Performance Evaluation of Novel Concentrating Photovoltaic Thermal Solar Collector under Quasi-Dynamic Conditions

: Concentrating Photovoltaic Thermal (CPVT) collectors are suitable for integration in limited roof space due to their higher solar conversion efﬁciency. Solar sunlight can be used more effectively by CPVT collectors in comparison to individual solar thermal collectors or PV modules. In this study, the experimental investigation of a novel CPVT collector called a PC (power collector) has been carried out in real outdoor conditions, and the test set-up has been designed based on ISO 9806:2013. A quasi-dynamic testing method has been used because of the advantages that this method can offer for collectors with a unique construction, such as the proposed collector, over the steady-state testing method. With a quasi-dynamic testing method, it is possible to characterize the collector within a wide range of incidence angles and a complex incidence angle modiﬁer proﬁle. The proposed novel collector has a gross area of 2.57 m 2 . A maximum power output per collector unit area of 1140 W is found at 0 ◦ C reduced temperature (1000 W/m 2 irradiance level), while at a higher reduced temperature (70 ◦ C), it drops down to 510 W for the same irradiance level. The data have been ﬁtted through a multiple linear regression method, and the obtained efﬁciency curve coefﬁcients are 0.39, 0.192, 1.294, 0.023, 0.2, 0, − 5929 and 0 for K θ d , b 0 , c 1 , c 2 , c 3 , c 4 , c 5 and c 6 , respectively. The experimental characterization carried out on the collector proved that the output powers calculated by using the obtained parameters of the quasi-dynamic testing method are in good agreement with experimental points.


Introduction
Over the past four decades, global energy consumption has been steadily increasing, and today, the environment and energy are the two main issues for humanity. Fast population and industrial growth over the last two centuries have caused in a huge rise in energy demand, with an annual increasing rate of 2.3% from the year 1949 to 2009 [1]. In 2008, the total annual consumption of energy reached 474 × 10 18 J, of which a very large majority (about 80-90%) comes from combustion of fossil fuels [2]. Emissions from consumption of fossil fuels are the primary reason for the rapid and accelerating growth in atmospheric CO 2 , which is directly linked to global warming [1][2][3].
Among the available renewable energy sources, solar is one of the most promising sources of energy, as it supplies clean, environmentally friendly and abundant energy [4,5]. In 2012, solar photovoltaic (PV) energy provided for only 0.04% of total primary energy demand, while solar thermal energy provided 0.5% of energy supply. Future developments are expected to continue in solar photovoltaic and solar thermal technologies due to increased concerns around environmental protection, energy saving and CO 2 emissions [2,6].
The conversion efficiencies of PV systems such as silicon solar cells, III-V multijunction solar cells and 4-junction solar cells (developed by the ISE Fraunhofer institute) Solar 2023, 3 197 three types of solar cell arrays (a super cell array, a gallium arsenide (GaAs) cell and a concentrating silicon cell). The thermal and average electrical efficiencies of the system with a super cell array were found to be 45.17 and 3.63%, respectively. For the systems with a GaAs cell and silicon cell array, the thermal efficiencies were 41.69%, and 34.53%, respectively.
Researchers from Tunisia, Germany, India and USA have studied CPVT systems. M. Chaabane et al. [14] studied the performance and commercial application of a PVT system including a 3.64 m long trough concentrating collector made of stainless steel, and a 1.825 m long rectangular absorber conduit made of black coated steel. Some 18 mono-crystalline PV modules of 20 W were attached to the absorber. The overall efficiency achieved was 26% (16% thermal efficiency and 10.2% electrical efficiency). The CFD model of the system was also carried out and validated with experiments. In addition to ray-tracing simulations, M. Proell et al. [39] conducted an experimental study on a CPVT system in order to examine the impact of eight different CPC reflectors' geometries on the PV efficiency in in situ conditions. An aluminium thermal absorber with a c-Si cell was used, and an average of 10-11% electrical efficiency of was obtained. S. Sharma et al. [40] studied a CPVT system for building integration based on linear asymmetric compound parabolic collectors with LGBC (laser-grooved buried contact) crystalline silicon solar cells using phase change material (paraffin wax). At 1000 Wm −2 , through use of PCM, the obtained electrical efficiency was improved by 7.7%. Furthermore, a novel optimized mathematical model for a building-integrated concentrating photovoltaic-PCM system was also presented. B.K. Widyolar et al. [41] designed, fabricated and tested a CPVT system equipped with PTC and a non-imaging compound parabolic concentrator (CPC) with a gallium arsenide (GaAs) solar cell. In the experimental setup, the obtained maximum outlet temperature, thermal efficiency and electric efficiency from the GaAs cells were 365 • C, 37% and 8%, respectively. In addition to performance analysis of basin-type solar still-integrated systems with a PVT-CPC, D.B. Singh et al. [42,43] investigates the productivity and enviro-economic and exergo-economic parameters of single and double-slope PVT-CPC solar distillation systems. Coated aluminium sheets were used to make the CPC collectors. The receiver area is half of the aperture area, and the obtained annual productivity showed that the system feasible from an energy point of view.
To forecast the energy production of diverse solar thermal systems, it is crucial to have knowledge about the thermal efficiency of a broad range of solar collector technologies. Numerous standards exist that can assess the efficiency of solar thermal collectors, However, it is important to note that the SRCC 600 2014-07 standard has a relatively high degree of similarity to ISO 9806 standard. Two different test approaches are proposed by the aforementioned standards for characterizing the thermal performance of solar thermal collectors: the quasi-dynamic test (QDT) and the steady-state test (SST) [51].
To conduct the SST method, it is crucial to keep all pertinent parameters for thermal performance constant within the permissible range of values defined by the standard during measurements. Additionally, the test must be carried out under clear sky conditions, with a low level of diffuse radiation. Consequently, the SST method model does not have a correction term for diffuse radiation, and normal incidence radiation is utilized to determine the efficiency curve parameters [44, 51,52].
On the other hand, the QDT method necessitates less involvement from the operator. Additionally, fewer sunny days are necessary to perform the QDT method successfully, as compared to the SST method [52]. Moreover, the QDT method provides a more comprehensive depiction of the collector compared to the SST method, as it incorporates correction terms, such as wind speed and long-wavelength radiation incident on the collector in certain cases. To execute the QDT method, tests must be conducted for a minimum of 3 h under varying sky conditions [44, [49][50][51]. Since the SST and QDT methods share similar principles, there is no clear basis for choosing one over the other [53]. In addition, several This paper aims to introduce the concept of a novel CPVT collector in addition to a detailed description of a collector test stand based on ISO 9806:2013 for evaluating its thermal performance using the QDT method. Previous studies on the thermal performance evaluation of novel CPVT designs were limited. Although CPVT technology has received increasing attention during the past decade, limited studies have been conducted on testing methods of novel CPVT collector designs. This study presents a detailed testing procedure of a novel CPVT collector called PC, based on QDT method. Testing according to the QDT method over the SST method is a result of the advantages that the QDT method offers, especially for collectors with a unique construction such as the proposed CPVT collector. Using the QDT method, it is possible to characterize the collector within a wide range of incidence angles and a complex incidence angle modifier (IAM) profile. Figure 1 shows an expanded view of the proposed novel CPVT collector. It is a concentrating hybrid solar photovoltaic and solar thermal panel (CPVT). The collector is concentrating due to its curved mirror that reflects and concentrates the sunlight on to the bottom side of the receiver of the collector. This reflector geometry is called MaReCo, and has been published elsewhere [63]. The collector combines solar photovoltaic (PV) generation of electricity with solar thermal (T) generation heat and therefore is a hybrid concept. The manufacturer states that the collector has a thermal efficiency of 52%, and a linear loss coefficient of 3.47 W/(m 2 ·K) [64]. This paper aims to introduce the concept of a novel CPVT collector in addition to a detailed description of a collector test stand based on ISO 9806:2013 for evaluating its thermal performance using the QDT method. Previous studies on the thermal performance evaluation of novel CPVT designs were limited. Although CPVT technology has received increasing attention during the past decade, limited studies have been conducted on testing methods of novel CPVT collector designs. This study presents a detailed testing procedure of a novel CPVT collector called PC, based on QDT method. Testing according to the QDT method over the SST method is a result of the advantages that the QDT method offers, especially for collectors with a unique construction such as the proposed CPVT collector. Using the QDT method, it is possible to characterize the collector within a wide range of incidence angles and a complex incidence angle modifier (IAM) profile. Figure 1 shows an expanded view of the proposed novel CPVT collector. It is a concentrating hybrid solar photovoltaic and solar thermal panel (CPVT). The collector is concentrating due to its curved mirror that reflects and concentrates the sunlight on to the bottom side of the receiver of the collector. This reflector geometry is called MaReCo, and has been published elsewhere [63]. The collector combines solar photovoltaic (PV) generation of electricity with solar thermal (T) generation heat and therefore is a hybrid concept. The manufacturer states that the collector has a thermal efficiency of 52%, and a linear loss coefficient of 3.47 W/(m 2 K) [64]. The total size of the PC is 2.31 × 0.955 m, and it consists of two major components: the collector box and the receiver core. The box contains the concentrating mirrors and houses the receiver. The collector box can be sub-divided into four components, as follows:

Description of Collector
A black plastic frame, which is made of support ribs and a covering sheet of plastic. The total size of the PC is 2.31 × 0.955 m, and it consists of two major components: the collector box and the receiver core. The box contains the concentrating mirrors and houses the receiver. The collector box can be sub-divided into four components, as follows: A black plastic frame, which is made of support ribs and a covering sheet of plastic. The transparent gables, which are constructed from polymethyl-methacrylate (PPMA) and provide sealing for both sides of the collector. The manufacturer guarantees a transparency of 90%.
Tempered solar glass, whichhas a thickness of 4 mm and is treated with an antireflective coating on both sides to reach an absorptance of 1.5% and a reflectance of 2% per side. An aluminium reflector, which consists of a compound parabolic and circular reflective sections that concentrate the solar radiation onto the receiver. It has a reflectance of 92% and achieves a concentration ratio of 1.7 with this particular geometry. Studies from M. Rönnelid et al. and M. Adsten et al. [63,65] describe the geometry of the reflector in more detail.
With a length of 2321 mm, a width of 165 mm, and a thickness of 14.5 mm, the aluminium receiver contains solar cells on both of its sides, as depicted in Figure 2. These solar cells are encapsulated in highly transparent silicone with a reported transparency of 97%.
The transparent gables, which are constructed from polymethyl-methacrylate (PPMA) and provide sealing for both sides of the collector. The manufacturer guarantees a transparency of 90%.
Tempered solar glass, whichhas a thickness of 4 mm and is treated with an anti-reflective coating on both sides to reach an absorptance of 1.5% and a reflectance of 2% per side.
An aluminium reflector, which consists of a compound parabolic and circular reflective sections that concentrate the solar radiation onto the receiver. It has a reflectance of 92% and achieves a concentration ratio of 1.7 with this particular geometry. Studies from M. Rönnelid et al. and M. Adsten et al. [63,65] describe the geometry of the reflector in more detail.
With a length of 2321 mm, a width of 165 mm, and a thickness of 14.5 mm, the aluminium receiver contains solar cells on both of its sides, as depicted in Figure 2. These solar cells are encapsulated in highly transparent silicone with a reported transparency of 97%. As shown in Figure 3, the receiver comprises an aluminium structure containing eight elliptical channels, through which the cooling fluid flows to extract heat from the collector. The core of the receiver is made from extruded aluminium. Utilizing standard monocrystalline solar silicon cells with an efficiency of 19.7%, the collector has a cell string layout of four strings at the bottom and four at the top side of the receiver, as shown in Figure 4.

Description of Collector Test Rig
To conduct tests using the QDT method, a solar thermal collector test rig was established on a rooftop, in compliance with the European standard EN 12975-2:2006 (the predecessor to the present ISO standard). Figure 5 depicts a rotatable mounting platform that As shown in Figure 3, the receiver comprises an aluminium structure containing eight elliptical channels, through which the cooling fluid flows to extract heat from the collector. The core of the receiver is made from extruded aluminium. Utilizing standard monocrystalline solar silicon cells with an efficiency of 19.7%, the collector has a cell string layout of four strings at the bottom and four at the top side of the receiver, as shown in Figure 4.
The transparent gables, which are constructed from polymethyl-methacrylate (PPMA) and provide sealing for both sides of the collector. The manufacturer guarantees a transparency of 90%.
Tempered solar glass, whichhas a thickness of 4 mm and is treated with an anti-reflective coating on both sides to reach an absorptance of 1.5% and a reflectance of 2% per side.
An aluminium reflector, which consists of a compound parabolic and circular reflective sections that concentrate the solar radiation onto the receiver. It has a reflectance of 92% and achieves a concentration ratio of 1.7 with this particular geometry. Studies from M. Rönnelid et al. and M. Adsten et al. [63,65] describe the geometry of the reflector in more detail.
With a length of 2321 mm, a width of 165 mm, and a thickness of 14.5 mm, the aluminium receiver contains solar cells on both of its sides, as depicted in Figure 2. These solar cells are encapsulated in highly transparent silicone with a reported transparency of 97%. As shown in Figure 3, the receiver comprises an aluminium structure containing eight elliptical channels, through which the cooling fluid flows to extract heat from the collector. The core of the receiver is made from extruded aluminium. Utilizing standard monocrystalline solar silicon cells with an efficiency of 19.7%, the collector has a cell string layout of four strings at the bottom and four at the top side of the receiver, as shown in Figure 4.

Description of Collector Test Rig
To conduct tests using the QDT method, a solar thermal collector test rig was established on a rooftop, in compliance with the European standard EN 12975-2:2006 (the predecessor to the present ISO standard). Figure 5 depicts a rotatable mounting platform that

Description of Collector Test Rig
To conduct tests using the QDT method, a solar thermal collector test rig was established on a rooftop, in compliance with the European standard EN 12975-2:2006 (the predecessor to the present ISO standard). Figure 5 depicts a rotatable mounting platform that was used for the installation and testing of thermal collectors on the rooftop. The test rig is located at latitude and longitude of 60.48 • and 15.44 • , respectively. The collector azimuth is 0 • . was used for the installation and testing of thermal collectors on the rooftop. The test rig is located at latitude and longitude of 60.48° and 15.44°, respectively. The collector azi muth is 0°. The test rig includes an advanced hydraulic circuit that can maintain testing condi tions for two distinct collectors and is designed in accordance with the circuit layout rec ommended by the ISO 9806:2013 standard. All test measurements are captured by a data acquisition device, which is linked to a computer that records the readings every 10 s. A diagram of the data measurement and logging system is shown in Figure 6, while Table provides information on the temperature and flow regulation system.  Industry standard for monitoring and logging solar irradiance Sensitivity 7 µV·W-1·m − ² − 14 µV·W-1·m − ² Non-linearity <0.2% The test rig includes an advanced hydraulic circuit that can maintain testing conditions for two distinct collectors and is designed in accordance with the circuit layout recommended by the ISO 9806:2013 standard. All test measurements are captured by a data acquisition device, which is linked to a computer that records the readings every 10 s. A diagram of the data measurement and logging system is shown in Figure 6, while Table 1 provides information on the temperature and flow regulation system. was used for the installation and testing of thermal collectors on the rooftop. The test rig is located at latitude and longitude of 60.48° and 15.44°, respectively. The collector azimuth is 0°. The test rig includes an advanced hydraulic circuit that can maintain testing conditions for two distinct collectors and is designed in accordance with the circuit layout recommended by the ISO 9806:2013 standard. All test measurements are captured by a data acquisition device, which is linked to a computer that records the readings every 10 s. A diagram of the data measurement and logging system is shown in Figure 6, while Table 1 provides information on the temperature and flow regulation system.  Industry standard for monitoring and logging solar irradiance Sensitivity 7 µV·W-1·m − ² − 14 µV·W-1·m − ² Non-linearity <0.2% To maintain the operational set values, a temperature and flow regulation control panel is utilized, which is depicted in Figure 7. The control panel allows for the regulation of the pump speed, heating and cooling elements, to achieve the required test boundaries set by the standard. Additionally, Table 2 provides specifics about the temperature and flow regulation system. Highly sophisticated programmab data measurement, and export dev capable of high-resolution voltage current, and resistance measureme simultaneously with PC interface f logging To maintain the operational set values, a temperature and flow regulation cont panel is utilized, which is depicted in Figure 7. The control panel allows for the regulat of the pump speed, heating and cooling elements, to achieve the required test boundar set by the standard. Additionally, Table 2 provides specifics about the temperature a flow regulation system.

QDT Testing Procedure
Though testing under SST conditions can yield useful results, testing under dynamic conditions using the QDT method offers characterization of a different type of collectors under a wider range of operating and ambient conditions. In addition, more complete and complex characterization of collectors is achievable with the QDT method. Looking at the thermal collector model under the QDT procedure, the quasi-dynamic thermal collector model equation, as adapted by the ISO 9806:2013, can be identified by Equation (1).  The model includes various coefficients: c 1 represents the heat loss coefficient when the temperature difference between T m and T a is zero, c 2 accounts for the temperature dependence of the heat loss coefficient, c 3 considers the wind speed dependence of the heat loss coefficient, c 4 represents the dependence of the heat loss coefficient on the long wave irradiance, c 5 is the effective thermal capacitance, and c 6 accounts for the wind speed dependence of the zero loss efficiency. K b (θ L , θ T ) is the IAM for beam radiation, and defined as 66]. To test the performance of the PC using the QDT method, full-day tests covering all possible day sequences were carried out for a total of 17 days, and data were recorded every 10 s. The collected raw data, which comprised roughly 145,000 data points, were filtered to remove any unusable data. The input values were averaged over a 10 min period to determine the thermal capacitance. The data were then visually inspected to ensure that they met the QDT criteria. Only 262 conditioned and averaged points were used to characterize the collector by MLR (multiple linear regression) to determine the required coefficients. Figure 8 shows that the chosen data entry points cover five different inlet temperature levels and the data points are spread over a slightly narrow range of irradiance levels, with not many points over 800 W/m 2 . As a first step of visual inspection, it is ensured that all the inlet temperatures tested can be identified. In addition, wind speed, deviation of measured inlet temperature, the average value of measured mass flux and the irradiation distribution over the incidence angles were checked. Table 3 presents the proposed test conditions and the permitted deviations from average values by ISO 9806:2013, based on the QDT method. In addition, the proposed limits based on the SST method also presented for comparison. Figure 9 shows the wind speed distribution over the range of irradiance that is needed to confirm the diversity of the wind speed data; it is in the range of 0-4 m/s, as imposed by the standard in the QDT method.  Table 3 presents the proposed test conditions and the permitted deviations from average values by ISO 9806:2013, based on the QDT method. In addition, the proposed limits based on the SST method also presented for comparison.  Figure 9 shows the wind speed distribution over the range of irradiance that is needed to confirm the diversity of the wind speed data; it is in the range of 0-4 m/s, as imposed by the standard in the QDT method.
0.02 ±1% 0.02 ±1% Figure 8. Reduced temperature (Tm-Ta) versus the total irradiance. Table 3 presents the proposed test conditions and the permitted deviations from average values by ISO 9806:2013, based on the QDT method. In addition, the proposed limits based on the SST method also presented for comparison.  Figure 9 shows the wind speed distribution over the range of irradiance that is needed to confirm the diversity of the wind speed data; it is in the range of 0-4 m/s, as imposed by the standard in the QDT method.  During the thermal efficiency measurements of PC, the deviation of the inlet temperature of collector is less than 1 K for all test points. Furthermore, the mass flux is fixed at 0.02 kg·s −1 ·m −2 , with deviation under 1% (as proposed by ISO 9806:2013 based on QDT method).
In addition, based on ISO 9806:2017, the standard specific heat capacity of water at 1 to 12 bars is a polynomial function of the average temperature of the heat transfer fluid. Therefore, the uncertainty of the Cp is smaller than 0.04%.
In order to obtain a complex collector model that has the incident angle modifiers for the full range to be validated over any given incident angel, the distribution of direct and diffuse irradiation over the full range of incidence angles is necessary. Furthermore, this will have a more pronounced effect in modelling of collectors. Figure 10 shows the distribution of direct and diffuse irradiation over the full range of incidence angles for PC. 0.02 kgs −1 m −2 , with deviation under 1% (as proposed by ISO 9806:2013 based on QDT method).
In addition, based on ISO 9806:2017, the standard specific heat capacity of water at 1 to 12 bars is a polynomial function of the average temperature of the heat transfer fluid. Therefore, the uncertainty of the Cp is smaller than 0.04%.
In order to obtain a complex collector model that has the incident angle modifiers for the full range to be validated over any given incident angel, the distribution of direct and diffuse irradiation over the full range of incidence angles is necessary. Furthermore, this will have a more pronounced effect in modelling of collectors. Figure 10 shows the distribution of direct and diffuse irradiation over the full range of incidence angles for PC. Figure 10. Irradiation distribution over the incidence angels.

QDT Testing Results
The MLR method is the most widely used mathematical tool and referred to in the EN 12975-2 standard. In this method, the equation is written as a sum of functions weighted by the parameters to be determined and can be highly nonlinear [66,67].
For unglazed collectors, all the model parameters presented in Equation (1) are required. For glazed collectors, the wind-induced losses and the long wave radiation both have negligible weight in the absolute losses and gains; therefore, they are often recommended to be omitted at the start (c3, c4 and c6). However, since the wind speed has been measured and recorded, this study considers it.
The gross area of PC Is 2.57 m 2 , and the fluid flow rate used for the tests is fixed at 0.04 kg/s. Figure 11 shows the power output of PC per collector unit for three different irradiance levels. The obtained peak power per collector unit is 1140 W.

QDT Testing Results
The MLR method is the most widely used mathematical tool and referred to in the EN 12975-2 standard. In this method, the equation is written as a sum of functions weighted by the parameters to be determined and can be highly nonlinear [66,67].
For unglazed collectors, all the model parameters presented in Equation (1) are required. For glazed collectors, the wind-induced losses and the long wave radiation both have negligible weight in the absolute losses and gains; therefore, they are often recommended to be omitted at the start (c 3 , c 4 and c 6 ). However, since the wind speed has been measured and recorded, this study considers it.
The gross area of PC Is 2.57 m 2 , and the fluid flow rate used for the tests is fixed at 0.04 kg/s. Figure 11 shows the power output of PC per collector unit for three different irradiance levels. The obtained peak power per collector unit is 1140 W.  (2) and (3)).

̅ = ̅
(2) Figure 11. Power output per collector unit area. MLR adjusts a set of N experimental points (x l , y i ) as a linear combination of M arbitrary functions X k (x), and the objective of the adjustment is to minimize the merit function (χ 2 ) (Equations (2) and (3)).
The least-squares method assumes that the uncertainty of the experimental point (u i ) remains constant, whereas in reality, each data point has its own uncertainty which almost never remains constant for all observations. Therefore, the weighted least-squares method is more appropriate for fitting the measurement data [68][69][70]. The contributions to the uncertainty of the thermal efficiency are calculated, and the use of calibrated RTD Pt100s ensures that the uncertainties of inlet and outlet temperature evaluations for the given set-up are low, even at high temperatures, with a contribution of 21.5% to the uncertainty of ∆T. The measurement of radiation accounts for about three-quarters of the uncertainty contribution, while the contribution to the uncertainty of other measured values on thermal efficiency is less than 3%. Since the uncertainty values were very small compared to their measured quantities (due to proper measurement device selection and system design), the combined standard absolute uncertainty for the thermal efficiency obtained by propagating the errors is less than 0.8%. In Equation (3), u i 2 is the variance of the difference, and this weighting uncertainty is calculated by Equation (4) for uncertainty in x (the independent variable) and in y (the dependent variable).
Therefore, Equation (3) is nonlinear, and the Levenberg-Marquardt method can be used to identification of parameters. However, the least-squares method is also acceptable to use in order to first obtain and new set of parameters from which one calculates the uncertainties [44,45]. Table 4 shows the regression parameters related to Equation (1), and their standard deviation-based MLR method. In addition, the change in the thermal performance of the collector resulting from the incident angle is called the incident angle modifier (IAM) K θ (θ). With the QDT method, K θ (θ) is defined as two distinct parameters for diffuse and direct radiation. The term for direct radiation, K θb (θ), is modelled as a function of the incident angle, and the term for diffuse radiation, K θd , is modelled as a constant value. Table 5 shows the incident angle modifier values for direct radiation (K θb (θ)) as a function of the incident angle.   Figure 12 shows that the actual measured power production and production calculated using the extracted parameters are in harmony, and this indicates a successful parameterization.

C1
1  Figure 12 shows that the actual measured power production and production calculated using the extracted parameters are in harmony, and this indicates a successful parameterization. Figure 12. Actual measured production compared to model predicted generation. Figure 13 shows the power output of the PC per collector unit using the obtained parameters of QDT (mentioned in Table 5) at 1000 W/m 2 hemispherical irradiance with no diffuse radiation. The wind speed is 3 m/s, and there is zero incidence angle for the zero loss efficiency. The results from the previous study based on the SST method and performed at AEL are also presented in Figure 13. The efficiency curve coefficients, including η, a1 and a2, obtained from SST method in AEL, are 0.496, 3.155 W/m 2 K and 0.022 W/m 2 K 2 , respectively. Further details on the AEL test mentioned in this part can be found in [71].  Figure 13 shows the power output of the PC per collector unit using the obtained parameters of QDT (mentioned in Table 5) at 1000 W/m 2 hemispherical irradiance with no diffuse radiation. The wind speed is 3 m/s, and there is zero incidence angle for the zero loss efficiency. The results from the previous study based on the SST method and performed at AEL are also presented in Figure 13. The efficiency curve coefficients, including η, a 1 and a 2 , obtained from SST method in AEL, are 0.496, 3.155 W/m 2 ·K and 0.022 W/m 2 ·K 2 , respectively. Further details on the AEL test mentioned in this part can be found in [71].   Figure 14 shows the thermal efficiency of the proposed novel CPVT collector in comparison with commercially available PVT technologies at a total solar irradiance of 800 W/m 2 , as a function of the difference between the mean solar collector fluid temperature of the PVT panel and the ambient air temperature. The proposed CPVT collector in this study proved to be the most promising solution at elevated temperatures, in comparison with commercially available non-concentrating PVT technologies [13].  Figure 14 shows the thermal efficiency of the proposed novel CPV parison with commercially available PVT technologies at a total solar W/m², as a function of the difference between the mean solar collector of the PVT panel and the ambient air temperature. The proposed CPV study proved to be the most promising solution at elevated temperatu with commercially available non-concentrating PVT technologies [13].

Thermodynamic Performance Evaluation
To evaluate the thermodynamic performance of novel CPVT co CAD model of receiver was created in Solidworks, and then importe Structural Workbench for steady-state analysis. The thermodynamic carried out by calculating the temperature distribution within a solid s thermal inputs (heat loads), outputs (heat loss), and thermal barriers (t sistance) in the design, using the finite element method. The thermal addresses the conjugate heat transfer problem by simulating thermal co tion, and radiation. In this study, structural analysis is carried out using tural Workbench. The boundary conditions applied are a global solar W/m 2 , a convection heat transfer (with ambient air) of 5 W/m 2 K, and a p bottom part of the collector. For this analysis, additional boundary co straints are required to specify how the collector is held within its frame ture. The collector is assumed to be fixed with its frame at the collecto temperature distribution is uniform in the layers, and the optical and t Figure 14. Thermal efficiency comparison between PC and commercially available PVT panels.

Thermodynamic Performance Evaluation
To evaluate the thermodynamic performance of novel CPVT collector (PC), a 3-D CAD model of receiver was created in Solidworks, and then imported into the ANSYS Structural Workbench for steady-state analysis. The thermodynamic performance was carried out by calculating the temperature distribution within a solid structure caused by thermal inputs (heat loads), outputs (heat loss), and thermal barriers (thermal contact resistance) in the design, using the finite element method. The thermal structural analysis addresses the conjugate heat transfer problem by simulating thermal conduction, convection, and radiation. In this study, structural analysis is carried out using the ANSYS Structural Workbench. The boundary conditions applied are a global solar irradiance of 750 W/m 2 , a convection heat transfer (with ambient air) of 5 W/m 2 ·K, and a perfectly insulated bottom part of the collector. For this analysis, additional boundary conditions and constraints are required to specify how the collector is held within its frame and overall structure. The collector is assumed to be fixed with its frame at the collector water inlet. The temperature distribution is uniform in the layers, and the optical and thermal properties of the materials and fluids are constant. In this model, no surrounding shading is taken into account, the ambient temperature is constant around the receiver, and solar irradiance and wind speed are uniform over the collector's surface area. In addition, the total water mass flow rate is distributed uniformly amongst all collector channels with a uniform inlet temperature. Figure 15 shows the equivalent 1-D thermal resistance circuit and heat flow for the PC receiver. of the materials and fluids are constant. In this model, no surrounding shading is taken into account, the ambient temperature is constant around the receiver, and solar irradiance and wind speed are uniform over the collectorʹs surface area. In addition, the total water mass flow rate is distributed uniformly amongst all collector channels with a uniform inlet temperature. Figure 15 shows the equivalent 1-D thermal resistance circuit and heat flow for the PC receiver.

Cost Assessment of Novel CPVT Collector
A simple cost assessment was carried out on the application of the proposed novel CPVT collector (PC) in a dairy farm at LVAT-ATB in Germany, within a project called RES4LIVE under European Union's Horizon 2020 research and innovation program [72]. The total estimated annual thermal energy demand at LVAT-ATB is 52,197 kWh, and the proposed solar system integrates 24 PC collectors. Cost savings calculations over each year and the payback period of the system have been made, with the total system price known and the amount saved. The total investment for a system with 24 PC collectors is EUR 34,000. The annual thermal production of collectors running at a mean design temperature of 45 °C is 14,151 kWh, and the annual electrical output is 4264 kWh. Figure 16 shows the cash flow of investment in 24 PC collectors at the LVAT-ATB farm. The payback period is less than 6 years, and due to the higher heat production of the proposed PC collector at elevated temperatures, the payback period is lower than common commercial PVT collectors, even if there is a higher investment and maintenance cost [72].

Cost Assessment of Novel CPVT Collector
A simple cost assessment was carried out on the application of the proposed novel CPVT collector (PC) in a dairy farm at LVAT-ATB in Germany, within a project called RES4LIVE under European Union's Horizon 2020 research and innovation program [72]. The total estimated annual thermal energy demand at LVAT-ATB is 52,197 kW·h, and the proposed solar system integrates 24 PC collectors. Cost savings calculations over each year and the payback period of the system have been made, with the total system price known and the amount saved. The total investment for a system with 24 PC collectors is EUR 34,000. The annual thermal production of collectors running at a mean design temperature of 45 • C is 14,151 kW·h, and the annual electrical output is 4264 kW·h. Figure 16 shows the cash flow of investment in 24 PC collectors at the LVAT-ATB farm. The payback period is less than 6 years, and due to the higher heat production of the proposed PC collector at elevated temperatures, the payback period is lower than common commercial PVT collectors, even if there is a higher investment and maintenance cost [72].
into account, the ambient temperature is constant around the receiver, and solar irradiance and wind speed are uniform over the collectorʹs surface area. In addition, the total water mass flow rate is distributed uniformly amongst all collector channels with a uniform inlet temperature. Figure 15 shows the equivalent 1-D thermal resistance circuit and heat flow for the PC receiver.

Cost Assessment of Novel CPVT Collector
A simple cost assessment was carried out on the application of the proposed novel CPVT collector (PC) in a dairy farm at LVAT-ATB in Germany, within a project called RES4LIVE under European Union's Horizon 2020 research and innovation program [72]. The total estimated annual thermal energy demand at LVAT-ATB is 52,197 kWh, and the proposed solar system integrates 24 PC collectors. Cost savings calculations over each year and the payback period of the system have been made, with the total system price known and the amount saved. The total investment for a system with 24 PC collectors is EUR 34,000. The annual thermal production of collectors running at a mean design temperature of 45 °C is 14,151 kWh, and the annual electrical output is 4264 kWh. Figure 16 shows the cash flow of investment in 24 PC collectors at the LVAT-ATB farm. The payback period is less than 6 years, and due to the higher heat production of the proposed PC collector at elevated temperatures, the payback period is lower than common commercial PVT collectors, even if there is a higher investment and maintenance cost [72].

Conclusions
In order to test the thermal performance of a collector in real outdoor conditions, the given test set-up, based on ISO 9806:2013, has been designed. The results of the tested PC in outdoor conditions show the behaviour of its performance at increasing temperatures, and the tests are based on experimental implementation of the QDT method. The PC has a gross area of 2.57 m 2 , and a maximum power output of 1140 W per collector unit is found at a reduced temperature of 0 • C (1000 W/m 2 irradiance level), while at a higher reduced temperature (70 • C), it drops down to 510 W for the same irradiance level. The data have been fitted through a multiple linear regression (MLR) method, and efficiency curve coefficients have been obtained. Based on the MLR Fit K θd , b 0 , c 1 , c 2 , c 3 , c 4 , c 5 and c 6 are 0.39, 0.192, 1.294, 0.023, 0.2, 0, −5929 and 0, respectively. The experimental characterization carried out on the PC proved that the output powers calculated using the obtained parameters of the QDT method are in good agreement with experimental points. Informed Consent Statement: Informed consent was obtained from all subjects involved in the study.
Data Availability Statement: Data will be made available on request.

Conflicts of Interest:
The authors declare no conflict of interest.