV potential per unit collector area in each country for the financing model 2. As compared with financing model 1, there is slightly better performance in NPV in most of the countries. Thus, not much variation has been identified in model 2 compared with model 1.

**Figure 25.** Country-wise NPV potential per unit collector area for financing model 2. **Figure 25.** Country-wise NPV potential per unit collector area for financing model 2.

The effect of NPV change due to financial model 2 compared to model 1 is shown in Figure 26. As expected, the countries with high interest rate have shown a negative effect on NPV and countries with less and zero interest rates have shown better NPV potential, such as United States, Australia, and most of the European countries. However, due to the high interest rate of 38% in Argentina, a huge negative impact is identified with financing model 2. Furthermore, a correlation is derived between NPV variations with an interest rate of a specific location in Figure 27. The effect of NPV change due to financial model 2 compared to model 1 is shown in Figure 26. As expected, the countries with high interest rate have shown a negative effect on NPV and countries with less and zero interest rates have shown better NPV potential, such as United States, Australia, and most of the European countries. However, due to the high interest rate of 38% in Argentina, a huge negative impact is identified with financing model 2. Furthermore, a correlation is derived between NPV variations with an interest rate of a specific location in Figure 27.

#### *4.3. Uncertainties*

In this paper, the authors acknowledge the possible uncertainties in energy performance analysis. For instance, the delivery water temperature is assumed to be 60 ◦C and 28 L DHW demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has been assumed as 80 L/m<sup>2</sup> for all locations, but since it may vary depending on the location and type of application, the resulted collector production would be slightly different in real time, but this approach has been assumed to achieve the goals of this paper.

*Buildings* **2020**, *10*, x FOR PEER REVIEW 27 of 30

**Figure 26.** NPV profit increase with financing model 2. **Figure 26.** NPV profit increase with financing model 2. **Figure 26.** NPV profit increase with financing model 2.

**Figure 27 -** Correlation of NPV potential variation with interest rate. **Figure 27 -** Correlation of NPV potential variation with interest rate. **Figure 27.** Correlation of NPV potential variation with interest rate.

*4.3. Uncertainties*  In this paper, the authors acknowledge the possible uncertainties in energy performance analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has been assumed as 80 liters/m2 for all locations, but since it may vary depending on the location and type of application, the resulted collector production would be slightly different in real time, but this approach has been assumed to achieve the goals of this paper. Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary energy price is taken as the generalized price for every specific country, whereas in the real-time case, *4.3. Uncertainties*  In this paper, the authors acknowledge the possible uncertainties in energy performance analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has been assumed as 80 liters/m2 for all locations, but since it may vary depending on the location and type of application, the resulted collector production would be slightly different in real time, but this approach has been assumed to achieve the goals of this paper. Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary energy price is taken as the generalized price for every specific country, whereas in the real-time case, Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary energy price is taken as the generalized price for every specific country, whereas in the real-time case, the energy price would be different for every state/city/municipality depending on localized energy policy. It has been considered because of the unavailability of precise data, which may not be significantly higher. The interest rate is chosen for each country for deriving the NPV potential difference between financing model 1 and model 2. However, only a few countries which have negative and zero interest rate have been assumed as 0.1%, due to the incapability of the simulation tool in accepting negative or null values. However, it has also been realized that the uncertainty of difference between the negative interest rates and assumed interest rates has not been less than 1%, which is not

the energy price would be different for every state/city/municipality depending on localized energy policy. It has been considered because of the unavailability of precise data, which may not be

the energy price would be different for every state/city/municipality depending on localized energy policy. It has been considered because of the unavailability of precise data, which may not be significantly affecting the NPV potential difference. Hence, the assumptions have been considered to achieve the aims in possible optimistic and realistic approaches irrespective of the uncertainties.
