Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

Santhan Reddy Penaka; Puneet Kumar Saini; Xingxing Zhang; Alejandro  del Amo

doi:10.3390/buildings10090148

Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

Reddy Penaka, Santhan;Kumar Saini, Puneet;Zhang, Xingxing;Amo, Alejandro del 2020-08-27 00:00:00 buildings Article Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities 1 , 2 1 , 3 1 , Santhan Reddy Penaka , Puneet Kumar Saini , Xingxing Zhang * and Alejandro del Amo Energy Technology, Dalarna University, 79188 Falun, Sweden; santhanreddypenaka@gmail.com (S.R.P.); pks@du.se (P.K.S.) Penaka Solar, 78452 Borlänge, Sweden Department of Engineering Science, Uppsala University, 75236 Uppsala, Sweden Abora Solar Company, 50196 Zaragoza, Spain; adelamo@abora-solar.com * Correspondence: xza@du.se; Tel.: +46-(0)23-77-87-89 Received: 25 June 2020; Accepted: 21 August 2020; Published: 27 August 2020 Abstract: Solar photovoltaic thermal (PVT) is an emerging technology capable of producing electrical and thermal energy using a single collector. However, to achieve larger market penetration of this technology, it is imperative to have an understanding of the energetic performance for dierent climatic conditions and the economic performance under various ﬁnancial scenarios. This paper thus presents a techno-economic evaluation of a typical water-based PVT system for a single-family house to generate electricity and domestic hot water applications in 85 locations worldwide. The simulations are performed using a validated tool with one-hour time step for output. The thermal performance of the collector is evaluated using energy utilization ratio and exergy eciency as key performance indicators, which are further visualized by the digital mapping approach. The economic performance is assessed using net present value and payback period under two ﬁnancial scenarios: (1) total system cost as a capital investment in the ﬁrst year; (2) only 25% of total system cost is a capital investment and the remaining 75% investment is considered for a ﬁnancing period with a certain interest rate. The results show that such a PVT system has better energy and exergy performance for the locations with a low annual ambient temperature and vice versa. Furthermore, it is seen that the system boundaries, such as load proﬁle, hot water storage volume, etc., can have a signiﬁcant eect on the annual energy production of the system. Economic analysis indicates that the average net present values per unit collector area are 1800 and 2200 EUR, respectively, among the 85 cities for ﬁnancial model 1 and ﬁnancial model 2. Nevertheless, from the payback period point of view, ﬁnancial model 1 is recommended for locations with high interest rate. The study is helpful to set an understanding of general factors inﬂuencing the techno-economic performance dynamics of PVT systems for various locations. Keywords: PVT; water-based PVT; techno-economic analysis; digital mapping 1. Introduction 1.1. Background and Existing Studies The concept of “electrify everything” considers solar energy as a key renewable technology with an aim of de-carbonization of domestic heating demand [1]. The rapid growth in photovoltaic (PV) installation capacity from the last few years has further strengthened the importance of PV as the main driver of renewable transformation [2]. PV remains an interesting subject area for many researchers, Buildings 2020, 10, 148; doi:10.3390/buildings10090148 www.mdpi.com/journal/buildings Buildings 2020, 10, 148 2 of 29 global leaders, and manufacturers because of its reliability, sustainability, ease of installation, and economic feasibility [3]. However, the concurrence of heat/electricity demand and limited roof area in domestic dwellings does require technologies which can generate energy eciently in both thermal and electrical form. Therefore, there is a huge potential for well-designed systems by combining both solar PV and solar thermal technologies. A relatively new commercialized concept of solar photovoltaic/thermal (PVT) technology can achieve such a goal by generating both electrical and thermal energy together using a single panel [4]. Realizing its importance, the Solar Heating and Cooling Program (SHC) of the International Energy Agency (IEA) has initiated Task 60 for PVT applications and solutions to Heating, Ventilation and Air Conditioning (HVAC) systems in buildings [5]. The task has been active from January 2018 and has built a huge knowledge base around PVT systems for its use in domestic and industrial applications. PVT systems can be categorized in several ways, however, the most common is based on the heat-transfer medium (air-based/liquid-based) used in the PVT collector [6]. The liquid-based types are dominating the current PVT market in terms of the number of installations due to high eciency, and ease of integration in existing hydronic systems [7]. In a standard liquid-based PVT collector, the heat carrier is usually water or brine mixture, which is allowed to circulate in a heat exchanger behind the PV cells. The circulation results in a heat transfer through the back sheet of the module, which raises the ﬂuid temperature enough to use for various applications such as, e.g., hot water and swimming pool heating. From a technical perspective, PVT technology is well developed, and it can be coupled with various energy systems. For instance, it can go hand-in-hand with the emerging awareness of heat pump technology with/without borehole storage [8]. However, the current main barriers in PVT development and deployment are lack of testing standards, uncertain ﬁnancial incentives, and business models across dierent regions in a niche market. Therefore, the business potential of PVT solution has not been fully explored, although it can be a very ecient solution for domestic and industrial heating requirements. There are several studies concerning the techno-economic analysis of PVT collectors with a focus on the component and system design [4,9–12]. The most common way is to assess the energetic performance ﬁrstly and then carry out an economic evaluation based on dependent variables [4,9,10,12–16]. The prevalent energy performance indexes are energy eciency and exergy eciencies [6] while the most popular economic indicators are represented by levelized cost of energy (LCOE), net present value (NPV), and payback period [4]. To name a few studies for technical evaluation, Fudholi et al. [13] investigated electrical and thermal performances on PVT water-based collectors by testing with speciﬁc inputs parameters ranging from 500 to 800 W/m solar irradiance and mass ﬂow rate of 0.011 to 0.041 kg/s. The test concluded that absorber performed better at a mass ﬂow rate of 0.041 kg/s and under 800 W/m irradiance, with a measured PV eciency of 13.8%, thermal eciency of 54.6%, and overall collector eciency of 68.4% [13]. Shah and Srinivasa [17] developed a theoretical model using COMSOL multi-physics validation tool with standard test conditions (STC) to measure the PV improved eciency when it is integrated with hybrid PVT system. Another study performed by Buonomano [18] developed a numerical model to conduct the technical and economic analysis of PVT collectors and compared it with conventional PV collectors installed in Italy. The tool was validated using TRNSYS platform for the energetic and economic performance of systems integrated with PV and PVT collectors together. Yazdanpanahi [19] presented a numerical simulation and experimental validation for evaluation of PVT exergy performance using a one-dimensional steady thermal model and a four-parameter current–voltage model for a PVT water collector. In terms of economic studies, Gu et al. [4] developed an analytical model on basis of combinations of Monte Carlo method to analyze techno-economic performances of solar PVT concentrator for Swedish climates, which considered several essential input uncertainties whereas economic variables were initially assessed. The developed 2 2 model has expressed results for capital cost range between 4482 and 5378 SEK/m for 10.37 m system cost during the system lifespan of 25 years. The paper results indicated an LCOE of 1.27 SEK/kWh and NPV of 18,812 SEK with a simple payback period of 10 years. It was concluded that the most Buildings 2020, 10, 148 3 of 29 important sensitivity factor is average daily solar irradiation followed by debt to equity ratio, capital price, regional heating price, and discount rate. Herrando et al. [20] performed techno-economic analysis of hybrid PVT systems for electricity and domestic hot water (DHW) demand for a typical house in London and concluded that such systems can meet 51% of electricity demand and 36% of DHW demand even during low solar global horizontal irradiation (GHI) and ambient temperatures. In the economic aspect, it was also concluded that hybrid PVT technology has better energy yield per unit roof area, which can result in attractive NPV for investor while mitigating the CO emissions. Riggs et al. [10] developed a combined LCOE techno-economic model for dierent types of hybrid PVT systems applied for process heat application in the United States. The sensitivity analysis of parameters aecting the levelized cost of heat (LCOH) was determined using technical, ﬁnancial, and site-speciﬁc variables. Ahn et al. [21] studied the importance of energy demands, solar energy resources, and economic performances of hybrid PVT systems at dierent PV penetration levels using Monte Carlo method, whereas the study found that irrespective of PV penetration levels, the uncertainties in energy demands and solar irradiance can inﬂuence the energy performance of PVT systems. Heck et al. [22] conducted Monte Carlo method for LCOE based on probability distribution, which concluded that this method provides more realistic information on risk/uncertainty, which triggers more scope of potential investment on electricity generation. However, author defended that the method is slightly complex to use point values. There is more literature available regarding PVT techno-economic performance than what is presented in this study. However, most of the existing studies focused on a single climate, with a straightforward economic–ﬁnancial analysis. Furthermore, complicated procedures or individual software (e.g., TRNSYS, Polysun) are used to estimate the performance of PVT collectors, which require detailed modelling skills, and higher computation time. There is a lack of a comprehensive simulation of PVT techno-economic performance through a common tool over a large geographic area, aiming for application feasibility and business potentials. Moreover, many studies have reported the solar energy resource potential of buildings at dierent spatial scales using digital mapping methods, such as digital numerical maps [23], digital surface model [24], satellite imageries and geographic information systems [25,26], and multi-scale uncertainty-aware ranking of dierent urban locations [27], which provide direct evaluations for solar application, leading to robust planning decisions. Nevertheless, no study has yet been found for mapping of techno-economic performance of PVT systems. As a result, this paper aims to ﬁll this research gap by utilizing a validated simulation tool to perform a comprehensive techno-economic performance simulation for a wide range of cities. The results are further analyzed and visualized using a digital numerical mapping approach to establish a comparison among various regions. 1.2. Aim and Objectives This study aims at simulation and mapping of the energetic and economic indicators of a typical PVT system over dierent regions to establish a digital performance database for various key performance indicators (KPIs). The economic feasibility of the PVT collector is obtained and compared under various ﬁnancial scenario models. The data obtained from simulations are used to establish a simple correlation between variables aecting the PVT system. The main objectives of this paper are to: (1) Assess the thermal and electrical performance of a typical PVT system [6] in 85 large geographical cities using a validated simulation tool. (2) Evaluate the economic performance using NPV and payback period using two ﬁnancial scenarios. (3) Analysis and visualization of energy and economic performance. The signiﬁcance of this paper lies in (1) understanding of typical PVT components behavior at the system level and (2) mapping of the collector energetic and economic performance for dierent Buildings 2020, 10, 148 4 of 29 Buildings 2020, 10, x FOR PEER REVIEW 4 of 30 climatic conditions across the world. This research results would reﬂect the concrete developments in this subject area and help the promotion of potential markets, e.g., discovering the economic feasibility feasibility of the PVT system and feasible financial solutions to the PVT system in different regions. of the PVT system and feasible ﬁnancial solutions to the PVT system in dierent regions. This paper This paper evaluates the related business benefits of a typical PVT system, which would help to evaluates the related business beneﬁts of a typical PVT system, which would help to develop a develop a database as repository of PVT performances in different regions and contexts. The research database as repository of PVT performances in dierent regions and contexts. The research results results will be useful for researchers, planners, and policymakers to further evaluate PVT potentials will be useful for researchers, planners, and policymakers to further evaluate PVT potentials in a in a net-zero/positive-energy district towards energy surplus and climate neutrality. net-zero/positive-energy district towards energy surplus and climate neutrality. 2. System Description and Research Methodology 2. System Description and Research Methodology 2.1. Water-Based PVT Collector 2.1. Water-Based PVT Collector Among the different types of PVT technology, the water-based PVT is the most common one Among the dierent types of PVT technology, the water-based PVT is the most common one that that has great possibilities for system integration [28]. This PVT collector type is structured similarly has great possibilities for system integration [28]. This PVT collector type is structured similarly to to the typical flat-plate collector, as shown in Figure 1. It is a sandwiched structure comprising several the typical ﬂat-plate collector, as shown in Figure 1. It is a sandwiched structure comprising several layers, including a glass cover placed on the top, a layer of PV cells or a commercial PV lamination layers, including a glass cover placed on the top, a layer of PV cells or a commercial PV lamination laid beneath the cover with a small air gap in between, heat-exchanging tubes or flowing channels laid beneath the cover with a small air gap in between, heat-exchanging tubes or ﬂowing channels through the absorber and closely adhered to the PV layer, and a thermally insulated layer located through the absorber and closely adhered to the PV layer, and a thermally insulated layer located right below the flow channels. All layers are fixed into a framed module using adequate clamps and right below the ﬂow channels. All layers are ﬁxed into a framed module using adequate clamps and connections. In the heat-exchanging tubes, water is the most commonly used heat carrier medium connections. In the heat-exchanging tubes, water is the most commonly used heat carrier medium due due to high specific heat capacity and ease of availability. The glass cover is often optional depending to high speciﬁc heat capacity and ease of availability. The glass cover is often optional depending on on the system design priority for the type of output required (i.e., electricity or heat). The glass cover the system design priority for the type of output required (i.e., electricity or heat). The glass cover helps to reduce heat convection losses, but it also causes high solar reflectance losses and thus lowers helps to reduce heat convection losses, but it also causes high solar reﬂectance losses and thus lowers optical efficiency. In many cases, the glass cover is used when higher heat output is expected, while optical eciency. In many cases, the glass cover is used when higher heat output is expected, while it it is removed when the system is optimized for higher electrical output. is removed when the system is optimized for higher electrical output. The electrical efficiency of PV cells increases when the pumped cooled water flows across the The electrical eciency of PV cells increases when the pumped cooled water ﬂows across rigid series or parallel tubes. The flow control is an important factor to achieve overall high the rigid series or parallel tubes. The ﬂow control is an important factor to achieve overall high performance of the PVT collectors [29]. In addition to electricity production, hot water is generated performance of the PVT collectors [29]. In addition to electricity production, hot water is generated by by absorbing extra heat from the PV layer, which can be used for several applications. The electrical absorbing extra heat from the PV layer, which can be used for several applications. The electrical and and thermal efficiencies of PVT generally depend on the PV cell type, fluid temperature, fluid flow thermal eciencies of PVT generally depend on the PV cell type, ﬂuid temperature, ﬂuid ﬂow rate, rate, flow channel size/configuration, and ambient climatic conditions. The collector energetic ﬂow channel size/conﬁguration, and ambient climatic conditions. The collector energetic performance performance can be measured in terms of energy utilization ratio and exergy efficiency [19]. can be measured in terms of energy utilization ratio and exergy eciency [19]. Figure 1. Schematic cross-section of a covered ﬂat-plate photovoltaic thermal (PVT) collector [30]. Figure 1. Schematic cross-section of a covered flat-plate photovoltaic thermal (PVT) collector [30]. This paper will focus on a typical PVT collector developed by a Spanish manufacturer named This paper will focus on a typical PVT collector developed by a Spanish manufacturer named Abora solar. The collector is available on the market, and more than 5700 m of the gross collector is Abora solar. The collector is available on the market, and more than 5700 m of the gross collector is installed for a broad range of applications. The collector is a covered PVT type with an additional layer installed for a broad range of applications. The collector is a covered PVT type with an additional of glass on the top of the collector (in addition to a glass layer for PV cells) to reduce the heat convection layer of glass on the top of the collector (in addition to a glass layer for PV cells) to reduce the heat convection losses. The rated power of the collector is 365 W at standard test conditions (STC) with a Buildings 2020, 10, 148 5 of 29 losses. The rated power of the collector is 365 W at standard test conditions (STC) with a collector area of 1.96 m consisting of 72 monocrystalline cells. The main speciﬁcations and characteristics of analyzed PVT collector are shown in Table 1. Table 1. Speciﬁcations and characteristics of the modeled PVT collector. Parameter Description Length width thickness 1970 mm 995 mm 107 mm Gross collector area 1.96 m Number of PV cells 72 Cell type Monocrystalline Rated power 365 Wp Electric eciency at STC 17% Thermal eciency at STC 70% Temperature coecient of PV 0.41%/ C Thermal eciency at zero mean temperature 0.7 Coecient of thermal losses, a 5.98 W/m K 2 2 Coecient of thermal losses, a 0.021 W/m K Internal water volume 1.78 L 2.2. Key Performance Indicators The performance of such PVT collectors is evaluated using standard key performance indicators. The performance of a collector over a speciﬁed period can be quantiﬁed using the energy utilization ratio ( ), which is deﬁned as below [31]: Output energy Output energy electrical thermal = + (1) GHI collector area GHI collector area 2 2 where GHI is global horizontal irradiation (kWh/m ), and the collector area is in m . However, the exergy value of both electricity and heat is dierent. Electricity can be regarded as pure exergy whereas heat contains some exergy value. To account for this, “energy” is replaced by “exergy”, which has the drawback of being somewhat less intuitive. The overall exergy eciency takes into account the dierence of energy grades between heat and electricity and involves a conversion of low-grade thermal energy into the equivalent high-grade electrical energy using the theory of the Carnot cycle. The overall exergy of the PVT (" ) . is deﬁned as following expression: " = + . (2) e c th el Carnot eciency (%) is deﬁned in the following Equation (3) in = 1 (3) out where , T , and T are thermal eciency, electrical eciency, outlet ﬂuid temperature, and th el, out in inlet ﬂuid temperature, respectively. NPV is deﬁned as a measurement of cumulative proﬁt calculated by subtracting the present values of cash outﬂows (including initial cost) from the present values of cash inﬂows over the PVT collector ’s lifetime. In this paper, we use NPV to evaluate a single investment to evaluate the acceptability of the project [4]. A positive NPV indicates that the projected earnings generated by a project or investment, exceed the anticipated costs. In general, an investment with a positive NPV will be a proﬁtable one, and the higher NPV means higher beneﬁts. This concept is the basis for the NPV decision rule, which dictates that the only investments that should be made are those with positive NPV values. NPV is calculated using Equation (4) as below: n1 CF NPV = C (4) (1 + r) t=0 Buildings 2020, 10, 148 6 of 29 Buildings 2020, 10, x FOR PEER REVIEW 6 of 30 Where, CFt, r, n, t, and are the cash flow of particular year (SEK), discount rate, number of years, where, CF , r, n, t, and C . are the cash ﬂow of particular year (SEK), discount rate, number of years, t 0 year of NPV evaluation, and capital cost, respectively. year of NPV evaluation, and capital cost, respectively. The payback period is the time for a project to break even or recover its initial investment funds, The payback period is the time for a project to break even or recover its initial investment funds, where the cash flow starts to turn positive and can be given as in Equation (5). where the cash ﬂow starts to turn positive and can be given as in Equation (5). (5) ( ) PP = T (5) (CF >0) 2.3. Research Methodology 2.3. Research Methodology The The simu simulation lationis is ca carried rriedusing using aa va validated lidated t tool ooldeveloped developed by the manufacturer by the manufacturer of of the studie the studiedd PVT collector. The Abora hybrid simulation tool [32] was used to map the performance across 85 PVT collector. The Abora hybrid simulation tool [32] was used to map the performance across 85 cities shown cities shown in Figurin Figur e 2. The e cities 2. The cities we were chosen re chos based on en b population ased on population density and density and geographicalgeogr coordinates aphical coordinates in different countries to represent a large market potential in these regions. A large in dierent countries to represent a large market potential in these regions. A large number of selected locations number o for f se analysis lected locat are concentrated ions for analy within sis are con Europe, centr with ated w limited ithin locations Europe, wit in h India, limitU ed nited locatStates, ions in India, United States, and Australia. The selection of locations is also restricted due to the availability and Australia. The selection of locations is also restricted due to the availability of weather and GHI of weather and GHI data in the simulation tool. The simulation tool accepts a wide range of design data in the simulation tool. The simulation tool accepts a wide range of design and ﬁnancial input and financial input parameters, e.g., location and weather resources, electrical and thermal demands, parameters, e.g., location and weather resources, electrical and thermal demands, local energy taris, local energy tariffs, specific storage volume, PVT panel and installation parameters, interest rate and speciﬁc storage volume, PVT panel and installation parameters, interest rate and ﬁnancing period, financing period, etc. The complete list of various inputs used is shown in Table 2. The performance etc. The complete list of various inputs used is shown in Table 2. The performance model used in model used in the tool for evaluation of PVT performance is validated in [24], where a heat pump the tool for evaluation of PVT performance is validated in [24], where a heat pump system integrated system integrated with 25 PVT modules was monitored, and measurements were also compared with with 25 PVT modules was monitored, and measurements were also compared with the dynamic the dynamic simulation model built in TRNSYS for Zaragoza, Spain. This model has observed simulation model built in TRNSYS for Zaragoza, Spain. This model has observed thermal and electrical thermal and electrical performance of collectors is accurate with measured data (4.2% deviation), performance of collectors is accurate with measured data (4.2% deviation), however, a slightly higher however, a slightly higher deviation in heat pump performance was noted due to limitations in the deviation in heat pump performance was noted due to limitations in the black-box model of the heat black-box model of the heat pump in the studied energy system. pump in the studied energy system. Figure 2. The simulated locations for techno-economic analysis. Figure 2. The simulated locations for techno-economic analysis. This paper further applies the digital numerical map approach based on heat maps to visualize the performance of various indicators across simulated locations. The simulation results for all locations are exported to Microsoft Excel for calculations of energy and exergy eciency [33]. After this, the results are visualized using QGIS tool, which provides a heat map rendering to design point layer data with a kernel density estimation processing algorithm [34]. Initially, a parametric study of the components at system level is considered according to the operation ﬂow of the simulation tool indicated in the ﬂow chart shown in Figure 3. Then, the simulations are carried with deﬁned boundary conditions and the Buildings 2020, 10, x FOR PEER REVIEW 7 of 30 Table 2. Technical and economic input parameters. Technical Parameters Economic Input Parameters Type of application (domestic/industrial) Type of mounting structure Type of demand (hot water/space heating) Type of inverter Type of auxiliary system Material profit margin Operation and maintenance Number of bedrooms margin Pricing of all system DHW temperature components Dwellings occupancy Annual maintenance cost Buildings 2020, 10, 148 7 of 29 Number of collectors Electricity price increment Collector tilt Auxiliary fuel price increment results are represented subsequently as monthly electrical and thermal performances, energy savings, Collector azimuth Financing period models economic parameters such as NPV, and payback period. Storage tank volume Interest rate Meteorological parameters (irradiation/ambient Table 2. Technical and economic input parameters. Opening interest rate temperature/albedo, etc.) Technical Parameters Economic Input Parameters Shadow loss percentage Type of application (domestic/industrial) Type of mounting structure Number of additional PV panels Type of demand (hot water/space heating) Type of inverter Type of auxiliary system Material proﬁt margin This paper further applies the digital numerical map approach based on heat maps to visualize Number of bedrooms Operation and maintenance margin the performance of various indicators across simulated locations. The simulation results for all DHW temperature Pricing of all system components locations are exported tDwellings o Microso occupancy ft Excel for calculations of energy and Annual exergy maintenance efficiency [33]. After cost Number of collectors Electricity price increment this, the results are visualized using QGIS tool, which provides a heat map rendering to design point Collector tilt Auxiliary fuel price increment layer data with a kernel density estimation processing algorithm [34]. Initially, a parametric study of Collector azimuth Financing period models the components at system level is considered according to the operation flow of the simulation tool Storage tank volume Interest rate indic Meteor ated ological in the flow parameters chart (irradiation shown in /ambient Figure 3 temperatur . Then, the e/ simulations albedo, etc.) are carrOpening ied withinter defined boundar est rate y Shadow loss percentage conditions and the results are represented subsequently as monthly electrical and thermal Number of additional PV panels performances, energy savings, economic parameters such as NPV, and payback period. Figure Figure 3. 3. Operation Operation flow ﬂow of th of the e simulation simulation to tool. ol. This paper also considers the economic performance of the collector in two dierent ﬁnancial This paper also considers the economic performance of the collector in two different financial models, which are described below: models, which are described below: Model 1: The total system cost is invested in the ﬁrst year. • Model 1: The total system cost is invested in the first year. • Model Model 2: 2: Onl Only y 25% 25% o of f t total otal syst system em co cost st is is a a c capital apital inve investment stment and and t the he rem remaining aining 7 75% 5% invest investment ment is considered with the financing period with a certain interest rate. is considered with the ﬁnancing period with a certain interest rate. The economic analysis results highlight the economic parameters, such as NPV and payback The economic analysis results highlight the economic parameters, such as NPV and payback period per unit collector area, for all locations. Furthermore, the uncertainty and sensitivity period per unit collector area, for all locations. Furthermore, the uncertainty and sensitivity parameters parameters are discussed, and the strategy in decision-making for investing in PVT technology is are discussed, and the strategy in decision-making for investing in PVT technology is recommended. recommended. The digital mapping method is applied to compile and format the techno-economic The digital mapping method is applied to compile and format the techno-economic performance data into a virtual image, which aims to produce a general map with KPIs of such a PVT system that gives appropriate representations of the dedicated areas. 3. Simulation Tool and Boundary Conditions 3.1. Location and Detailed Demand Analysis The simulation tool considers the Meteonorm [35] weather database to determine solar and meteorological resources, such as GHI, ambient temp, and wind speed. The thermal and electrical demands change with dierent categories of buildings, i.e., single and multifamily houses, tertiary buildings (such as hospitals, hotels, and gyms, etc.), and can be selected individually within the tool interface. Speciﬁc key parameters are included, such as load proﬁles, the current auxiliary source of Buildings 2020, 10, 148 8 of 29 electricity, and energy system details. The simulation engine assesses the total monthly and annual total demand depending on inputs for each application. The monthly energy load (L) needed to raise the temperature of supply water to the desired hot water temperature is calculated using Equation (6): L = m C N (T T ) (6) p d s where ‘m’ indicates the amount of hot water required per person in a day (in liters), ‘C ’ is the speciﬁc heat capacity (J/kgK), ‘N’ is several days in a month (days), ‘T ’ is desired water temperature ( C), and ‘T ’ cold supply water temperature in ( C). The monthly demand can also be customized based on consumer utilization in that speciﬁc month. For a single-family house, the amount of DHW for one person in a day is considered as 28 L/person/day at 100% occupancy. The demand is kept constant to minimize the variables in the overall system and, thus, to have a fair comparison of collector performance for various locations. The fraction of occupancy can be parameterized to meet the speciﬁc thermal demand for the individual location. For tertiary buildings (such as industrial applications), tools consider a dierent consumption depending on process characteristics. This simulation tool oers to choose an auxiliary heating system to meet the load demand. This tool also accommodates for the fact that the total collector electricity generation can be utilized for self-consumption or if there is excess electrical energy, it can be sold to the electricity grid in the context of a positive-energy building. 3.2. System Variables This simulation tool consists of several PVT collectors and also recommends the number of collectors that would be required based on optimization of total demand and the storage tank capacity. The speciﬁc volume capacity (v/a), which is ratio of tank volume (liter) to collector gross area (m ) can be changed depending on the number of storage duration hours. The shading loss fraction on PVT modules can be adjusted manually. There is the provision to integrate PV and PVT collectors in a scenario if the thermal demand is ﬁrst fully met by PVT modules, and electrical demand is not fully covered. 3.3. Working Principle of the Simulation Tool The simulation tool also optimizes the collector and installation parameters based on the demand, availability, and metrological conditions for a particular location. Simulation results highlight essential parameters such as GHI, irradiation on a tilted surface, thermal demand, thermal production, thermal solar coverage, electrical production, total electric and thermal savings, and environmental impact. The maximum power point P (in kW) generated by the PV cells is obtained using Equation (7) depending on the global irradiation on the surface of the module G (W/m ), ambient temperature T ( C), cell temperature T ( C), nominal power of photovoltaic collector P (kW), G irradiance under c n STC 2 2 STC (W/m ), i.e., 1000 W/m , and the temperature variation coecient of power ( ) (%/ C) [36]. P = P (1 (T 25)) (7) m n c STC The cell temperature T is linked to the temperature of the absorber plate, which is dependent on the temperature of ﬂuid going in and out of the module. Cell temperature is calculated for each simulation time step based on inlet and outlet temperatures, and electrical output is then calculated depending on the temperature coecient of the module. The instantaneous thermal eciency of the collector is calculated based on Equation (8) 0 1 B (T T ) C T T m a m a B C B C = a a B C (8) o 2 th 1 @ A G G where is optical eciency, a is ﬁrst order heat loss coecient (W/m K), a is the second order heat o 1 2 2 2 loss coecient (W/m K ), T is the average ﬂuid temperature ( C), and T is ambient temperature m a Buildings 2020, 10, 148 9 of 29 ( C). The various characteristics of the simulated module are listed in Table 1 and are validated by real measurements as explained in [25]. The temperature leaving the PVT module T is determined using Equation (9) m C T = T + (9) th where T , m, and C . represents inlet temperature ( C), ﬂuid mass ﬂow rate (kg/s), and ﬂuid speciﬁc i p heat (kJ/kgK), respectively. Thermal solar coverage (T ) is calculated using Equation (10) in this solar simulation tool Total collector thermal production (kWh) T (%) = 100. (10) solar Total thermal demand (kWh) 3.4. System Pricing and Optimization 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: The total system cost is invested in the ﬁrst year as a capital investment. The 100% of total system cost can be invested in several years with monthly payment at a certain open and ﬁxed interest rate. The 75% of total system cost can be invested in several years with monthly payment at a certain open and ﬁxed interest rate and the remaining 25% of total system cost is to be invested initially as capital investment. 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 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. Parameter Description Type of application Single-family house Type of demand Electricity demand and thermal demand for DHW Auxiliary system Electrical heater Auxiliary system energy price This is selected individually for each location No. of people in house 5 DHW temperature 60° PVT Collector model aH72SK No. of collectors 1 Specific volume capacity 80 liters/m Selected optimally based on a parametric study for Inclination maximum energy production Type of mounting structure Tilted Type of inverter Single-phase inverter Assumed that no maintenance is required for a single Annual maintenance cost collector to reduce uncertainties Electricity and combustible price 6% per year is assumed for all the location increment System lifetime 25 years Interest rate Selected appropriately for each location Buildings 2020, 10, 148 10 of 29 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. Parameter Description Type of application Single-family house Type of demand Electricity demand and thermal demand for DHW Auxiliary system Electrical heater Auxiliary system energy price This is selected individually for each location No. of people in house 5 DHW temperature 60 PVT Collector model aH72SK No. of collectors 1 Speciﬁc volume capacity 80 L/m Selected optimally based on a parametric study for maximum Inclination energy production Type of mounting structure Tilted Type of inverter Single-phase inverter Assumed that no maintenance is required for a single collector Annual maintenance cost to reduce uncertainties Electricity and combustible price increment 6% per year is assumed for all the location System lifetime 25 years Interest rate Selected appropriately for each location Initially, the energy performance of the PVT system is simulated in 85 dierent locations using the simulation tool. In order to discover and compare the collector energy performance in dierent locations, the thermal demand is maintained the same in all selected locations. Therefore, the simulated system considers a single PVT collector (1.96 m ), 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 eect 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 dierence 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 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 Buildings 2020, 10, x FOR PEER REVIEW 11 of 30 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 ), 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 Buildings 2020, 10, 148 11 of 29 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 PVT modules is fed to a heat sink (air/water heat exchanger), and this spilled energy from the collector production. The specific volume capacity is assumed 80 liters/m for all the locations which is is not counted as part of useful energy output. equivalent to total 150 liters of storage tank capacity. Figure 5. Thermal and electrical system configurations. Figure 5. Thermal and electrical system conﬁgurations. In the proposed simp In the electrical system lifie conﬁguration, d energy systethe m, PVT generated collector i DCspower directly will connected to the ta be converted tonk wi AC power thout any internal or external heat exchanger. The cold water from the tank enters the PVT module, using an inverter. Then, it is utilized for household purposes and the remaining will be sent to the exchange electricitys h grid, eat f wher rom t eas he a the bsorb excess er, and electricity hot wat demand er is fed to the top is taken from ofthe the ta grid nk. T connection he DHW col as shown d water in enters at bottom of the tank, and hot water leaves from top of the tank for DHW supply in the Figure 5. As the tilt angle of the PVT collector is a key parameter that will also decide the collector build production, ing. The a DHW d preliminary istribparametric ution system study and assoc is carried iated heat lo for each sse location s are not considered in to determine the the analy optimalstilt is. The maximum DHW supply temperature is set at 60 °C, and an electric auxiliary heater is provisioned angle for maximum annual collector production. in the t The ank total for period systems wh costen the ener is determined gy from using PVT variables module such s is not a module enough to cost, meet the DHW system components load. Electric heater starts and stops at the determined dead band to optimize energy consumption while cost, annual operation, and maintenance cost. The electricity and auxiliary energy price escalation is maintaining the fixed supply DHW temperature. During the periods when tank temperature exceeds assumed to be 6% per year for all the locations. Various parameters considered for economic analysis the set limit, the energy from PVT modules is fed to a heat sink (air/water heat exchanger), and this are shown in Table 4. spilled energy from the collector is not counted as part of useful energy output. Table 4. Parameters considered for economic analysis. 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 Parameter Value electricity grid, whereas the excess electricity demand is taken from the grid connection as shown in Abora PVT collector 350 EUR Figure 5. As the tilt angle of the PVT collector is a key parameter that will also decide the collector Cost for Connection kit 128 EUR production, a preliminary parametric study is carried for each location to determine the optimal tilt Tilted mounting structure 243 EUR Storage tank 1553 EUR angle for maximum annual collector production. Valve (servo meter) 127 EUR The total system cost is determined using variables such a module cost, system components cost, Flowmeter 142 EUR annual operation, and maintenance cost. The electricity and auxiliary energy price escalation is Copper tubes 19 EUR assumed to be 6% per year for all the locations. Various parameters considered for economic analysis Isolation tubes 14 EUR are shown in Table 4. Heat sink 474 EUR Microinverter 500 EUR Legal regulations 377 EUR Electricity price increment 6% annually System lifetime 25 years Electricity price Variable based on each location 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. The economic performance of the collector in two dierent ﬁnancial models is evaluated based on: Model 1: The total system cost is invested as initial capital investment in the ﬁrst year; Model 2: 25% of total system cost is capital investment and remaining 75 % is paid within ﬁnancial period of 7 years with a certain variable interest rate with every location. Buildings 2020, 10, x FOR PEER REVIEW 12 of 30 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 Electricity price Variable based on each location The payback time and NPV are estimated by considering a reference system using an electric Buildings 2020, 10, 148 12 of 29 heater. The price of electricity considered for various locations is shown in Figure 6 below. 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Figure 6. Considered electricity prices in all countries [37]. Figure 6. Considered electricity prices in all countries [37]. 4. Results and Discussion The economic performance of the collector in two different financial models is evaluated based This section details the simulation results using the digital mapping approach. Table 5 shows the on: Buildings 2020, 10, x FOR PEER REVIEW 16 of 30 inputs and results of key performance indicators for all selected locations, and the results are discussed. • Model 1: The total system cost is invested as initial capital investment in the first year; • 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 financial period of 7 years with a certain variable interest rate with every location. 4.1.1. Collector Thermal Production 4.1.1. Collector Thermal Production 4. Results and Discussion The simulated results are visualized using geospatial maps, as they provide clear indication for The simulated results are visualized using geospatial maps, as they provide clear indication for understanding This section regional details ttr hends e simul for atthermal ion result and s us electrical ing the digit output al meven apping appro in the case ach of . Table large 5 sho datasets. ws understanding regional trends for thermal and electrical output even in the case of large datasets. tFigur he input e 7 shows s and res theuvariation lts of key perf in theorman thermal ce ind output icato of rsthe for collector all select . ed locations, and the results are Figure 7 shows the variation in the thermal output of the collector. discussed. 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/m ) 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 , respectively. Similar thermal output is obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m 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 ). 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 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 collector output. Electricty price (€/kWh) Italy Portugal Spain Switzerland Sweden Denmark Finland Germany Iceland Norway Belgium Bulgaria France Greece Luxembourg Poland Romania Ukraine United kingdom China Qatar Saudi arabia Singapore India United states of America Mexico Australia Argentina Brazil Chile Colombia Algeria Egypt Morocco Buildings 2020, 10, 148 13 of 29 Table 5. All simulated data of key performance indicators. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Catania 38 1967 18 1790 487 5140 5541 Florence 44 1632 16 1520 413 4039 4451 Italy Milan 45 1233 12 1153 317 2528 2955 Rome 42 1585 17 1464 401 3797 4211 Bari 41 1824 17 1679 458 4691 5096 Lisbon 39 1939 18 1770 483 4766 5171 Portugal Porto 41 1765 16 1640 447 4246 4657 Setubal 39 1997 18 1823 495 4966 5368 Sevilla 37 2134 20 1882 520 4972 5361 Valencia 39 2043 18 1831 505 4776 5167 Zaragoza 42 2002 16 1795 498 4649 5041 Spain Barcelona 41 1904 18 1728 479 4387 4782 Lugo 43 1567 13 1464 406 3393 3798 Madrid 40 2019 15 1810 504 4709 5101 Bern 47 1335 10 1270 351 2576 3002 Davos 47 1612 4 1562 426 2863 3286 Switzerland Lausanne 47 1408 12 1329 364 2108 2539 Zurich 47 1249 10 1186 331 1648 1935 Gothenburg 58 1138 10 1073 305 1287 1726 Linkoping 58 1132 8 1061 304 1257 1697 Sweden Malmo 56 1183 9 1113 316 1424 1863 Stockholm 59 1179 8 1105 317 1407 1846 Uppsala 60 1099 8 1024 297 1142 1583 Alborg 57 1116 8 1047 298 3041 3463 Denmark Copenhagen 56 1144 10 1079 305 3195 3615 Odense 55 1102 9 1040 295 2987 3409 Helsinki 60 1160 6 1086 312 1021 1464 Finland Oulu 65 1182 4 1112 321 1104 1545 Buildings 2020, 10, 148 14 of 29 Table 5. Cont. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Berlin 53 1194 10 1128 315 4582 4988 Dortmund 52 1093 11 1037 291 4034 4446 Germany Frankfurt 50 1143 11 1078 302 4291 4701 Hamburg 54 1146 11 1091 306 4363 4772 Munich 48 1318 11 1257 345 5348 5747 Iceland Reykjavik 64 968 6 932 266 145 186 Bergen 60 926 9 875 253 576 163 Norway Oslo 60 1029 7 962 277 408 3 Trondheim 64 1166 7 1107 317 136 273 Belgium Brussels 51 1151 12 1094 306 3244 3664 Bulgaria Soﬁa 43 1335 13 1264 348 364 813 Lyon 46 1422 14 1337 368 1899 2333 Nantes 47 1408 13 1333 367 1889 2323 France Paris 49 1204 13 1134 315 1279 1718 Toulouse 44 1522 15 1437 391 2197 2628 Greece Athinai 38 1915 21 1731 474 3119 3540 Luxembourg Luxembourg 50 1194 9 1128 318 1661 2096 Krakow 50 1191 10 1126 315 868 1267 Poland Warsaw 52 1213 10 1137 320 909 1307 Bucharest 44 1589 13 1482 406 1841 2153 Romania Cluj-Napoca 47 1443 11 1365 374 1516 1831 Ukraine Kyiv 50 1330 10 1242 348 1287 1368 Glasgow 56 1097 10 1045 294 2096 2527 United Liverpool 53 1013 11 965 273 1765 2199 Kingdom London 52 1107 13 1048 294 2109 2540 China Hong Kong 22 1338 24 1251 329 461 725 Qatar Doha 25 1957 28 1715 462 1468 1168 Saudi Arabia Medina 25 2349 29 1966 540 828 401 Singapore Singapore 1 1618 27 1473 390 1461 1569 Buildings 2020, 10, 148 15 of 29 Table 5. Cont. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Bangalore 13 2093 25 1847 489 12 178 Bombay 19 1910 28 1687 445 213 21 Hyderabad 17 2005 28 1765 466 112 79 Lucknow 27 1921 27 1717 453 174 17 India New Delhi 29 2157 27 1878 505 35 224 Surat 21 2168 28 1874 500 26 215 Wadhwan 23 2159 28 1866 496 17 207 Yavatmal 20 1938 28 1715 453 179 13 Chicago 42 1564 11 1475 402 987 1432 Denver 40 1912 11 1796 483 1695 2133 Houston 30 1720 21 1582 422 1211 1655 Las Vegas 36 2278 21 1987 545 2136 2570 USA Los Angeles 34 1973 20 1808 489 1722 2161 New York 41 1597 14 1508 407 1052 1496 Portland 46 1436 12 1361 374 732 1179 San 38 1886 15 1757 478 1616 2056 Francisco Washington 39 1602 15 1510 407 1053 1497 Mexico Mexico City 20 1848 18 1727 451 342 224 Brisbane 27 1898 21 1720 452 3940 4339 Melbourne 38 1528 15 1426 371 2872 3282 Australia Perth 32 1930 19 1731 455 3990 4389 Buenos Argentina 35 1703 18 1550 406 65 2077 Aires Brazil Brasilia 16 1928 22 1762 467 1985 2197 Chile Santiago 33 1732 15 1570 411 1785 2171 Colombia Bogota 5 1560 14 1510 394 856 1107 Algeria Algiers 37 2017 18 1835 495 1027 747 Egypt Cairo 30 2009 22 1791 485 1551 1589 Morocco Rabat 34 2094 18 1907 517 1616 1950 Buildings 2020, 10, 148 16 of 29 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 ) 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 , respectively. Similar thermal output is obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m 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 ). 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 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 collector output. Buildings 2020, 10, x FOR PEER REVIEW 17 of 30 GHI Ambient temperature Linear (GHI) Linear (Ambient temperature) 300 40 –5 0 50 100 150 200 250 –50 –10 Monthly thermal production (kWh/m /month) Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature. 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 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, 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. 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 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, 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 etc. The collector performed slightly better in Spain, Portugal, and Australia, with more than 400 kWh annually. However, it shows there is no signiﬁcant dierence in thermal and electrical production 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 trends. Furthermore, a correlation of collector electrical production with GHI and ambient is developed based on all monthly points from all chosen locations and a positive correlation is realized temperature is developed based on all monthly points from all chosen locations and a positive as shown in Figure 10. A large variation in electrical output for similar values of ambient temperature correlation is realized as shown in Figure 10. A large variation in electrical output for similar values can be observed, which again shows that GHI is the critical parameter governing the electrical output of ambient temperature can be observed, which again shows that GHI is the critical parameter of the collector. governing the electrical output of the collector. Figure 9. Annual average collector electrical performance. GHI (kWh) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 17 of 30 GHI Ambient temperature Linear (GHI) Linear (Ambient temperature) 300 40 –5 0 50 100 150 200 250 –50 –10 Monthly thermal production (kWh/m /month) Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature. 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 Buildings 2020, 10, 148 17 of 29 governing the electrical output of the collector. Buildings 2020, 10, x FOR PEER REVIEW 18 of 30 Figure 9. Annual average collector electrical performance. Figure 9. Annual average collector electrical performance. 300 40 GHI Ambient temperature 150 15 –5 0 –10 0 10203040506070 Monthly electrical production (kWh/m /month) Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and ambient temperature. ambient temperature. A large variation in thermal and electrical output is seen for many countries and is reﬂected in 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 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. 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 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 GHI (kWh) GHI (kWh) Ambient temperature (°C) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 18 of 30 300 40 GHI Ambient temperature 150 15 Buildings 2020, 10, 148 18 of 29 –5 0 –10 0 10203040506070 such as Madrid, Stockholm, and Berlin. In Medina, although GHI and ambient temperatures are higher Monthly electrical production (kWh/m /month) 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 Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and tank losses will be higher as the tank temperature increases. Higher tank temperature results in lower ambient temperature. 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 A large variation in thermal and electrical output is seen for many countries and is reflected in and July months. In Stockholm, the variation between the months is signiﬁcant because of seasonal Figures 7 and 9. The range of collector output with a maximum and minimum value of thermal and variation in GHI, and the same is lower in Medina, which results in more uniform monthly production. electrical production is shown in Figure 11. Buildings 2020, 10, x FOR PEER REVIEW 19 of 30 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 Figure 11. Country-wise collector thermal performance uncertainty. Figure 11. Country-wise collector thermal performance uncertainty. results in more uniform monthly production. The trends for monthly electrical production are slightly different than thermal output. For The minimum thermal production in blue color represents the minimum production for The trends for monthly electrical production are slightly dierent than thermal output. For example, example, in Medina, electrical production is higher in July than in October even though the ambient analyzed location, while the maximum thermal production is indicated with an orange color that in Medina, electrical production is higher in July than in October even though the ambient temperature temperature is maximum in July. This is due to high GHI in July and is in line with findings that the represents the highest thermal production of a city in each country. The results show likely high is maximum in July. This is due to high GHI in July and is in line with ﬁndings that the major factor major factor influencing the electrical production is GHI, rather than ambient temperature. variation in Italy, Spain, United States, and Australia, as many cities were simulated in those inﬂuencing the electrical production is GHI, rather than ambient temperature. 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 Madrid Stockholm Berlin Medina Melbourne January April July October Figure 12. Collector monthly thermal production variation. Figure 12. Collector monthly thermal production variation. Madrid Stockholm Berlin Medina Melbourne January April July October Figure 13. Collector monthly electrical production variation. GHI (kWh) Thermal production (kWh) Electrical production (kWh) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 19 of 30 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 results in more uniform monthly production. 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. Madrid Stockholm Berlin Medina Melbourne January April July October Buildings 2020, 10, 148 19 of 29 Figure 12. Collector monthly thermal production variation. Madrid Stockholm Berlin Medina Melbourne January April July October Buildings 2020, 10, x FOR P Figure EER RE 13. VIEW Collector monthly electrical production variation. 20 of 30 Figure 13. Collector monthly electrical production variation. 4.1.3. Collector Energy Utilization Ratio 4.1.3. Collector Energy Utilization Ratio The eThe energy nergy utiliz u attiili on zat raion r tio oa fttih o of t e colh lee col ctor lfe ocrto vr for va arious lrio oca uts iolocat ns ision shs i owsn shown in Figuin F re 1i4gur . Te h e14 c. The orrela tion correlation trends between energy utilization ratio and annual average ambient temperature are trends between energy utilization ratio and annual average ambient temperature are shown in shown in Figure 15 with consideration of all selected 85 geographical locations to derive a possible Figure 15 with consideration of all selected 85 geographical locations to derive a possible trend between trend between the parameters. the parameters. Brasilia, Brazil New Delhi, India Cairo, Egypt Melbourne, Australia Chicago, USA Medina, Saudi arabia Athinai, Greece Berlin, Germany Stockholm, Sweden Davos, Switzerland Madrid, Spain Rome, Italy 50% 52% 54% 56% 58% 60% 62% 64% Energy utilization ratio Figure 14. Collector energy utilization ratio. Figure 14. Collector energy utilization ratio. Some locations show interesting results of system boundaries on PVT collector performance. 64% This can be realized by comparing the energy utilization ratio for Medina (high irradiation) and Davos 63% (low irradiation location). The energy utilization for Davos (63%) is higher compared to Medina (52.5%), 62% even though the absolute value of total energy output is higher for Medina (2506 kWh) compared 61% to Davos (1988 kWh). This is because the load demand for Medina is comparably lower, while the 60% other system design parameters remain the same (collector area, tank volume, etc.), which resulted in 59% higher average tank temp and thus lower collector eciency for Medina. Results show that the total 58% thermal demand for every location varies depending on the ambient temperature as shown in Figure 16. 57% This is because 56%of the temperature dierence between the annual average ambient temperature of each 55% 54% 53% 0 5 10 15 20 25 30 35 Ambient temperature (°C) Energy utilization ratio Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. Thermal production (kWh) Electrical production (kWh) Energy utilization ratio (%) Buildings 2020, 10, x FOR PEER REVIEW 20 of 30 4.1.3. Collector Energy Utilization Ratio 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. Brasilia, Brazil New Delhi, India Cairo, Egypt Melbourne, Australia Chicago, USA Medina, Saudi arabia Athinai, Greece Berlin, Germany Stockholm, Sweden Davos, Switzerland Madrid, Spain Rome, Italy 50% 52% 54% 56% 58% 60% 62% 64% Buildings 2020, 10, 148 20 of 29 Energy utilization ratio location and desired water temperature (assumed 60 C), which has to be covered by the collector thermal production. Figure 14. Collector energy utilization ratio. 64% 63% 62% 61% 60% Buildings 2020, 10, x FOR PEER REVIEW 21 of 30 59% 58% Some locations show interesting results of system boundaries on PVT collector performance. 57% This can be realized by comparing the energy utilization ratio for Medina (high irradiation) and Davos (low irrad 56% iation location). The energy utilization for Davos (63%) is higher compared to Medina 55% (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 54% lower, while the other system design parameters remain the same (collector area, tank volume, etc.), 53% which resulted in higher average tank temp and thus lower collector efficiency for Medina. Results 0 5 10 15 20 25 30 35 show that the total thermal demand for every location varies depending on the ambient temperature Ambient temperature (°C) as shown in Figure 16. This is because of the temperature difference between the annual average Energy utilization ratio ambient temperature of each location and desired water temperature (assumed 60 °C), which has to be covered by the collector thermal production. Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. 3,500 3,300 3,100 2,900 2,700 2,500 2,300 2,100 1,900 0 5 10 15 20 25 30 35 Annual avg. ambient temperature (˚C) Figure 16. Total thermal demand of single-family house relation with the average ambient temperature. Figure 16. Total thermal demand of single-family house relation with the average ambient 4.1.4. Collector Exergy Eciency temperature. From the Carnot eciency, it can be noted that exergy eciency is a function of inlet temperature 4.1.4. Collector Exergy Efficiency and thermal output of the collector (assumed that the desired output temperature is ﬁxed at 60 C). From the Carnot efficiency, it can be noted that exergy efficiency is a function of inlet Hence, it can be derived that locations with higher ambient temperature will result in less quality of tempera exergy and, ture thus, and therm lowera exer l output of the coll getic eciency. ector (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 Figure 17 shows the correlation of exergetic eciency with ambient temperature based on all less quality of exergy selected 85 geographical and, t locations hus, lower to derive exergetic e a possible fficien tr cy. end between the parameters. Similar trends Figure 17 shows the correlation of exergetic efficiency with ambient temperature based on all can be seen for some speciﬁc locations shown in Figure 18. It can be seen that even though the energy select eciency ed 85 of ge Madrid ographi ischigher al locatcompar ions to d ed er to ive Davos, a possi the ble exer trend between the p gy eciency of Davos aram is eters. higher Sim due ilar trends to lower can be seen for some specific locations shown in Figure 18. It can be seen that even though the energy 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. Energy utilization ratio (%) Thermal demand (kWh) Buildings 2020, 10, x FOR PEER REVIEW 22 of 30 Buildings 2020, 10, 148 21 of 29 Buildings 2020, 10, x FOR PEER REVIEW 22 of 30 25% 25% 24% 24% 23% 23% 22% 22% 21% 21% 20% 20% 19% 19% 18% 18% 17% 17% 16% 16% 15% 15% 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Ambient temperature (°C) Ambient temperature (°C) Figure 17. Correlation of exergy efficiency with the annual average ambient temperature. Figure Figure 17. 17. Correlation of Correlation of exergy effici exergy eciency ency wit with h the the annual average ambient temperature. annual average ambient temperature. Brasilia, Brazil Brasilia, Brazil New Delhi, India New Delhi, India Cairo, Egypt Cairo, Egypt Melbourne, Australia Melbourne, Australia Chicago, USA Chicago, USA Medina, Saudi arabia Medina, Saudi arabia Athinai, Greece Athinai, Greece Berlin, Germany Berlin, Germany Stockholm, Sweden Stockholm, Sweden Davos, Switzerland Davos, Switzerland Madrid, Spain Madrid, Spain Rome, Italy Rome, Italy 0% 5% 10% 15% 20% 25% 0% 5% 10% 15% 20% 25% Figure 18. Collector exegetic eciency. 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 Based on the above energy performance, the economic performance of such a PVT system is investigated in the 85 dierent 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. 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 This financing model scenario has assumed that the total cost of the system is invested in the year of the system period. As the total system cost will be invested in the ﬁrst year, the interest rate is 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 not considered. Figure 19 is the digital representation of NPV potential per unit collector area with 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 ﬁnancial model 1 in all 85 geographical cities across the world and Figure 20 shows the NPV potential 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 per unit collector area in geographical cities in the European continent. 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. Exerg Exerg etic efficiency etic efficiency (%) (%) Buildings 2020, 10, 148 22 of 29 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 The cities with larger dots represent the high NPV potential and cities with smaller dots size 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 represents the least NPV potential. The cities Catania and Munich have the highest potential of 5140 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, and 5348 EUR, respectively, followed by the cities Bari, Lisbon, Setubal, Sevilla, Valencia, Zaragoza, 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 Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due to to their high available GHI and electricity grid price, so the energy savings are high in these locations to their high available GHI and electricity grid price, so the energy savings are high in these locations 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., which is reflected in huge NPV potential for this system. Cities such as Oslo, Bergen, Reykjavik, etc., 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. with relatively less electricity grid price resulted in having negative NPV due to lower available GHI. 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 The cities with high collector production such as Medina, Algeria, and Cairo have shown negative The cities with high collector production such as Medina, Algeria, and Cairo have shown negative NPV NPV potential due to a much lower electricity grid price which eventually showed fewer energy NPV potential due to a much lower electricity grid price which eventually showed fewer energy potential due to a much lower electricity grid price which eventually showed fewer energy savings. savings. savings. The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the 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 appropriate countries to define the NPV range per unit collector area of each country as shown in Buildings 2020, 10, 148 23 of 29 The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the Buildings 2020, 10, x FOR PEER REVIEW 24 of 30 appropriate countries to deﬁne the NPV range per unit collector area of each country as shown in 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 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 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 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 as China, Argentina, Brazil, etc., because only one city has been simulated in this paper, which is part of the key uncertainty. of the key uncertainty. of the key uncertainty. 12,000 12,000 NPV minimum NPV maximum NPV minimum NPV maximum 10,000 10,000 8,000 8,000 6,000 6,000 4,000 4,000 2,000 2,000 –2000 –2000 –4000 –4000 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. Figure 22 shows the payback period of this PVT system for a single-family house of 5 people in Figure 22 shows the payback period of this PVT system for a single-family house of 5 people 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 in several countries based on ﬁnancial model 1. The results show that the total system cost will be 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, returned in the ﬁrst 10 years in countries such as Australia, Belgium, Denmark, Germany, Greece, 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 Italy, Portugal, Spain, Switzerland, etc. This is due to high collector production and high electricity 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 grid price. Although countries such as Algeria, Saudi Arabia, and Egypt have the highest collector 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 production, product the ion, t grid he grid price price is comparatively is comparatively lower lower, wh , which ich reflects th reﬂects the e payb payback ack pe period riod of more t of morh ean 20 than years. 20 years. 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. NPV (Euros) NPV (Euros) Italy Portugal Italy Spain Portugal Switzerland Spain Sweden Switzerland Denmark Sweden Finland Denmark Germany Finland Iceland Germany Norway Iceland Belgium Norway Bulgaria Belgium France Bulgaria Greece France Luxemburg Greece Poland Luxemburg Romania Poland Ukraine Romania United kingdom Ukraine China United kingdom Qatar China Saudi arabia Qatar Singapore Saudi arabia India Singapore USA India Mexico USA Australia Mexico Argentina Australia Brazil Argentina Chile Brazil Colombia Chile Algeria Colombia Egypt Algeria Morocco Egypt Morocco Buildings 2020, 10, 148 24 of 29 Buildings 2020, 10, x FOR PEER REVIEW 25 of 30 Buildings 2020, 10, x FOR PEER REVIEW 25 of 30 4.2.2. Collector Economic Performance in Financing Model 2 4.2.2. Collector Economic Performance in Financing Model 2 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 This financing model has been analyzed by assuming that 75% of total system cost is paid within a ﬁnancing This fin period ancinof g model has b 7 years with een an a certain alyzed inter by assum est rate and ing tth ha att 7 the 5%r o emaining f total sys25% tem c of os total t is psystem aid with cost in a financing period of 7 years with a certain interest rate and that the remaining 25% of total system a financing period of 7 years with a certain interest rate and that the remaining 25% of total system is invested in the ﬁrst year without any interest rate. The NPV potential per unit collector area with cost is invested in the first year without any interest rate. The NPV potential per unit collector area cost is invested in the first year without any interest rate. The NPV potential per unit collector area ﬁnancing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV potential with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV per unit collector area in a speciﬁc European continent is shown in Figure 24. potential per unit collector area in a specific European continent is shown in Figure 24. potential per unit collector area in a specific European continent is shown in Figure 24. 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. Buildings 2020, 10, 148 25 of 29 Buildings 2020, 10, x FOR PEER REVIEW 26 of 30 The cities with larger dots represent the high NPV potential cities and those with smaller dots 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, 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, 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 were because of the almost zero interest rates in those countries. This is because if the interest rate is is zero, the user needs to pay part of the system cost in later years, and the present value of this 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 investment will be lower due to the time value of money. This will reduce the accumulated and thus higher NPV. However, if the interest rate is high, the extra amount paid due to high interest investment and thus higher NPV. However, if the interest rate is high, the extra amount paid due to in later years will overweigh the advantage due to the time value of money, and it will decrease the high interest in later years will overweigh the advantage due to the time value of money, and it will overall NPV. Therefore, ﬁnancial model 1 is recommended for countries with a high interest rate to decrease the overall NPV. Therefore, financial model 1 is recommended for countries with a high maximize the NPV and minimize the payback. Meanwhile, ﬁnancial model 2 is recommended for interest rate to maximize the NPV and minimize the payback. Meanwhile, financial model 2 is countries with zero or lower interest rates to maximize the NPV. recommended for countries with zero or lower interest rates to maximize the NPV. Figure 25 shows the NPV potential per unit collector area in each country for the ﬁnancing model 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 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. countries. Thus, not much variation has been identified in model 2 compared with model 1. 12,000 NPV minimum NPV maximum 10,000 8,000 6,000 4,000 2,000 –2000 –4000 –6000 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 eect of NPV change due to ﬁnancial model 2 compared to model 1 is shown in Figure 26. 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 eect on NPV and countries 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, 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 and most of the European countries. However, due to the high interest rate of 38% in Argentina, a negative impact is identiﬁed with ﬁnancing model 2. Furthermore, a correlation is derived between huge negative impact is identified with financing model 2. Furthermore, a correlation is derived NPV variations with an interest rate of a speciﬁc location in Figure 27. 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 for all locations, but since it may vary depending on the location and type of application, the resulted collector production would be slightly dierent in real time, but this approach has been assumed to achieve the goals of this paper. NPV (Euros) Buildings 2020, 10, 148 26 of 29 Buildings 2020, 10, x FOR PEER REVIEW 27 of 30 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. 1,000 1,000 Interst rate Linear (Interst rate) Interst rate Linear (Interst rate) –500 –500 –1000 –1000 –1500 –1500 –2000 –2000 –2500 –2500 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Interest rate Interest rate (%) (%) Figure 27. Correlation of NPV potential variation with interest rate. Figure 27 - Figure 27 - Correlation of Correlation of NP NP V potential V potential variation with variation with inte interest rate. rest rate. Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary 4.3. Uncertainties 4.3. Uncertainties energy price is taken as the generalized price for every speciﬁc country, whereas in the real-time In this paper, the authors acknowledge the possible uncertainties in energy performance In this paper, the authors acknowledge the possible uncertainties in energy performance case, the energy price would be dierent for every state/city/municipality depending on localized analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW energy policy. It has been considered because of the unavailability of precise data, which may not demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has be signiﬁcantly higher. The interest rate is chosen for each country for deriving the NPV potential been assumed as 80 liters/m 2 for all locations, but since it may vary depending on the location and been assumed as 80 liters/m for all locations, but since it may vary depending on the location and dierence between ﬁnancing model 1 and model 2. However, only a few countries which have negative type of application, the resulted collector production would be slightly different in real time, but this type of application, the resulted collector production would be slightly different in real time, but this and zero interest rate have been assumed as 0.1%, due to the incapability of the simulation tool in approach has been assumed to achieve the goals of this paper. approach has been assumed to achieve the goals of this paper. accepting negative or null values. However, it has also been realized that the uncertainty of dierence Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary between the negative interest rates and assumed interest rates has not been less than 1%, which is not energy price is taken as the generalized price for every specific country, whereas in the real-time case, 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 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 policy. It has been considered because of the unavailability of precise data, which may not be NPV (Euros) NPV (Euros) Buildings 2020, 10, 148 27 of 29 signiﬁcantly aecting the NPV potential dierence. Hence, the assumptions have been considered to achieve the aims in possible optimistic and realistic approaches irrespective of the uncertainties. 5. Conclusions The performance of a solar PVT consists of PVT collector and storage tank is evaluated for 85 locations across large cities. The optimal tilt angle of the PVT collector, load demand, and electricity prices are chosen appropriately for each simulated location. The results show that the major parameter inﬂuencing the PVT performance is GHI, and results derived a strong linear correlation between collector output and GHI. The other factor inﬂuencing energetic performance is ambient temperature, source, and load water temperatures. The energetic utilization ratio is dependent on total thermal demand and speciﬁc volume ratio (v/a ratio) as it can have a major inﬂuence on the ﬂuid temperature in the storage tank and, thus, collector total production. The electrical production by PVT collector is higher in high ambient temperature locations. The highest and lowest energy utilization ratio of the collector is recorded in Reykjavik, Iceland (63%), and Medina, Saudi Arabia (54%), respectively. The highest and lowest exergetic eciency of the collector has been recorded in Reykjavik, Iceland (23%), and Medina, Saudi Arabia (17%), respectively. Most importantly, the results show that the higher energetic output does not guarantee high economic feasibility. There are several factors such as electricity price, interest rate, and selection of ﬁnancial model which can highly aect the economic feasibility of PVT collector. The average NPV per unit collector area of 85 geographical cities for ﬁnancial model 1 and ﬁnancial model 2 is 1886 and 2221 EUR, respectively. The NPV and payback period analysis of the PVT system has shown positive results for the cities, which have high collector production and high electricity grid price reﬂecting high energy savings. However, the ﬁnancing model 1 is highly recommended for the locations with high interest rates and ﬁnancial model 2 is beneﬁcial for the locations with less interest rates. This paper oers potential insights into the promotion of the PVT market in dierent regions. Author Contributions: S.R.P. worked on simulation, analysis, and writing. X.Z. contributed to supervision, concept development, structuring, and writing. P.K.S. contributed to simulation, analysis, and writing. A.d.A. dedicated eorts to simulation and analysis. All authors have read and agreed to the published version of the manuscript. Funding: This research received funding from the Germany–Sweden joint project: ‘Product and process development for the preparing and realization of complete buildings of various types of use using energy ecient, partially energy independent lightweight construction solutions, ENSECO’. Acknowledgments: The authors acknowledge the useful gains from the IEA SHC Task 60, and the open access support from Dalarna University, Sweden. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Sommerfeldt, N.; Madani, H. In-depth techno-economic analysis of PV/Thermal plus ground source and heat pump systems for multi-family houses in a heating dominated climate. Sol. Energy 2019, 190, 44–62. [CrossRef] 2. Joshi, S.; Dhoble, A.S. Photovoltaic -Thermal systems (PVT): Technology review and future trends. Renew. Sustain. Energy Rev. 2018, 92, 848–882. [CrossRef] 3. Al-Waeli, A.H.; Sopian, K.; Kazem, H.A.; Chaichan, M.T. 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Abstract

buildings Article Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities 1 , 2 1 , 3 1 , Santhan Reddy Penaka , Puneet Kumar Saini , Xingxing Zhang * and Alejandro del Amo Energy Technology, Dalarna University, 79188 Falun, Sweden; santhanreddypenaka@gmail.com (S.R.P.); pks@du.se (P.K.S.) Penaka Solar, 78452 Borlänge, Sweden Department of Engineering Science, Uppsala University, 75236 Uppsala, Sweden Abora Solar Company, 50196 Zaragoza, Spain; adelamo@abora-solar.com * Correspondence: xza@du.se; Tel.: +46-(0)23-77-87-89 Received: 25 June 2020; Accepted: 21 August 2020; Published: 27 August 2020 Abstract: Solar photovoltaic thermal (PVT) is an emerging technology capable of producing electrical and thermal energy using a single collector. However, to achieve larger market penetration of this technology, it is imperative to have an understanding of the energetic performance for dierent climatic conditions and the economic performance under various ﬁnancial scenarios. This paper thus presents a techno-economic evaluation of a typical water-based PVT system for a single-family house to generate electricity and domestic hot water applications in 85 locations worldwide. The simulations are performed using a validated tool with one-hour time step for output. The thermal performance of the collector is evaluated using energy utilization ratio and exergy eciency as key performance indicators, which are further visualized by the digital mapping approach. The economic performance is assessed using net present value and payback period under two ﬁnancial scenarios: (1) total system cost as a capital investment in the ﬁrst year; (2) only 25% of total system cost is a capital investment and the remaining 75% investment is considered for a ﬁnancing period with a certain interest rate. The results show that such a PVT system has better energy and exergy performance for the locations with a low annual ambient temperature and vice versa. Furthermore, it is seen that the system boundaries, such as load proﬁle, hot water storage volume, etc., can have a signiﬁcant eect on the annual energy production of the system. Economic analysis indicates that the average net present values per unit collector area are 1800 and 2200 EUR, respectively, among the 85 cities for ﬁnancial model 1 and ﬁnancial model 2. Nevertheless, from the payback period point of view, ﬁnancial model 1 is recommended for locations with high interest rate. The study is helpful to set an understanding of general factors inﬂuencing the techno-economic performance dynamics of PVT systems for various locations. Keywords: PVT; water-based PVT; techno-economic analysis; digital mapping 1. Introduction 1.1. Background and Existing Studies The concept of “electrify everything” considers solar energy as a key renewable technology with an aim of de-carbonization of domestic heating demand [1]. The rapid growth in photovoltaic (PV) installation capacity from the last few years has further strengthened the importance of PV as the main driver of renewable transformation [2]. PV remains an interesting subject area for many researchers, Buildings 2020, 10, 148; doi:10.3390/buildings10090148 www.mdpi.com/journal/buildings Buildings 2020, 10, 148 2 of 29 global leaders, and manufacturers because of its reliability, sustainability, ease of installation, and economic feasibility [3]. However, the concurrence of heat/electricity demand and limited roof area in domestic dwellings does require technologies which can generate energy eciently in both thermal and electrical form. Therefore, there is a huge potential for well-designed systems by combining both solar PV and solar thermal technologies. A relatively new commercialized concept of solar photovoltaic/thermal (PVT) technology can achieve such a goal by generating both electrical and thermal energy together using a single panel [4]. Realizing its importance, the Solar Heating and Cooling Program (SHC) of the International Energy Agency (IEA) has initiated Task 60 for PVT applications and solutions to Heating, Ventilation and Air Conditioning (HVAC) systems in buildings [5]. The task has been active from January 2018 and has built a huge knowledge base around PVT systems for its use in domestic and industrial applications. PVT systems can be categorized in several ways, however, the most common is based on the heat-transfer medium (air-based/liquid-based) used in the PVT collector [6]. The liquid-based types are dominating the current PVT market in terms of the number of installations due to high eciency, and ease of integration in existing hydronic systems [7]. In a standard liquid-based PVT collector, the heat carrier is usually water or brine mixture, which is allowed to circulate in a heat exchanger behind the PV cells. The circulation results in a heat transfer through the back sheet of the module, which raises the ﬂuid temperature enough to use for various applications such as, e.g., hot water and swimming pool heating. From a technical perspective, PVT technology is well developed, and it can be coupled with various energy systems. For instance, it can go hand-in-hand with the emerging awareness of heat pump technology with/without borehole storage [8]. However, the current main barriers in PVT development and deployment are lack of testing standards, uncertain ﬁnancial incentives, and business models across dierent regions in a niche market. Therefore, the business potential of PVT solution has not been fully explored, although it can be a very ecient solution for domestic and industrial heating requirements. There are several studies concerning the techno-economic analysis of PVT collectors with a focus on the component and system design [4,9–12]. The most common way is to assess the energetic performance ﬁrstly and then carry out an economic evaluation based on dependent variables [4,9,10,12–16]. The prevalent energy performance indexes are energy eciency and exergy eciencies [6] while the most popular economic indicators are represented by levelized cost of energy (LCOE), net present value (NPV), and payback period [4]. To name a few studies for technical evaluation, Fudholi et al. [13] investigated electrical and thermal performances on PVT water-based collectors by testing with speciﬁc inputs parameters ranging from 500 to 800 W/m solar irradiance and mass ﬂow rate of 0.011 to 0.041 kg/s. The test concluded that absorber performed better at a mass ﬂow rate of 0.041 kg/s and under 800 W/m irradiance, with a measured PV eciency of 13.8%, thermal eciency of 54.6%, and overall collector eciency of 68.4% [13]. Shah and Srinivasa [17] developed a theoretical model using COMSOL multi-physics validation tool with standard test conditions (STC) to measure the PV improved eciency when it is integrated with hybrid PVT system. Another study performed by Buonomano [18] developed a numerical model to conduct the technical and economic analysis of PVT collectors and compared it with conventional PV collectors installed in Italy. The tool was validated using TRNSYS platform for the energetic and economic performance of systems integrated with PV and PVT collectors together. Yazdanpanahi [19] presented a numerical simulation and experimental validation for evaluation of PVT exergy performance using a one-dimensional steady thermal model and a four-parameter current–voltage model for a PVT water collector. In terms of economic studies, Gu et al. [4] developed an analytical model on basis of combinations of Monte Carlo method to analyze techno-economic performances of solar PVT concentrator for Swedish climates, which considered several essential input uncertainties whereas economic variables were initially assessed. The developed 2 2 model has expressed results for capital cost range between 4482 and 5378 SEK/m for 10.37 m system cost during the system lifespan of 25 years. The paper results indicated an LCOE of 1.27 SEK/kWh and NPV of 18,812 SEK with a simple payback period of 10 years. It was concluded that the most Buildings 2020, 10, 148 3 of 29 important sensitivity factor is average daily solar irradiation followed by debt to equity ratio, capital price, regional heating price, and discount rate. Herrando et al. [20] performed techno-economic analysis of hybrid PVT systems for electricity and domestic hot water (DHW) demand for a typical house in London and concluded that such systems can meet 51% of electricity demand and 36% of DHW demand even during low solar global horizontal irradiation (GHI) and ambient temperatures. In the economic aspect, it was also concluded that hybrid PVT technology has better energy yield per unit roof area, which can result in attractive NPV for investor while mitigating the CO emissions. Riggs et al. [10] developed a combined LCOE techno-economic model for dierent types of hybrid PVT systems applied for process heat application in the United States. The sensitivity analysis of parameters aecting the levelized cost of heat (LCOH) was determined using technical, ﬁnancial, and site-speciﬁc variables. Ahn et al. [21] studied the importance of energy demands, solar energy resources, and economic performances of hybrid PVT systems at dierent PV penetration levels using Monte Carlo method, whereas the study found that irrespective of PV penetration levels, the uncertainties in energy demands and solar irradiance can inﬂuence the energy performance of PVT systems. Heck et al. [22] conducted Monte Carlo method for LCOE based on probability distribution, which concluded that this method provides more realistic information on risk/uncertainty, which triggers more scope of potential investment on electricity generation. However, author defended that the method is slightly complex to use point values. There is more literature available regarding PVT techno-economic performance than what is presented in this study. However, most of the existing studies focused on a single climate, with a straightforward economic–ﬁnancial analysis. Furthermore, complicated procedures or individual software (e.g., TRNSYS, Polysun) are used to estimate the performance of PVT collectors, which require detailed modelling skills, and higher computation time. There is a lack of a comprehensive simulation of PVT techno-economic performance through a common tool over a large geographic area, aiming for application feasibility and business potentials. Moreover, many studies have reported the solar energy resource potential of buildings at dierent spatial scales using digital mapping methods, such as digital numerical maps [23], digital surface model [24], satellite imageries and geographic information systems [25,26], and multi-scale uncertainty-aware ranking of dierent urban locations [27], which provide direct evaluations for solar application, leading to robust planning decisions. Nevertheless, no study has yet been found for mapping of techno-economic performance of PVT systems. As a result, this paper aims to ﬁll this research gap by utilizing a validated simulation tool to perform a comprehensive techno-economic performance simulation for a wide range of cities. The results are further analyzed and visualized using a digital numerical mapping approach to establish a comparison among various regions. 1.2. Aim and Objectives This study aims at simulation and mapping of the energetic and economic indicators of a typical PVT system over dierent regions to establish a digital performance database for various key performance indicators (KPIs). The economic feasibility of the PVT collector is obtained and compared under various ﬁnancial scenario models. The data obtained from simulations are used to establish a simple correlation between variables aecting the PVT system. The main objectives of this paper are to: (1) Assess the thermal and electrical performance of a typical PVT system [6] in 85 large geographical cities using a validated simulation tool. (2) Evaluate the economic performance using NPV and payback period using two ﬁnancial scenarios. (3) Analysis and visualization of energy and economic performance. The signiﬁcance of this paper lies in (1) understanding of typical PVT components behavior at the system level and (2) mapping of the collector energetic and economic performance for dierent Buildings 2020, 10, 148 4 of 29 Buildings 2020, 10, x FOR PEER REVIEW 4 of 30 climatic conditions across the world. This research results would reﬂect the concrete developments in this subject area and help the promotion of potential markets, e.g., discovering the economic feasibility feasibility of the PVT system and feasible financial solutions to the PVT system in different regions. of the PVT system and feasible ﬁnancial solutions to the PVT system in dierent regions. This paper This paper evaluates the related business benefits of a typical PVT system, which would help to evaluates the related business beneﬁts of a typical PVT system, which would help to develop a develop a database as repository of PVT performances in different regions and contexts. The research database as repository of PVT performances in dierent regions and contexts. The research results results will be useful for researchers, planners, and policymakers to further evaluate PVT potentials will be useful for researchers, planners, and policymakers to further evaluate PVT potentials in a in a net-zero/positive-energy district towards energy surplus and climate neutrality. net-zero/positive-energy district towards energy surplus and climate neutrality. 2. System Description and Research Methodology 2. System Description and Research Methodology 2.1. Water-Based PVT Collector 2.1. Water-Based PVT Collector Among the different types of PVT technology, the water-based PVT is the most common one Among the dierent types of PVT technology, the water-based PVT is the most common one that that has great possibilities for system integration [28]. This PVT collector type is structured similarly has great possibilities for system integration [28]. This PVT collector type is structured similarly to to the typical flat-plate collector, as shown in Figure 1. It is a sandwiched structure comprising several the typical ﬂat-plate collector, as shown in Figure 1. It is a sandwiched structure comprising several layers, including a glass cover placed on the top, a layer of PV cells or a commercial PV lamination layers, including a glass cover placed on the top, a layer of PV cells or a commercial PV lamination laid beneath the cover with a small air gap in between, heat-exchanging tubes or flowing channels laid beneath the cover with a small air gap in between, heat-exchanging tubes or ﬂowing channels through the absorber and closely adhered to the PV layer, and a thermally insulated layer located through the absorber and closely adhered to the PV layer, and a thermally insulated layer located right below the flow channels. All layers are fixed into a framed module using adequate clamps and right below the ﬂow channels. All layers are ﬁxed into a framed module using adequate clamps and connections. In the heat-exchanging tubes, water is the most commonly used heat carrier medium connections. In the heat-exchanging tubes, water is the most commonly used heat carrier medium due due to high specific heat capacity and ease of availability. The glass cover is often optional depending to high speciﬁc heat capacity and ease of availability. The glass cover is often optional depending on on the system design priority for the type of output required (i.e., electricity or heat). The glass cover the system design priority for the type of output required (i.e., electricity or heat). The glass cover helps to reduce heat convection losses, but it also causes high solar reflectance losses and thus lowers helps to reduce heat convection losses, but it also causes high solar reﬂectance losses and thus lowers optical efficiency. In many cases, the glass cover is used when higher heat output is expected, while optical eciency. In many cases, the glass cover is used when higher heat output is expected, while it it is removed when the system is optimized for higher electrical output. is removed when the system is optimized for higher electrical output. The electrical efficiency of PV cells increases when the pumped cooled water flows across the The electrical eciency of PV cells increases when the pumped cooled water ﬂows across rigid series or parallel tubes. The flow control is an important factor to achieve overall high the rigid series or parallel tubes. The ﬂow control is an important factor to achieve overall high performance of the PVT collectors [29]. In addition to electricity production, hot water is generated performance of the PVT collectors [29]. In addition to electricity production, hot water is generated by by absorbing extra heat from the PV layer, which can be used for several applications. The electrical absorbing extra heat from the PV layer, which can be used for several applications. The electrical and and thermal efficiencies of PVT generally depend on the PV cell type, fluid temperature, fluid flow thermal eciencies of PVT generally depend on the PV cell type, ﬂuid temperature, ﬂuid ﬂow rate, rate, flow channel size/configuration, and ambient climatic conditions. The collector energetic ﬂow channel size/conﬁguration, and ambient climatic conditions. The collector energetic performance performance can be measured in terms of energy utilization ratio and exergy efficiency [19]. can be measured in terms of energy utilization ratio and exergy eciency [19]. Figure 1. Schematic cross-section of a covered ﬂat-plate photovoltaic thermal (PVT) collector [30]. Figure 1. Schematic cross-section of a covered flat-plate photovoltaic thermal (PVT) collector [30]. This paper will focus on a typical PVT collector developed by a Spanish manufacturer named This paper will focus on a typical PVT collector developed by a Spanish manufacturer named Abora solar. The collector is available on the market, and more than 5700 m of the gross collector is Abora solar. The collector is available on the market, and more than 5700 m of the gross collector is installed for a broad range of applications. The collector is a covered PVT type with an additional layer installed for a broad range of applications. The collector is a covered PVT type with an additional of glass on the top of the collector (in addition to a glass layer for PV cells) to reduce the heat convection layer of glass on the top of the collector (in addition to a glass layer for PV cells) to reduce the heat convection losses. The rated power of the collector is 365 W at standard test conditions (STC) with a Buildings 2020, 10, 148 5 of 29 losses. The rated power of the collector is 365 W at standard test conditions (STC) with a collector area of 1.96 m consisting of 72 monocrystalline cells. The main speciﬁcations and characteristics of analyzed PVT collector are shown in Table 1. Table 1. Speciﬁcations and characteristics of the modeled PVT collector. Parameter Description Length width thickness 1970 mm 995 mm 107 mm Gross collector area 1.96 m Number of PV cells 72 Cell type Monocrystalline Rated power 365 Wp Electric eciency at STC 17% Thermal eciency at STC 70% Temperature coecient of PV 0.41%/ C Thermal eciency at zero mean temperature 0.7 Coecient of thermal losses, a 5.98 W/m K 2 2 Coecient of thermal losses, a 0.021 W/m K Internal water volume 1.78 L 2.2. Key Performance Indicators The performance of such PVT collectors is evaluated using standard key performance indicators. The performance of a collector over a speciﬁed period can be quantiﬁed using the energy utilization ratio ( ), which is deﬁned as below [31]: Output energy Output energy electrical thermal = + (1) GHI collector area GHI collector area 2 2 where GHI is global horizontal irradiation (kWh/m ), and the collector area is in m . However, the exergy value of both electricity and heat is dierent. Electricity can be regarded as pure exergy whereas heat contains some exergy value. To account for this, “energy” is replaced by “exergy”, which has the drawback of being somewhat less intuitive. The overall exergy eciency takes into account the dierence of energy grades between heat and electricity and involves a conversion of low-grade thermal energy into the equivalent high-grade electrical energy using the theory of the Carnot cycle. The overall exergy of the PVT (" ) . is deﬁned as following expression: " = + . (2) e c th el Carnot eciency (%) is deﬁned in the following Equation (3) in = 1 (3) out where , T , and T are thermal eciency, electrical eciency, outlet ﬂuid temperature, and th el, out in inlet ﬂuid temperature, respectively. NPV is deﬁned as a measurement of cumulative proﬁt calculated by subtracting the present values of cash outﬂows (including initial cost) from the present values of cash inﬂows over the PVT collector ’s lifetime. In this paper, we use NPV to evaluate a single investment to evaluate the acceptability of the project [4]. A positive NPV indicates that the projected earnings generated by a project or investment, exceed the anticipated costs. In general, an investment with a positive NPV will be a proﬁtable one, and the higher NPV means higher beneﬁts. This concept is the basis for the NPV decision rule, which dictates that the only investments that should be made are those with positive NPV values. NPV is calculated using Equation (4) as below: n1 CF NPV = C (4) (1 + r) t=0 Buildings 2020, 10, 148 6 of 29 Buildings 2020, 10, x FOR PEER REVIEW 6 of 30 Where, CFt, r, n, t, and are the cash flow of particular year (SEK), discount rate, number of years, where, CF , r, n, t, and C . are the cash ﬂow of particular year (SEK), discount rate, number of years, t 0 year of NPV evaluation, and capital cost, respectively. year of NPV evaluation, and capital cost, respectively. The payback period is the time for a project to break even or recover its initial investment funds, The payback period is the time for a project to break even or recover its initial investment funds, where the cash flow starts to turn positive and can be given as in Equation (5). where the cash ﬂow starts to turn positive and can be given as in Equation (5). (5) ( ) PP = T (5) (CF >0) 2.3. Research Methodology 2.3. Research Methodology The The simu simulation lationis is ca carried rriedusing using aa va validated lidated t tool ooldeveloped developed by the manufacturer by the manufacturer of of the studie the studiedd PVT collector. The Abora hybrid simulation tool [32] was used to map the performance across 85 PVT collector. The Abora hybrid simulation tool [32] was used to map the performance across 85 cities shown cities shown in Figurin Figur e 2. The e cities 2. The cities we were chosen re chos based on en b population ased on population density and density and geographicalgeogr coordinates aphical coordinates in different countries to represent a large market potential in these regions. A large in dierent countries to represent a large market potential in these regions. A large number of selected locations number o for f se analysis lected locat are concentrated ions for analy within sis are con Europe, centr with ated w limited ithin locations Europe, wit in h India, limitU ed nited locatStates, ions in India, United States, and Australia. The selection of locations is also restricted due to the availability and Australia. The selection of locations is also restricted due to the availability of weather and GHI of weather and GHI data in the simulation tool. The simulation tool accepts a wide range of design data in the simulation tool. The simulation tool accepts a wide range of design and ﬁnancial input and financial input parameters, e.g., location and weather resources, electrical and thermal demands, parameters, e.g., location and weather resources, electrical and thermal demands, local energy taris, local energy tariffs, specific storage volume, PVT panel and installation parameters, interest rate and speciﬁc storage volume, PVT panel and installation parameters, interest rate and ﬁnancing period, financing period, etc. The complete list of various inputs used is shown in Table 2. The performance etc. The complete list of various inputs used is shown in Table 2. The performance model used in model used in the tool for evaluation of PVT performance is validated in [24], where a heat pump the tool for evaluation of PVT performance is validated in [24], where a heat pump system integrated system integrated with 25 PVT modules was monitored, and measurements were also compared with with 25 PVT modules was monitored, and measurements were also compared with the dynamic the dynamic simulation model built in TRNSYS for Zaragoza, Spain. This model has observed simulation model built in TRNSYS for Zaragoza, Spain. This model has observed thermal and electrical thermal and electrical performance of collectors is accurate with measured data (4.2% deviation), performance of collectors is accurate with measured data (4.2% deviation), however, a slightly higher however, a slightly higher deviation in heat pump performance was noted due to limitations in the deviation in heat pump performance was noted due to limitations in the black-box model of the heat black-box model of the heat pump in the studied energy system. pump in the studied energy system. Figure 2. The simulated locations for techno-economic analysis. Figure 2. The simulated locations for techno-economic analysis. This paper further applies the digital numerical map approach based on heat maps to visualize the performance of various indicators across simulated locations. The simulation results for all locations are exported to Microsoft Excel for calculations of energy and exergy eciency [33]. After this, the results are visualized using QGIS tool, which provides a heat map rendering to design point layer data with a kernel density estimation processing algorithm [34]. Initially, a parametric study of the components at system level is considered according to the operation ﬂow of the simulation tool indicated in the ﬂow chart shown in Figure 3. Then, the simulations are carried with deﬁned boundary conditions and the Buildings 2020, 10, x FOR PEER REVIEW 7 of 30 Table 2. Technical and economic input parameters. Technical Parameters Economic Input Parameters Type of application (domestic/industrial) Type of mounting structure Type of demand (hot water/space heating) Type of inverter Type of auxiliary system Material profit margin Operation and maintenance Number of bedrooms margin Pricing of all system DHW temperature components Dwellings occupancy Annual maintenance cost Buildings 2020, 10, 148 7 of 29 Number of collectors Electricity price increment Collector tilt Auxiliary fuel price increment results are represented subsequently as monthly electrical and thermal performances, energy savings, Collector azimuth Financing period models economic parameters such as NPV, and payback period. Storage tank volume Interest rate Meteorological parameters (irradiation/ambient Table 2. Technical and economic input parameters. Opening interest rate temperature/albedo, etc.) Technical Parameters Economic Input Parameters Shadow loss percentage Type of application (domestic/industrial) Type of mounting structure Number of additional PV panels Type of demand (hot water/space heating) Type of inverter Type of auxiliary system Material proﬁt margin This paper further applies the digital numerical map approach based on heat maps to visualize Number of bedrooms Operation and maintenance margin the performance of various indicators across simulated locations. The simulation results for all DHW temperature Pricing of all system components locations are exported tDwellings o Microso occupancy ft Excel for calculations of energy and Annual exergy maintenance efficiency [33]. After cost Number of collectors Electricity price increment this, the results are visualized using QGIS tool, which provides a heat map rendering to design point Collector tilt Auxiliary fuel price increment layer data with a kernel density estimation processing algorithm [34]. Initially, a parametric study of Collector azimuth Financing period models the components at system level is considered according to the operation flow of the simulation tool Storage tank volume Interest rate indic Meteor ated ological in the flow parameters chart (irradiation shown in /ambient Figure 3 temperatur . Then, the e/ simulations albedo, etc.) are carrOpening ied withinter defined boundar est rate y Shadow loss percentage conditions and the results are represented subsequently as monthly electrical and thermal Number of additional PV panels performances, energy savings, economic parameters such as NPV, and payback period. Figure Figure 3. 3. Operation Operation flow ﬂow of th of the e simulation simulation to tool. ol. This paper also considers the economic performance of the collector in two dierent ﬁnancial This paper also considers the economic performance of the collector in two different financial models, which are described below: models, which are described below: Model 1: The total system cost is invested in the ﬁrst year. • Model 1: The total system cost is invested in the first year. • Model Model 2: 2: Onl Only y 25% 25% o of f t total otal syst system em co cost st is is a a c capital apital inve investment stment and and t the he rem remaining aining 7 75% 5% invest investment ment is considered with the financing period with a certain interest rate. is considered with the ﬁnancing period with a certain interest rate. The economic analysis results highlight the economic parameters, such as NPV and payback The economic analysis results highlight the economic parameters, such as NPV and payback period per unit collector area, for all locations. Furthermore, the uncertainty and sensitivity period per unit collector area, for all locations. Furthermore, the uncertainty and sensitivity parameters parameters are discussed, and the strategy in decision-making for investing in PVT technology is are discussed, and the strategy in decision-making for investing in PVT technology is recommended. recommended. The digital mapping method is applied to compile and format the techno-economic The digital mapping method is applied to compile and format the techno-economic performance data into a virtual image, which aims to produce a general map with KPIs of such a PVT system that gives appropriate representations of the dedicated areas. 3. Simulation Tool and Boundary Conditions 3.1. Location and Detailed Demand Analysis The simulation tool considers the Meteonorm [35] weather database to determine solar and meteorological resources, such as GHI, ambient temp, and wind speed. The thermal and electrical demands change with dierent categories of buildings, i.e., single and multifamily houses, tertiary buildings (such as hospitals, hotels, and gyms, etc.), and can be selected individually within the tool interface. Speciﬁc key parameters are included, such as load proﬁles, the current auxiliary source of Buildings 2020, 10, 148 8 of 29 electricity, and energy system details. The simulation engine assesses the total monthly and annual total demand depending on inputs for each application. The monthly energy load (L) needed to raise the temperature of supply water to the desired hot water temperature is calculated using Equation (6): L = m C N (T T ) (6) p d s where ‘m’ indicates the amount of hot water required per person in a day (in liters), ‘C ’ is the speciﬁc heat capacity (J/kgK), ‘N’ is several days in a month (days), ‘T ’ is desired water temperature ( C), and ‘T ’ cold supply water temperature in ( C). The monthly demand can also be customized based on consumer utilization in that speciﬁc month. For a single-family house, the amount of DHW for one person in a day is considered as 28 L/person/day at 100% occupancy. The demand is kept constant to minimize the variables in the overall system and, thus, to have a fair comparison of collector performance for various locations. The fraction of occupancy can be parameterized to meet the speciﬁc thermal demand for the individual location. For tertiary buildings (such as industrial applications), tools consider a dierent consumption depending on process characteristics. This simulation tool oers to choose an auxiliary heating system to meet the load demand. This tool also accommodates for the fact that the total collector electricity generation can be utilized for self-consumption or if there is excess electrical energy, it can be sold to the electricity grid in the context of a positive-energy building. 3.2. System Variables This simulation tool consists of several PVT collectors and also recommends the number of collectors that would be required based on optimization of total demand and the storage tank capacity. The speciﬁc volume capacity (v/a), which is ratio of tank volume (liter) to collector gross area (m ) can be changed depending on the number of storage duration hours. The shading loss fraction on PVT modules can be adjusted manually. There is the provision to integrate PV and PVT collectors in a scenario if the thermal demand is ﬁrst fully met by PVT modules, and electrical demand is not fully covered. 3.3. Working Principle of the Simulation Tool The simulation tool also optimizes the collector and installation parameters based on the demand, availability, and metrological conditions for a particular location. Simulation results highlight essential parameters such as GHI, irradiation on a tilted surface, thermal demand, thermal production, thermal solar coverage, electrical production, total electric and thermal savings, and environmental impact. The maximum power point P (in kW) generated by the PV cells is obtained using Equation (7) depending on the global irradiation on the surface of the module G (W/m ), ambient temperature T ( C), cell temperature T ( C), nominal power of photovoltaic collector P (kW), G irradiance under c n STC 2 2 STC (W/m ), i.e., 1000 W/m , and the temperature variation coecient of power ( ) (%/ C) [36]. P = P (1 (T 25)) (7) m n c STC The cell temperature T is linked to the temperature of the absorber plate, which is dependent on the temperature of ﬂuid going in and out of the module. Cell temperature is calculated for each simulation time step based on inlet and outlet temperatures, and electrical output is then calculated depending on the temperature coecient of the module. The instantaneous thermal eciency of the collector is calculated based on Equation (8) 0 1 B (T T ) C T T m a m a B C B C = a a B C (8) o 2 th 1 @ A G G where is optical eciency, a is ﬁrst order heat loss coecient (W/m K), a is the second order heat o 1 2 2 2 loss coecient (W/m K ), T is the average ﬂuid temperature ( C), and T is ambient temperature m a Buildings 2020, 10, 148 9 of 29 ( C). The various characteristics of the simulated module are listed in Table 1 and are validated by real measurements as explained in [25]. The temperature leaving the PVT module T is determined using Equation (9) m C T = T + (9) th where T , m, and C . represents inlet temperature ( C), ﬂuid mass ﬂow rate (kg/s), and ﬂuid speciﬁc i p heat (kJ/kgK), respectively. Thermal solar coverage (T ) is calculated using Equation (10) in this solar simulation tool Total collector thermal production (kWh) T (%) = 100. (10) solar Total thermal demand (kWh) 3.4. System Pricing and Optimization 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: The total system cost is invested in the ﬁrst year as a capital investment. The 100% of total system cost can be invested in several years with monthly payment at a certain open and ﬁxed interest rate. The 75% of total system cost can be invested in several years with monthly payment at a certain open and ﬁxed interest rate and the remaining 25% of total system cost is to be invested initially as capital investment. 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 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. Parameter Description Type of application Single-family house Type of demand Electricity demand and thermal demand for DHW Auxiliary system Electrical heater Auxiliary system energy price This is selected individually for each location No. of people in house 5 DHW temperature 60° PVT Collector model aH72SK No. of collectors 1 Specific volume capacity 80 liters/m Selected optimally based on a parametric study for Inclination maximum energy production Type of mounting structure Tilted Type of inverter Single-phase inverter Assumed that no maintenance is required for a single Annual maintenance cost collector to reduce uncertainties Electricity and combustible price 6% per year is assumed for all the location increment System lifetime 25 years Interest rate Selected appropriately for each location Buildings 2020, 10, 148 10 of 29 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. Parameter Description Type of application Single-family house Type of demand Electricity demand and thermal demand for DHW Auxiliary system Electrical heater Auxiliary system energy price This is selected individually for each location No. of people in house 5 DHW temperature 60 PVT Collector model aH72SK No. of collectors 1 Speciﬁc volume capacity 80 L/m Selected optimally based on a parametric study for maximum Inclination energy production Type of mounting structure Tilted Type of inverter Single-phase inverter Assumed that no maintenance is required for a single collector Annual maintenance cost to reduce uncertainties Electricity and combustible price increment 6% per year is assumed for all the location System lifetime 25 years Interest rate Selected appropriately for each location Initially, the energy performance of the PVT system is simulated in 85 dierent locations using the simulation tool. In order to discover and compare the collector energy performance in dierent locations, the thermal demand is maintained the same in all selected locations. Therefore, the simulated system considers a single PVT collector (1.96 m ), 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 eect 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 dierence 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 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 Buildings 2020, 10, x FOR PEER REVIEW 11 of 30 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 ), 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 Buildings 2020, 10, 148 11 of 29 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 PVT modules is fed to a heat sink (air/water heat exchanger), and this spilled energy from the collector production. The specific volume capacity is assumed 80 liters/m for all the locations which is is not counted as part of useful energy output. equivalent to total 150 liters of storage tank capacity. Figure 5. Thermal and electrical system configurations. Figure 5. Thermal and electrical system conﬁgurations. In the proposed simp In the electrical system lifie conﬁguration, d energy systethe m, PVT generated collector i DCspower directly will connected to the ta be converted tonk wi AC power thout any internal or external heat exchanger. The cold water from the tank enters the PVT module, using an inverter. Then, it is utilized for household purposes and the remaining will be sent to the exchange electricitys h grid, eat f wher rom t eas he a the bsorb excess er, and electricity hot wat demand er is fed to the top is taken from ofthe the ta grid nk. T connection he DHW col as shown d water in enters at bottom of the tank, and hot water leaves from top of the tank for DHW supply in the Figure 5. As the tilt angle of the PVT collector is a key parameter that will also decide the collector build production, ing. The a DHW d preliminary istribparametric ution system study and assoc is carried iated heat lo for each sse location s are not considered in to determine the the analy optimalstilt is. The maximum DHW supply temperature is set at 60 °C, and an electric auxiliary heater is provisioned angle for maximum annual collector production. in the t The ank total for period systems wh costen the ener is determined gy from using PVT variables module such s is not a module enough to cost, meet the DHW system components load. Electric heater starts and stops at the determined dead band to optimize energy consumption while cost, annual operation, and maintenance cost. The electricity and auxiliary energy price escalation is maintaining the fixed supply DHW temperature. During the periods when tank temperature exceeds assumed to be 6% per year for all the locations. Various parameters considered for economic analysis the set limit, the energy from PVT modules is fed to a heat sink (air/water heat exchanger), and this are shown in Table 4. spilled energy from the collector is not counted as part of useful energy output. Table 4. Parameters considered for economic analysis. 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 Parameter Value electricity grid, whereas the excess electricity demand is taken from the grid connection as shown in Abora PVT collector 350 EUR Figure 5. As the tilt angle of the PVT collector is a key parameter that will also decide the collector Cost for Connection kit 128 EUR production, a preliminary parametric study is carried for each location to determine the optimal tilt Tilted mounting structure 243 EUR Storage tank 1553 EUR angle for maximum annual collector production. Valve (servo meter) 127 EUR The total system cost is determined using variables such a module cost, system components cost, Flowmeter 142 EUR annual operation, and maintenance cost. The electricity and auxiliary energy price escalation is Copper tubes 19 EUR assumed to be 6% per year for all the locations. Various parameters considered for economic analysis Isolation tubes 14 EUR are shown in Table 4. Heat sink 474 EUR Microinverter 500 EUR Legal regulations 377 EUR Electricity price increment 6% annually System lifetime 25 years Electricity price Variable based on each location 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. The economic performance of the collector in two dierent ﬁnancial models is evaluated based on: Model 1: The total system cost is invested as initial capital investment in the ﬁrst year; Model 2: 25% of total system cost is capital investment and remaining 75 % is paid within ﬁnancial period of 7 years with a certain variable interest rate with every location. Buildings 2020, 10, x FOR PEER REVIEW 12 of 30 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 Electricity price Variable based on each location The payback time and NPV are estimated by considering a reference system using an electric Buildings 2020, 10, 148 12 of 29 heater. The price of electricity considered for various locations is shown in Figure 6 below. 0.35 0.3 0.25 0.2 0.15 0.1 0.05 Figure 6. Considered electricity prices in all countries [37]. Figure 6. Considered electricity prices in all countries [37]. 4. Results and Discussion The economic performance of the collector in two different financial models is evaluated based This section details the simulation results using the digital mapping approach. Table 5 shows the on: Buildings 2020, 10, x FOR PEER REVIEW 16 of 30 inputs and results of key performance indicators for all selected locations, and the results are discussed. • Model 1: The total system cost is invested as initial capital investment in the first year; • 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 financial period of 7 years with a certain variable interest rate with every location. 4.1.1. Collector Thermal Production 4.1.1. Collector Thermal Production 4. Results and Discussion The simulated results are visualized using geospatial maps, as they provide clear indication for The simulated results are visualized using geospatial maps, as they provide clear indication for understanding This section regional details ttr hends e simul for atthermal ion result and s us electrical ing the digit output al meven apping appro in the case ach of . Table large 5 sho datasets. ws understanding regional trends for thermal and electrical output even in the case of large datasets. tFigur he input e 7 shows s and res theuvariation lts of key perf in theorman thermal ce ind output icato of rsthe for collector all select . ed locations, and the results are Figure 7 shows the variation in the thermal output of the collector. discussed. 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/m ) 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 , respectively. Similar thermal output is obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m 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 ). 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 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 collector output. Electricty price (€/kWh) Italy Portugal Spain Switzerland Sweden Denmark Finland Germany Iceland Norway Belgium Bulgaria France Greece Luxembourg Poland Romania Ukraine United kingdom China Qatar Saudi arabia Singapore India United states of America Mexico Australia Argentina Brazil Chile Colombia Algeria Egypt Morocco Buildings 2020, 10, 148 13 of 29 Table 5. All simulated data of key performance indicators. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Catania 38 1967 18 1790 487 5140 5541 Florence 44 1632 16 1520 413 4039 4451 Italy Milan 45 1233 12 1153 317 2528 2955 Rome 42 1585 17 1464 401 3797 4211 Bari 41 1824 17 1679 458 4691 5096 Lisbon 39 1939 18 1770 483 4766 5171 Portugal Porto 41 1765 16 1640 447 4246 4657 Setubal 39 1997 18 1823 495 4966 5368 Sevilla 37 2134 20 1882 520 4972 5361 Valencia 39 2043 18 1831 505 4776 5167 Zaragoza 42 2002 16 1795 498 4649 5041 Spain Barcelona 41 1904 18 1728 479 4387 4782 Lugo 43 1567 13 1464 406 3393 3798 Madrid 40 2019 15 1810 504 4709 5101 Bern 47 1335 10 1270 351 2576 3002 Davos 47 1612 4 1562 426 2863 3286 Switzerland Lausanne 47 1408 12 1329 364 2108 2539 Zurich 47 1249 10 1186 331 1648 1935 Gothenburg 58 1138 10 1073 305 1287 1726 Linkoping 58 1132 8 1061 304 1257 1697 Sweden Malmo 56 1183 9 1113 316 1424 1863 Stockholm 59 1179 8 1105 317 1407 1846 Uppsala 60 1099 8 1024 297 1142 1583 Alborg 57 1116 8 1047 298 3041 3463 Denmark Copenhagen 56 1144 10 1079 305 3195 3615 Odense 55 1102 9 1040 295 2987 3409 Helsinki 60 1160 6 1086 312 1021 1464 Finland Oulu 65 1182 4 1112 321 1104 1545 Buildings 2020, 10, 148 14 of 29 Table 5. Cont. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Berlin 53 1194 10 1128 315 4582 4988 Dortmund 52 1093 11 1037 291 4034 4446 Germany Frankfurt 50 1143 11 1078 302 4291 4701 Hamburg 54 1146 11 1091 306 4363 4772 Munich 48 1318 11 1257 345 5348 5747 Iceland Reykjavik 64 968 6 932 266 145 186 Bergen 60 926 9 875 253 576 163 Norway Oslo 60 1029 7 962 277 408 3 Trondheim 64 1166 7 1107 317 136 273 Belgium Brussels 51 1151 12 1094 306 3244 3664 Bulgaria Soﬁa 43 1335 13 1264 348 364 813 Lyon 46 1422 14 1337 368 1899 2333 Nantes 47 1408 13 1333 367 1889 2323 France Paris 49 1204 13 1134 315 1279 1718 Toulouse 44 1522 15 1437 391 2197 2628 Greece Athinai 38 1915 21 1731 474 3119 3540 Luxembourg Luxembourg 50 1194 9 1128 318 1661 2096 Krakow 50 1191 10 1126 315 868 1267 Poland Warsaw 52 1213 10 1137 320 909 1307 Bucharest 44 1589 13 1482 406 1841 2153 Romania Cluj-Napoca 47 1443 11 1365 374 1516 1831 Ukraine Kyiv 50 1330 10 1242 348 1287 1368 Glasgow 56 1097 10 1045 294 2096 2527 United Liverpool 53 1013 11 965 273 1765 2199 Kingdom London 52 1107 13 1048 294 2109 2540 China Hong Kong 22 1338 24 1251 329 461 725 Qatar Doha 25 1957 28 1715 462 1468 1168 Saudi Arabia Medina 25 2349 29 1966 540 828 401 Singapore Singapore 1 1618 27 1473 390 1461 1569 Buildings 2020, 10, 148 15 of 29 Table 5. Cont. NPV per Unit Collector NPV per Unit Collector Annual Annual Average Annual Thermal Annual Electrical Country City Latitude Area for Financial Area for Financial GHI (kWh) Temperature ( C) Production (kWh) Production (kWh) Model 1 (EUR) Model 2 (EUR) Bangalore 13 2093 25 1847 489 12 178 Bombay 19 1910 28 1687 445 213 21 Hyderabad 17 2005 28 1765 466 112 79 Lucknow 27 1921 27 1717 453 174 17 India New Delhi 29 2157 27 1878 505 35 224 Surat 21 2168 28 1874 500 26 215 Wadhwan 23 2159 28 1866 496 17 207 Yavatmal 20 1938 28 1715 453 179 13 Chicago 42 1564 11 1475 402 987 1432 Denver 40 1912 11 1796 483 1695 2133 Houston 30 1720 21 1582 422 1211 1655 Las Vegas 36 2278 21 1987 545 2136 2570 USA Los Angeles 34 1973 20 1808 489 1722 2161 New York 41 1597 14 1508 407 1052 1496 Portland 46 1436 12 1361 374 732 1179 San 38 1886 15 1757 478 1616 2056 Francisco Washington 39 1602 15 1510 407 1053 1497 Mexico Mexico City 20 1848 18 1727 451 342 224 Brisbane 27 1898 21 1720 452 3940 4339 Melbourne 38 1528 15 1426 371 2872 3282 Australia Perth 32 1930 19 1731 455 3990 4389 Buenos Argentina 35 1703 18 1550 406 65 2077 Aires Brazil Brasilia 16 1928 22 1762 467 1985 2197 Chile Santiago 33 1732 15 1570 411 1785 2171 Colombia Bogota 5 1560 14 1510 394 856 1107 Algeria Algiers 37 2017 18 1835 495 1027 747 Egypt Cairo 30 2009 22 1791 485 1551 1589 Morocco Rabat 34 2094 18 1907 517 1616 1950 Buildings 2020, 10, 148 16 of 29 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 ) 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 , respectively. Similar thermal output is obtained for locations in countries such as Sweden, Finland, United Kingdom, Denmark, etc., with less than 510 kWh/m 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 ). 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 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 collector output. Buildings 2020, 10, x FOR PEER REVIEW 17 of 30 GHI Ambient temperature Linear (GHI) Linear (Ambient temperature) 300 40 –5 0 50 100 150 200 250 –50 –10 Monthly thermal production (kWh/m /month) Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature. 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 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, 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. 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 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, 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 etc. The collector performed slightly better in Spain, Portugal, and Australia, with more than 400 kWh annually. However, it shows there is no signiﬁcant dierence in thermal and electrical production 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 trends. Furthermore, a correlation of collector electrical production with GHI and ambient is developed based on all monthly points from all chosen locations and a positive correlation is realized temperature is developed based on all monthly points from all chosen locations and a positive as shown in Figure 10. A large variation in electrical output for similar values of ambient temperature correlation is realized as shown in Figure 10. A large variation in electrical output for similar values can be observed, which again shows that GHI is the critical parameter governing the electrical output of ambient temperature can be observed, which again shows that GHI is the critical parameter of the collector. governing the electrical output of the collector. Figure 9. Annual average collector electrical performance. GHI (kWh) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 17 of 30 GHI Ambient temperature Linear (GHI) Linear (Ambient temperature) 300 40 –5 0 50 100 150 200 250 –50 –10 Monthly thermal production (kWh/m /month) Figure 8. Correlation of collector thermal production with global horizontal irradiation (GHI) and ambient temperature. 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 Buildings 2020, 10, 148 17 of 29 governing the electrical output of the collector. Buildings 2020, 10, x FOR PEER REVIEW 18 of 30 Figure 9. Annual average collector electrical performance. Figure 9. Annual average collector electrical performance. 300 40 GHI Ambient temperature 150 15 –5 0 –10 0 10203040506070 Monthly electrical production (kWh/m /month) Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and ambient temperature. ambient temperature. A large variation in thermal and electrical output is seen for many countries and is reﬂected in 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 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. 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 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 GHI (kWh) GHI (kWh) Ambient temperature (°C) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 18 of 30 300 40 GHI Ambient temperature 150 15 Buildings 2020, 10, 148 18 of 29 –5 0 –10 0 10203040506070 such as Madrid, Stockholm, and Berlin. In Medina, although GHI and ambient temperatures are higher Monthly electrical production (kWh/m /month) 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 Figure 10. Correlation of collector electrical production with global horizontal irradiation (GHI) and tank losses will be higher as the tank temperature increases. Higher tank temperature results in lower ambient temperature. 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 A large variation in thermal and electrical output is seen for many countries and is reflected in and July months. In Stockholm, the variation between the months is signiﬁcant because of seasonal Figures 7 and 9. The range of collector output with a maximum and minimum value of thermal and variation in GHI, and the same is lower in Medina, which results in more uniform monthly production. electrical production is shown in Figure 11. Buildings 2020, 10, x FOR PEER REVIEW 19 of 30 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 Figure 11. Country-wise collector thermal performance uncertainty. Figure 11. Country-wise collector thermal performance uncertainty. results in more uniform monthly production. The trends for monthly electrical production are slightly different than thermal output. For The minimum thermal production in blue color represents the minimum production for The trends for monthly electrical production are slightly dierent than thermal output. For example, example, in Medina, electrical production is higher in July than in October even though the ambient analyzed location, while the maximum thermal production is indicated with an orange color that in Medina, electrical production is higher in July than in October even though the ambient temperature temperature is maximum in July. This is due to high GHI in July and is in line with findings that the represents the highest thermal production of a city in each country. The results show likely high is maximum in July. This is due to high GHI in July and is in line with ﬁndings that the major factor major factor influencing the electrical production is GHI, rather than ambient temperature. variation in Italy, Spain, United States, and Australia, as many cities were simulated in those inﬂuencing the electrical production is GHI, rather than ambient temperature. 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 Madrid Stockholm Berlin Medina Melbourne January April July October Figure 12. Collector monthly thermal production variation. Figure 12. Collector monthly thermal production variation. Madrid Stockholm Berlin Medina Melbourne January April July October Figure 13. Collector monthly electrical production variation. GHI (kWh) Thermal production (kWh) Electrical production (kWh) Ambient temperature (°C) Buildings 2020, 10, x FOR PEER REVIEW 19 of 30 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 results in more uniform monthly production. 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. Madrid Stockholm Berlin Medina Melbourne January April July October Buildings 2020, 10, 148 19 of 29 Figure 12. Collector monthly thermal production variation. Madrid Stockholm Berlin Medina Melbourne January April July October Buildings 2020, 10, x FOR P Figure EER RE 13. VIEW Collector monthly electrical production variation. 20 of 30 Figure 13. Collector monthly electrical production variation. 4.1.3. Collector Energy Utilization Ratio 4.1.3. Collector Energy Utilization Ratio The eThe energy nergy utiliz u attiili on zat raion r tio oa fttih o of t e colh lee col ctor lfe ocrto vr for va arious lrio oca uts iolocat ns ision shs i owsn shown in Figuin F re 1i4gur . Te h e14 c. The orrela tion correlation trends between energy utilization ratio and annual average ambient temperature are trends between energy utilization ratio and annual average ambient temperature are shown in shown in Figure 15 with consideration of all selected 85 geographical locations to derive a possible Figure 15 with consideration of all selected 85 geographical locations to derive a possible trend between trend between the parameters. the parameters. Brasilia, Brazil New Delhi, India Cairo, Egypt Melbourne, Australia Chicago, USA Medina, Saudi arabia Athinai, Greece Berlin, Germany Stockholm, Sweden Davos, Switzerland Madrid, Spain Rome, Italy 50% 52% 54% 56% 58% 60% 62% 64% Energy utilization ratio Figure 14. Collector energy utilization ratio. Figure 14. Collector energy utilization ratio. Some locations show interesting results of system boundaries on PVT collector performance. 64% This can be realized by comparing the energy utilization ratio for Medina (high irradiation) and Davos 63% (low irradiation location). The energy utilization for Davos (63%) is higher compared to Medina (52.5%), 62% even though the absolute value of total energy output is higher for Medina (2506 kWh) compared 61% to Davos (1988 kWh). This is because the load demand for Medina is comparably lower, while the 60% other system design parameters remain the same (collector area, tank volume, etc.), which resulted in 59% higher average tank temp and thus lower collector eciency for Medina. Results show that the total 58% thermal demand for every location varies depending on the ambient temperature as shown in Figure 16. 57% This is because 56%of the temperature dierence between the annual average ambient temperature of each 55% 54% 53% 0 5 10 15 20 25 30 35 Ambient temperature (°C) Energy utilization ratio Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. Thermal production (kWh) Electrical production (kWh) Energy utilization ratio (%) Buildings 2020, 10, x FOR PEER REVIEW 20 of 30 4.1.3. Collector Energy Utilization Ratio 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. Brasilia, Brazil New Delhi, India Cairo, Egypt Melbourne, Australia Chicago, USA Medina, Saudi arabia Athinai, Greece Berlin, Germany Stockholm, Sweden Davos, Switzerland Madrid, Spain Rome, Italy 50% 52% 54% 56% 58% 60% 62% 64% Buildings 2020, 10, 148 20 of 29 Energy utilization ratio location and desired water temperature (assumed 60 C), which has to be covered by the collector thermal production. Figure 14. Collector energy utilization ratio. 64% 63% 62% 61% 60% Buildings 2020, 10, x FOR PEER REVIEW 21 of 30 59% 58% Some locations show interesting results of system boundaries on PVT collector performance. 57% This can be realized by comparing the energy utilization ratio for Medina (high irradiation) and Davos (low irrad 56% iation location). The energy utilization for Davos (63%) is higher compared to Medina 55% (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 54% lower, while the other system design parameters remain the same (collector area, tank volume, etc.), 53% which resulted in higher average tank temp and thus lower collector efficiency for Medina. Results 0 5 10 15 20 25 30 35 show that the total thermal demand for every location varies depending on the ambient temperature Ambient temperature (°C) as shown in Figure 16. This is because of the temperature difference between the annual average Energy utilization ratio ambient temperature of each location and desired water temperature (assumed 60 °C), which has to be covered by the collector thermal production. Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. Figure 15. Correlation of energy utilization ratio with the annual average ambient temperature. 3,500 3,300 3,100 2,900 2,700 2,500 2,300 2,100 1,900 0 5 10 15 20 25 30 35 Annual avg. ambient temperature (˚C) Figure 16. Total thermal demand of single-family house relation with the average ambient temperature. Figure 16. Total thermal demand of single-family house relation with the average ambient 4.1.4. Collector Exergy Eciency temperature. From the Carnot eciency, it can be noted that exergy eciency is a function of inlet temperature 4.1.4. Collector Exergy Efficiency and thermal output of the collector (assumed that the desired output temperature is ﬁxed at 60 C). From the Carnot efficiency, it can be noted that exergy efficiency is a function of inlet Hence, it can be derived that locations with higher ambient temperature will result in less quality of tempera exergy and, ture thus, and therm lowera exer l output of the coll getic eciency. ector (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 Figure 17 shows the correlation of exergetic eciency with ambient temperature based on all less quality of exergy selected 85 geographical and, t locations hus, lower to derive exergetic e a possible fficien tr cy. end between the parameters. Similar trends Figure 17 shows the correlation of exergetic efficiency with ambient temperature based on all can be seen for some speciﬁc locations shown in Figure 18. It can be seen that even though the energy select eciency ed 85 of ge Madrid ographi ischigher al locatcompar ions to d ed er to ive Davos, a possi the ble exer trend between the p gy eciency of Davos aram is eters. higher Sim due ilar trends to lower can be seen for some specific locations shown in Figure 18. It can be seen that even though the energy 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. Energy utilization ratio (%) Thermal demand (kWh) Buildings 2020, 10, x FOR PEER REVIEW 22 of 30 Buildings 2020, 10, 148 21 of 29 Buildings 2020, 10, x FOR PEER REVIEW 22 of 30 25% 25% 24% 24% 23% 23% 22% 22% 21% 21% 20% 20% 19% 19% 18% 18% 17% 17% 16% 16% 15% 15% 0 5 10 15 20 25 30 35 0 5 10 15 20 25 30 35 Ambient temperature (°C) Ambient temperature (°C) Figure 17. Correlation of exergy efficiency with the annual average ambient temperature. Figure Figure 17. 17. Correlation of Correlation of exergy effici exergy eciency ency wit with h the the annual average ambient temperature. annual average ambient temperature. Brasilia, Brazil Brasilia, Brazil New Delhi, India New Delhi, India Cairo, Egypt Cairo, Egypt Melbourne, Australia Melbourne, Australia Chicago, USA Chicago, USA Medina, Saudi arabia Medina, Saudi arabia Athinai, Greece Athinai, Greece Berlin, Germany Berlin, Germany Stockholm, Sweden Stockholm, Sweden Davos, Switzerland Davos, Switzerland Madrid, Spain Madrid, Spain Rome, Italy Rome, Italy 0% 5% 10% 15% 20% 25% 0% 5% 10% 15% 20% 25% Figure 18. Collector exegetic eciency. 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 Based on the above energy performance, the economic performance of such a PVT system is investigated in the 85 dierent 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. 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 This financing model scenario has assumed that the total cost of the system is invested in the year of the system period. As the total system cost will be invested in the ﬁrst year, the interest rate is 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 not considered. Figure 19 is the digital representation of NPV potential per unit collector area with 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 ﬁnancial model 1 in all 85 geographical cities across the world and Figure 20 shows the NPV potential 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 per unit collector area in geographical cities in the European continent. 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. Exerg Exerg etic efficiency etic efficiency (%) (%) Buildings 2020, 10, 148 22 of 29 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 The cities with larger dots represent the high NPV potential and cities with smaller dots size 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 represents the least NPV potential. The cities Catania and Munich have the highest potential of 5140 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, and 5348 EUR, respectively, followed by the cities Bari, Lisbon, Setubal, Sevilla, Valencia, Zaragoza, 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 Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due Madrid, and Berlin, which have potentially more than 4500 EUR per unit collector area. This is due to to their high available GHI and electricity grid price, so the energy savings are high in these locations to their high available GHI and electricity grid price, so the energy savings are high in these locations 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., which is reflected in huge NPV potential for this system. Cities such as Oslo, Bergen, Reykjavik, etc., 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. with relatively less electricity grid price resulted in having negative NPV due to lower available GHI. 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 The cities with high collector production such as Medina, Algeria, and Cairo have shown negative The cities with high collector production such as Medina, Algeria, and Cairo have shown negative NPV NPV potential due to a much lower electricity grid price which eventually showed fewer energy NPV potential due to a much lower electricity grid price which eventually showed fewer energy potential due to a much lower electricity grid price which eventually showed fewer energy savings. savings. savings. The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the 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 appropriate countries to define the NPV range per unit collector area of each country as shown in Buildings 2020, 10, 148 23 of 29 The NPV potential in all 85 simulated cities has been selected, divided, and segmented for the Buildings 2020, 10, x FOR PEER REVIEW 24 of 30 appropriate countries to deﬁne the NPV range per unit collector area of each country as shown in 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 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 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 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 as China, Argentina, Brazil, etc., because only one city has been simulated in this paper, which is part of the key uncertainty. of the key uncertainty. of the key uncertainty. 12,000 12,000 NPV minimum NPV maximum NPV minimum NPV maximum 10,000 10,000 8,000 8,000 6,000 6,000 4,000 4,000 2,000 2,000 –2000 –2000 –4000 –4000 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. Figure 22 shows the payback period of this PVT system for a single-family house of 5 people in Figure 22 shows the payback period of this PVT system for a single-family house of 5 people 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 in several countries based on ﬁnancial model 1. The results show that the total system cost will be 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, returned in the ﬁrst 10 years in countries such as Australia, Belgium, Denmark, Germany, Greece, 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 Italy, Portugal, Spain, Switzerland, etc. This is due to high collector production and high electricity 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 grid price. Although countries such as Algeria, Saudi Arabia, and Egypt have the highest collector 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 production, product the ion, t grid he grid price price is comparatively is comparatively lower lower, wh , which ich reflects th reﬂects the e payb payback ack pe period riod of more t of morh ean 20 than years. 20 years. 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. NPV (Euros) NPV (Euros) Italy Portugal Italy Spain Portugal Switzerland Spain Sweden Switzerland Denmark Sweden Finland Denmark Germany Finland Iceland Germany Norway Iceland Belgium Norway Bulgaria Belgium France Bulgaria Greece France Luxemburg Greece Poland Luxemburg Romania Poland Ukraine Romania United kingdom Ukraine China United kingdom Qatar China Saudi arabia Qatar Singapore Saudi arabia India Singapore USA India Mexico USA Australia Mexico Argentina Australia Brazil Argentina Chile Brazil Colombia Chile Algeria Colombia Egypt Algeria Morocco Egypt Morocco Buildings 2020, 10, 148 24 of 29 Buildings 2020, 10, x FOR PEER REVIEW 25 of 30 Buildings 2020, 10, x FOR PEER REVIEW 25 of 30 4.2.2. Collector Economic Performance in Financing Model 2 4.2.2. Collector Economic Performance in Financing Model 2 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 This financing model has been analyzed by assuming that 75% of total system cost is paid within a ﬁnancing This fin period ancinof g model has b 7 years with een an a certain alyzed inter by assum est rate and ing tth ha att 7 the 5%r o emaining f total sys25% tem c of os total t is psystem aid with cost in a financing period of 7 years with a certain interest rate and that the remaining 25% of total system a financing period of 7 years with a certain interest rate and that the remaining 25% of total system is invested in the ﬁrst year without any interest rate. The NPV potential per unit collector area with cost is invested in the first year without any interest rate. The NPV potential per unit collector area cost is invested in the first year without any interest rate. The NPV potential per unit collector area ﬁnancing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV potential with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV with financing model 2 in 85 geographical cities across the world is shown in Figure 23, and NPV per unit collector area in a speciﬁc European continent is shown in Figure 24. potential per unit collector area in a specific European continent is shown in Figure 24. potential per unit collector area in a specific European continent is shown in Figure 24. 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. Buildings 2020, 10, 148 25 of 29 Buildings 2020, 10, x FOR PEER REVIEW 26 of 30 The cities with larger dots represent the high NPV potential cities and those with smaller dots 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, 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, 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 were because of the almost zero interest rates in those countries. This is because if the interest rate is is zero, the user needs to pay part of the system cost in later years, and the present value of this 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 investment will be lower due to the time value of money. This will reduce the accumulated and thus higher NPV. However, if the interest rate is high, the extra amount paid due to high interest investment and thus higher NPV. However, if the interest rate is high, the extra amount paid due to in later years will overweigh the advantage due to the time value of money, and it will decrease the high interest in later years will overweigh the advantage due to the time value of money, and it will overall NPV. Therefore, ﬁnancial model 1 is recommended for countries with a high interest rate to decrease the overall NPV. Therefore, financial model 1 is recommended for countries with a high maximize the NPV and minimize the payback. Meanwhile, ﬁnancial model 2 is recommended for interest rate to maximize the NPV and minimize the payback. Meanwhile, financial model 2 is countries with zero or lower interest rates to maximize the NPV. recommended for countries with zero or lower interest rates to maximize the NPV. Figure 25 shows the NPV potential per unit collector area in each country for the ﬁnancing model 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 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. countries. Thus, not much variation has been identified in model 2 compared with model 1. 12,000 NPV minimum NPV maximum 10,000 8,000 6,000 4,000 2,000 –2000 –4000 –6000 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 eect of NPV change due to ﬁnancial model 2 compared to model 1 is shown in Figure 26. 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 eect on NPV and countries 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, 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 and most of the European countries. However, due to the high interest rate of 38% in Argentina, a negative impact is identiﬁed with ﬁnancing model 2. Furthermore, a correlation is derived between huge negative impact is identified with financing model 2. Furthermore, a correlation is derived NPV variations with an interest rate of a speciﬁc location in Figure 27. 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 for all locations, but since it may vary depending on the location and type of application, the resulted collector production would be slightly dierent in real time, but this approach has been assumed to achieve the goals of this paper. NPV (Euros) Buildings 2020, 10, 148 26 of 29 Buildings 2020, 10, x FOR PEER REVIEW 27 of 30 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. 1,000 1,000 Interst rate Linear (Interst rate) Interst rate Linear (Interst rate) –500 –500 –1000 –1000 –1500 –1500 –2000 –2000 –2500 –2500 0 5 10 15 20 25 30 35 40 0 5 10 15 20 25 30 35 40 Interest rate Interest rate (%) (%) Figure 27. Correlation of NPV potential variation with interest rate. Figure 27 - Figure 27 - Correlation of Correlation of NP NP V potential V potential variation with variation with inte interest rate. rest rate. Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary 4.3. Uncertainties 4.3. Uncertainties energy price is taken as the generalized price for every speciﬁc country, whereas in the real-time In this paper, the authors acknowledge the possible uncertainties in energy performance In this paper, the authors acknowledge the possible uncertainties in energy performance case, the energy price would be dierent for every state/city/municipality depending on localized analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW analysis. For instance, the delivery water temperature is assumed to be 60 °C and 28 liters DHW energy policy. It has been considered because of the unavailability of precise data, which may not demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has demand per person for all locations across all cities. In addition, the specific volume ratio (v/a) has be signiﬁcantly higher. The interest rate is chosen for each country for deriving the NPV potential been assumed as 80 liters/m 2 for all locations, but since it may vary depending on the location and been assumed as 80 liters/m for all locations, but since it may vary depending on the location and dierence between ﬁnancing model 1 and model 2. However, only a few countries which have negative type of application, the resulted collector production would be slightly different in real time, but this type of application, the resulted collector production would be slightly different in real time, but this and zero interest rate have been assumed as 0.1%, due to the incapability of the simulation tool in approach has been assumed to achieve the goals of this paper. approach has been assumed to achieve the goals of this paper. accepting negative or null values. However, it has also been realized that the uncertainty of dierence Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary Furthermore, as the grid price is a key parameter of the total system energy savings, the auxiliary between the negative interest rates and assumed interest rates has not been less than 1%, which is not energy price is taken as the generalized price for every specific country, whereas in the real-time case, 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 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 policy. It has been considered because of the unavailability of precise data, which may not be NPV (Euros) NPV (Euros) Buildings 2020, 10, 148 27 of 29 signiﬁcantly aecting the NPV potential dierence. Hence, the assumptions have been considered to achieve the aims in possible optimistic and realistic approaches irrespective of the uncertainties. 5. Conclusions The performance of a solar PVT consists of PVT collector and storage tank is evaluated for 85 locations across large cities. The optimal tilt angle of the PVT collector, load demand, and electricity prices are chosen appropriately for each simulated location. The results show that the major parameter inﬂuencing the PVT performance is GHI, and results derived a strong linear correlation between collector output and GHI. The other factor inﬂuencing energetic performance is ambient temperature, source, and load water temperatures. The energetic utilization ratio is dependent on total thermal demand and speciﬁc volume ratio (v/a ratio) as it can have a major inﬂuence on the ﬂuid temperature in the storage tank and, thus, collector total production. The electrical production by PVT collector is higher in high ambient temperature locations. The highest and lowest energy utilization ratio of the collector is recorded in Reykjavik, Iceland (63%), and Medina, Saudi Arabia (54%), respectively. The highest and lowest exergetic eciency of the collector has been recorded in Reykjavik, Iceland (23%), and Medina, Saudi Arabia (17%), respectively. Most importantly, the results show that the higher energetic output does not guarantee high economic feasibility. There are several factors such as electricity price, interest rate, and selection of ﬁnancial model which can highly aect the economic feasibility of PVT collector. The average NPV per unit collector area of 85 geographical cities for ﬁnancial model 1 and ﬁnancial model 2 is 1886 and 2221 EUR, respectively. The NPV and payback period analysis of the PVT system has shown positive results for the cities, which have high collector production and high electricity grid price reﬂecting high energy savings. However, the ﬁnancing model 1 is highly recommended for the locations with high interest rates and ﬁnancial model 2 is beneﬁcial for the locations with less interest rates. This paper oers potential insights into the promotion of the PVT market in dierent regions. Author Contributions: S.R.P. worked on simulation, analysis, and writing. X.Z. contributed to supervision, concept development, structuring, and writing. P.K.S. contributed to simulation, analysis, and writing. A.d.A. dedicated eorts to simulation and analysis. All authors have read and agreed to the published version of the manuscript. Funding: This research received funding from the Germany–Sweden joint project: ‘Product and process development for the preparing and realization of complete buildings of various types of use using energy ecient, partially energy independent lightweight construction solutions, ENSECO’. Acknowledgments: The authors acknowledge the useful gains from the IEA SHC Task 60, and the open access support from Dalarna University, Sweden. Conﬂicts of Interest: The authors declare no conﬂict of interest. References 1. Sommerfeldt, N.; Madani, H. In-depth techno-economic analysis of PV/Thermal plus ground source and heat pump systems for multi-family houses in a heating dominated climate. Sol. Energy 2019, 190, 44–62. [CrossRef] 2. Joshi, S.; Dhoble, A.S. Photovoltaic -Thermal systems (PVT): Technology review and future trends. Renew. Sustain. Energy Rev. 2018, 92, 848–882. [CrossRef] 3. Al-Waeli, A.H.; Sopian, K.; Kazem, H.A.; Chaichan, M.T. 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Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

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Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

Digital Mapping of Techno-Economic Performance of a Water-Based Solar Photovoltaic/Thermal (PVT) System for Buildings over Large Geographical Cities

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