Experimental Investigation of the Influence of Longitudinal Tilt Angles on the Thermal Performance of a Small-Scale Linear Fresnel Reflector

: This paper analyses the influence of the longitudinal tilt angle of the secondary system of a low-concentration photovoltaic system based on a small-scale linear Fresnel reflector. Several evaluation indicators, such as useful heat gain, thermal efficiency, incident solar irradiance gain on the photovoltaic cells, and total useful energy gain, were evaluated for five wind speed conditions and six locations in the Northern Hemisphere. The tests were performed with two small-scale linear Fresnel reflector configurations: the classical large-scale linear Fresnel reflector configuration (base configuration) and the optimal longitudinal tilt angle configuration (longitudinal tilt configuration). An experimental platform based on an open-loop wind tunnel was designed and built for this purpose. As far as useful heat production, the longitudinal tilt configuration performs worse as the longitudinal tilt angle and wind speed increase. A useful heat gain 33.91% lower than the base configuration is obtained with a wind speed of 10.03 (m/s) at the 36.86 ( ◦ ) latitude location. Thermal efficiency decreases with increasing wind speed and longitudinal tilt angle. The thermal efficiency is between 0.3 and 0.2 with wind speeds of 4.99 (m/s) and 10.03 (m/s). The longitudinal tilt configuration shows the best increase in total useful energy gain in the absence of wind (up to 53% at a latitude of 36.86 ( ◦ )). This increase is 25% at this same location with a wind speed of 10.03 (m/s). It can be concluded that the effect of the longitudinal tilt of the secondary system has a positive effect. To highlight the importance of this work, the results obtained in the configuration comparison were used to compare a nonconcentrating photovoltaic system and a low-concentration photovoltaic system. The incident solar irradiance on the photovoltaic cells is much higher with nonconcentrating photovoltaic technology. This solar irradiance gain is over 60% for the base configuration and 45% for the longitudinal tilt configuration. The total useful energy gain is 70% in the absence of wind and at the 36.86 ( ◦ ) latitude location in favour of the low-concentration photovoltaic system. The nonconcentrating photovoltaic system performs better with a wind speed of 10.03 (m/s).


Introduction
The decarbonisation process endorsed by European Union (EU) countries in the 2015 Paris Agreement [1] was revalidated at the 2022 United Nations climate change conference in Cairo, Egypt, with more ambitious targets.Achieving these goals requires the use of renewable energies such as solar energy, wind energy, etc.Although global solar and wind electricity production in 2022 reached 1322.6 (TWh) and 2104.8 (TWh) [2], respectively, the level of renewable energy needed to mitigate climate change has not yet been reached.In 2022, photovoltaic (PV) power generation capacity was 1.05 (TW), while wind capacity was 0.89 (TW) [2].These data confirm photovoltaic technology as one of the renewable energy sources that will be able to replace fossil fuels given that this energy is clean, free, and unlimited.
Photovoltaic systems produce electricity directly and can be divided into two technologies: nonconcentrating photovoltaic systems (NCPVs) and concentrating photovoltaic systems (CPVs).In an NCPV system, the PV cells receive nonconcentrating solar irradiance.These systems can use a solar tracking system or remain at a fixed tilt angle throughout the year.Solar tracking systems are classified according to their motion: (i) two rotation axes (dual-axis trackers) or (ii) a single rotation axis (single-axis trackers).Although dual-axis trackers generate the most power, single-axis trackers are the most widely used.In contrast, in a CPV system, optical devices (mirrors, lenses) concentrate the solar irradiance incident on the collector area into a much smaller area, achieving a significant increase in the flow of solar energy incident on the photovoltaic cells.These systems require a solar tracking system.Depending on the geometric concentration ratio (defined as the number of times solar irradiance is concentrated), expressed in number of suns (1 sun equals 1000 (W/m 2 ), CPV technology can be classified into [3] high-concentration photovoltaics (HCPVs) (between 100 suns and 1000 suns), medium-concentration photovoltaics (MCPVs) (between 10 suns and 100 suns), and low-concentration photovoltaics (LCPVs) (from 2 suns to 10 suns).
Some of the differences between concentrating and nonconcentrating systems are shown below: (i) PV cell efficiency.NCPV systems use commercial silicon cells with efficiencies between 10% and 20% [4].In contrast, CPV systems use multijunction cells with an efficiency as high as 39% [4].(ii) The solar tracking system.A solar tracking system is mandatory in a CPV system.
However, solar tracking is optional in an NCPV system even though the use thereof increases electricity production.The use of solar tracking systems in CPV and NCPV systems complicates their implementation and increases their cost.(iii) Incident solar irradiance on PV cells.The beam, diffuse, and ground-reflected components of solar irradiance are incident on the PV cells in NCPV systems.In contrast, only the beam component is incident on the PV cells in CPV systems.The available diffuse solar irradiance often represents a significant fraction of the solar irradiance on a tilted surface.There are even some locations where this component is decisive.(iv) The operating temperature of the PV cells.The energy production of a PV system depends on the operating temperature of the PV cells [5].For example, manufacturers of crystalline photovoltaic cells estimate a decrease of between 0.4% and 0.65% in electrical efficiency per • C increase over the reference operating temperature [6].In CPV systems, the concentration of solar irradiance causes an increase in the temperature of the PV cells, but it is easier to implement a cooling system due to the size of the PV cell system.In contrast, it is not possible to implement a cooling system in NCPV system due to the large size of the PV cell system.In addition to reducing the electrical efficiency of PV cells, the high temperatures to which a PV cell system is subjected damage its backsheet, encapsulants, edge seals, and optical coatings [7].(v) The system cost.Due to the low efficiency of PV cells, NCPV systems require large PV cell surfaces.In contrast, CPV systems are equipped with cheaper optical materials (e.g., mirrors or lenses), which reduces the cost of these devices.Even so, it has been estimated that the cost of an LCPV system can be more than double (2.3 times) the cost of an NCPV system [8].However, Moreno et al. [9] presented a study showing that under certain conditions ((i) high beam solar irradiance (>2.5 (MWh/m 2 year)) and (ii) at utility scale) CPV technologies can be competitive with NCPV systems.(vi) Waste PV cells.The lifetime of PV modules is estimated at 25 years.PV modules must be recycled after this period.In its report [10], the International Energy Agency Photovoltaic Power Systems (IEA − PVPS) estimates that 1.7 million tonnes of PV modules will need to be recycled by 2030 and 60 million tonnes by 2050.CPV systems use a fraction of the PV cell surface area that NCPV systems use, so the resulting waste in CPV systems will also be a fraction.This is one of the main advantages of CPV systems.(vii) The cogeneration system.Cogeneration systems are a very important element nowadays in reducing global warming [11].Both thermal energy and electrical energy are necessary in the building sector.CPV systems can produce heat and electricity simultaneously, for increased efficiency, whereas NCPV systems can only produce electrical energy.(viii) The surface area required for system implementation.The deployment of PV technologies in buildings is limited by the available surface area on building roofs.Silva and Fernandes [12] presented a study showing that LCPV systems require 60% less surface area to produce the same thermal and electrical performance compared to the combined use of flat thermal and NCPV systems.
The traditional concentrators used in CPV systems are (i) parabolic trough concentrators, (ii) parabolic dish concentrators, and (iii) linear Fresnel reflectors.Concentrators (i) and (ii) use curved reflecting surfaces [13], resulting in a low level of uniformity in the illumination of the PV cells and, therefore, a noticeable decrease in the electrical efficiency of the PV cells.In contrast, linear Fresnel reflectors can be equipped with flat mirrors, which allows a high level of solar irradiance uniformity on the PV cells [14].This difference, together with their lower cost and lower maintenance [15], allows linear Fresnel reflectors to improve the overall efficiency of CPV systems.In addition, several studies have concluded that CPV systems are effective technologies for increasing power output and reducing investment cost [16][17][18].HCPV systems characterised by a high geometric concentration ratio always have a high cost [19].However, an LCPV system with a low geometric concentration ratio will have a low cost [19], meaning it is more suitable for concentrating solar PV power production [20,21].A linear Fresnel reflector (LFR) collects sunlight using rows of mirrors to reflect the Sun's rays onto a linear receiver at the top.These mirrors are flat, long, and narrow.Due to the large dimensions of large-scale LFRs, their design is characterised by the following: (i) the rows of mirrors are parallel to the horizontal plane, and (ii) the receiver is parallel to the horizontal plane.In contrast, small-scale linear Fresnel reflectors (SSLFRs) can incorporate some geometric modifications designed to improve their efficiency given that they are smaller in size.
In [22], a parametric study of an SSLFR was presented analysing four configurations in which the rows of mirrors and/or the receiver were tilted with respect to the horizontal plane.The results showed a noticeable increase in incident solar irradiance on the receiver when the receiver was tilted with respect to the horizontal plane.The study did not take into account the effects of receiver tilt or the effects of wind speed on useful energy.Furthermore, the analysed SSLFR only generated thermal energy.
The effect of mirror rows and/or receiver tilt on the performance of SSLFRs was analysed in [23].The study was conducted in five cities in the Northern Hemisphere.The receiver tilt angle was varied from 0 ( • ) to the latitude of the location analysed in 10% intervals.The results also showed a noticeable increase in the energy received by the receiver.This was especially true for those locations where the beam component of the solar irradiance was high.However, the effects of receiver tilt on thermal losses and wind speed were not analysed.The SSLFR studied only the thermal energy generated.Ref. [24] theoretically demonstrated the optimum receiver tilt angle for the maximum energy received by the receiver.It concluded that the optimum tilt angle is the one that coincides with the location latitude.The study was implemented in five cities in the Northern Hemisphere.The study did not consider thermal losses due to wind speed.The SSLFR only considered the thermal energy generated.
An analysis of the effects of wind (speed and direction) on the heat losses from a receiver at a tilt angle to the horizontal plane of an SSLFR using a 3D computational fluid dynamics model was presented in [25].The SSLFR was used to obtain thermal energy.
In accordance with the studies analysed, the following conclusions were drawn: (i) Only a few studies in the literature consider the inclination of the receiver.Studies that take this geometrical design into account discuss obtaining thermal energy.
(ii) There are very few studies in the literature that take into account the inclination of the receiver and the thermal losses due to the action of the wind.These systems are used to generate thermal energy.In addition, they usually use a 3D computational fluid dynamics model.
(iii) The studies analysed used the SSLFR to generate thermal energy only.
The contributions of this paper can be summarised in the following points: (i) The tested SSLFR is used in an LCPV system.To our knowledge, there is no study similar to the one proposed in this paper.
(ii) An experimental platform was designed and built for the development of the tests, allowing the receiver to be tilted.
(iii) The multiple tests carried out took into account five wind speed conditions and seven different conditions: six Northern Hemisphere cities and the classical configuration of large-scale LFRs.Four evaluation indicators were used, including useful heat gain, thermal efficiency, solar irradiance gain incident on the PV cells, and total useful energy gain.
(iv) An analysis was performed of electrical efficiency as a function of thermal power and ambient temperature.
(v) A comparison was made between a nonconcentration PV system and a lowconcentration PV system.This paper is organised as follows.Section 2 introduces the basic construction aspects of a low-concentration PV system based on a small-scale linear Fresnel reflector.Section 3 presents the experimental platform, the prototype, the electrical subsystem, the thermal subsystem, the measuring instruments, the experimental procedure, and the evaluation indicators.Section 4 sets forth the experimental results for different tilt angles and different wind speeds.Finally, the conclusions are given in Section 5.

An Overview of the LCPV System Based on an SSLFR
The LCPV system studied in this paper is based on an SSLFR.The characteristics of this LCPV system are described in [14].The elements comprising the SSLFR are shown in Figure 1a.The system is roughly composed of two main parts: a primary reflector system and a secondary system.In Figure 1a, the secondary system is aligned with a north-south orientation.
Rows of mirrors are used in this type of solar concentrator to redirect the Sun's rays during the day to a secondary system on top of the fixed structure.The movement of the mirror rows is computer-controlled to keep their reflective surface perpendicular to the angle divider between the directions of the Sun and the secondary system [26].
To more easily understand the SSLFR, this study was divided into two planes [26,27]: a transversal plane and a longitudinal plane.Therefore, the angle of incidence of solar irradiance is divided into the transversal angle of incidence (θ t ) and the longitudinal angle of incidence (θ l ).
The primary reflector (PR) system (see Figure 1a) is composed of the parallel mirror rows and the tracking system.This design has a central mirror and an equal number of mirrors on either side of it.The PR system was installed on a mobile structure to provide longitudinal movement.
The parameters required for the transversal design of the PR system are shown in Figure 1b and can be defined as follows: f is the height to the receiver, N is the number of mirrors on each side of the central mirror (therefore, the total number of mirrors is 2N + 1), W Mi is the width of the i-th mirror, β i is the angle which mirror i forms with the horizontal, L i is the position of each mirror with respect to the central mirror (in central mirror i = 0, L 0 = 0, and β 0 ), d i is the separation between two consecutive mirrors, and θ i is the angle between the vertical at the focal point and the line connecting the centre point of each mirror to the focal point.The parameters required for the longitudinal design of the PR system are shown in Figure 1c and can be defined as follows: β M is the angle between the mirror axis and the horizontal plane, and L M is the length of the mirrors.
The secondary (S) system (see Figure 2) is composed of the PV system, the active cooling system, the secondary structure, the isolation material, the protective casing, and the shaft.The shaft of the S system is installed on a fixed structure.The parameters required for the transversal design of the S system are shown in Figure 1b and can be defined as follows: W PV is the width of the PV cells, and W AC is the width of the active cooling system.The parameters required for the longitudinal design of the S system are shown in Figure 1c and can be defined as follows: β S is the angle between the PV system and the horizontal plane, L PV is the length of the PV system, and L AC is the length of the active cooling system.

Mirrors' Movement
As shown in [26], the motion of each mirror in the primary reflector system is defined by β i (transversal design).But only the central mirror is controlled, since the rest of the mirrors move at the same angular speed but with a different initial position than the central mirror.The control of the central mirror can be found with the equation The initial position of the mirrors on the right side can be found with and the initial position of the mirrors on the left side can be found with

The Longitudinal Tilt Angle of the Secondary System
Several studies have shown the positive effects of SSLFR configurations with a longitudinal tilt angle on the primary reflector system and/or the secondary system [23,24,28].These positive effects are related to the energy absorbed by the secondary system and the surface area required for installation.
A study on the influence of the longitudinal tilt angle on the energy absorbed by the secondary system was presented in [23].The study was carried out in five cities in the Northern Hemisphere: Almeria (Spain), Rome (Italy), Budapest (Hungary), Berlin (Germany), and Helsinki (Finland).The results obtained were compared with the longitudinal tilt angle used in large-scale LFRs, i.e., β S = 0 ( • ).When β S = λ ( • ), the increase in the energy absorbed by the secondary system was maximum [24].Specifically, there was an increase of 164.14% for Almeria [23].However, the useful energy was not determined in that study, i.e., thermal losses were not considered, hence the aim of this paper.

Experimental Setup
The energy analysis of the influence of the secondary system longitudinal tilt angle focuses on the cooling system, as the primary reflector system and the solar tracking system are considered to be the same and are, therefore, outside the scope of this energy analysis.
An experimental setup was designed and constructed to investigate the consequences of the longitudinal inclination of the secondary system on the efficiency of an LCPV system.The experimental data were obtained considering all relevant parameters influencing the overall efficiency of the SSLFR secondary system.These parameters are (i) the longitudinal tilt angle of the secondary system, (ii) the dissipated thermal power, (iii) the wind speed, and (iv) the ambient temperature.The width and length of the cooling system and the insulation of the secondary system remained constant throughout the study.Comprehensive experiments were carried out to analyse the behaviour of the secondary system.

Experimental Platform
As shown in Figure 3, the experimental platform is composed of an SSLFR secondary system, an open-loop wind tunnel, an electrical subsystem, a thermal subsystem, the longitudinal inclination of the secondary system, and measuring equipment.The secondary system cooling circuit is connected to the thermal subsystem, and the electrical subsystem simulates the power that the PV cells do not transform into electricity.
Figure 4 shows the experimental platform in detail.The experimental analysis was carried out in an open-loop wind tunnel.The air flow was generated by an industrial centrifugal fan.The wind tunnel comprised a flow straightener, a nozzle, a test section, and a diffuser (see Figure 4a).The wind tunnel test section had a diameter of 600 (mm).Figure 4b shows the arrangement of the secondary system inside the wind tunnel test section.Figure 4c shows the longitudinal inclination of the secondary system.The experimental platform is located at the Department of Electrical Engineering of the University of Oviedo in Gijón, Spain.

The Prototype
LCPV systems require uniform illumination of the PV cells, otherwise their fill factor and overall electrical efficiency decrease [29] and may even damage the cells [30].In [14], SSLFR parameters were identified which reflect a bad design that can cause nonuniform illumination on PV cells.These parameters are as follows: (i) the contribution of shading and blocking phenomena between adjacent mirrors (small d), (ii) high mirror spacing (large d), (iii) the number of mirrors, and (iv) the width of the PV system.
Therefore, an SSLFR for LCPV system applications can be considered to be optimally designed when the so-called "optimal design conditions" are met [14]: (i) the flux density over the PV cells is homogeneous; (ii) there is no shading phenomenon between adjacent mirrors; and (iii) there is no blocking phenomenon between adjacent mirrors.
Before defining the measurements of the secondary system being tested, the parameters of the SSLFR need to be calculated.The method proposed in [14] can be used for this purpose.The following parameters were used to apply the methodology proposed in [14]: (i) The width and length of the prototype are limited by the dimensions of the available wind tunnel.Therefore, a commercial PV cell with a width of 60 (mm) and a length of 30 (mm) was chosen.A total of 21 PV cells were arranged in the PV system.Therefore, the length of the PV system was 658 (mm) ( 21• 30 (mm)).(ii) Thermal interface material plays a key role in devices operating at high temperatures, such as photovoltaic concentrator devices or integrated microelectronic devices [31].
Silicone grease [32] was used as the thermal interface material between the PV cells and the cooling system.(iii) Normally, the height to receiver ( f ) is taken as 1500 (mm) [14,33,34].(iv) The choice of the number of mirrors is directly related to the cost of the SSLFR [35].
Nine mirrors were chosen so the cost would not be too high.Therefore, N = 4. (v) Based on the length of the PV system, a mirror length of 658 (mm) was chosen.(vi) The optical properties of the materials used in the calculations were already used in previous studies [14,36]: mirror reflectivity ρ = 0.94 [37], mirror cleanliness CI m = 0.96 [38], glass cleanliness CI g = 0.96 [38], glass transmissivity τ g = 0.92 [39], encapsulant transmissivity τ e = 0.90 [40], and PV cell absorptivity α = 0.90 [40].(vii) The optimal design conditions are impossible to meet from sunrise to sunset.Therefore, Ref. [14] defines the so-called "optimum operation interval" (θ t 0 ).This θ t 0 guarantees the homogeneous distribution of solar irradiance without shadows or blocking.
Several aspects have to be taken into account when choosing θ t 0 , such as the length of the SSLFR, the optimal hours of operation, and the total annual solar irradiation effectively reaching the PV cells.As an example, Figure 5 shows three curves related to the choice of θ t 0 for the city of Almeria, Spain (latitude 36 • 50 ′ 07 ′′ N, longitude 02 • 24 ′ 08 ′′ W, and elevation 22 (m)), as well as the parameters chosen in this section.
Figure 5a shows the relationship between the number of hours with a guaranteed homogeneous distribution of solar irradiance without shading or blocking and the optimum operation interval.If θ t 0 is high, the number of guaranteed hours will also be high.Figure 5b shows the variation of the % of annual irradiation that actually reaches the PV system as a function of θ t 0 .If θ t 0 is high, the % of annual irradiation will also be high.Figure 5c shows the optimal width of the SSLFR for each value of θ t 0 .This curve is convex with a large derivative for larger values of θ t 0 .If θ t 0 is high, the available roof area will also be high.It should be noted that the available roof area that can accommodate the SSLFR is a critical parameter [41].Therefore, a balance between the three curves shown in Figure 5 must be found.Based on other studies, θ t 0 is considered to be 46 ( • ) [14,36].This choice guarantees 74.65% of the unattainable ideal value of 100% annual solar irradiation.In addition, the width of the SSLFR shall be 786.88(mm), resulting in a nearly square SSLFR area.Mathematica™ Computer Algebra System software, version 11 was used to determine the optimal parameters.Table 1 shows the optimal design parameters for the primary reflector system.As there are nine mirrors, the central mirror is number 5. As can be seen, there is symmetry in the results, which would be normal for this type of design.Having defined the primary reflector system and the PV system, the dimensions of the prototype can be specified.
A prototype suitable for wind tunnel testing was constructed in order to examine the performance of the secondary system at various inclinations and under real conditions.This prototype is composed of a flat tube (active cooling system) and the corresponding insulation.The cooling medium, which is water in this case, flows through the flat tube.The flat tube is fixed to the secondary system structure by means of u-shaped lateral supports to keep the flat tube in the correct position.The PV cells are installed on one side of the flat tube, and the other side is insulated with glass fibre.For this study, the PV cells were replaced by an electrical resistor simulating the power that the PV cells do not convert into electricity.The prototype is shown in Figure 6. Figure 6a,b show several photographs of the prototype.Figure 6c,d show several schematics of the prototype.The dimensions of the prototype were chosen so that it could be tested in the available wind tunnel.The prototype is made of the following materials: (i) the flat tube is a carbon steel commercial tube 70.00 (mm) width, 34.00 (mm) height, 658.00 (mm) length, and 2.00 (mm) thick, and the area of the flat tube is 0.046 (m 2 ); (ii) the insulation comprises a glass wool filling 100 (mm) thick; (iii) the structure is made of a steel square hollow section (mm); (iv) the shaft is a 16 (mm) diameter commercial carbon steel tube; (iv) the electrical resistance has a nominal power of 500 (W) and a nominal voltage of 230 (V).
The secondary system can be rotated on the east-west axis.The secondary system is positioned at a certain longitudinal angle of inclination with respect to the horizontal plane depending on the geographical location of the SSLFR and remains in such a position for the duration of the experimental campaign.Therefore, it is essential to have a system (the secondary system inclination system) that meets these requirements.The inclination system is shown in Figure 7.The inclination system includes two bearings (standard bearing type FAG 7205 B.TVP), two bearing supports (standard bearing support type UCP212), and an angle measuring device.

The Electrical Subsystem
The main objective of the electrical subsystem is to simulate different operating points of the PV system from a thermal perspective, i.e., to simulate the thermal power that the PV cells do not convert into electricity.The electrical subsystem is composed of a 0-240 (V), 1000 (VA) single-phase variable autotransformer and electrical protections.

The Thermal Subsystem
In order to examine the performance of the secondary system at various longitudinal inclination angles, a thermal subsystem was constructed.The construction of the thermal subsystem used to dissipate the heat generated in the secondary system was based on ISO 9806: 2017-Test methods for solar thermal collectors [42].The main objective of the thermal subsystem is to simulate a thermal load that allows the heat generated in the secondary system to be removed.The schematic diagram of the thermal subsystem is shown in Figure 3, and a photograph of this subsystem is shown in Figure 8.The thermal subsystem comprises a pump, an expansion tank, a valve, a heat exchanger, a fan, a pressure gauge, an air bleeder valve, a temperature sensor, and a flow meter.The connection of these devices can be seen in Figure 3.The thermal subsystem comprises a closed circuit with a centrifugal pump taking the water from the outlet of the secondary system where the heating process takes place and pushing it through a heat exchanger, finally returning it to the secondary system inlet.As this is a closed circuit, a heat exchanger (radiator with fan) must be installed to transfer the heat recovered from the secondary system to the environment.Two temperature sensors are also available to record the secondary system inlet and outlet water temperatures.A pressure gauge and a flow meter are present to ensure the circuit pressure and the water flow rate remain constant during the experimental campaign.The fact that the recommended volumetric flow rate for liquid heating solar collectors is between 10 and 50 (L/h) [43] and that thermosyphon-driven liquid-heated solar collectors can reach up to 55 (kg/h) of water mass flow rate [44] was taken into account.The power consumed by the metering equipment, the auxiliary equipment, and centrifugal pump were disregarded as they fall outside the scope of this energy analysis.A constant volumetric water flow rate of 0.5 (L/min) was established for all tests.

Measuring Instruments
Experimental measurements included the electrical power, ambient temperature, flow rate, water temperature at the cooling system outlet and inlet, and wind speed.The power absorbed by the electrical resistance was measured with a digital wattmeter type PX120 from MATRIX [45].The ambient temperature was measured with a Testo 400 measuring instrument [46] and a T-type thermocouple.The flow rate was measured with a flow sensor type OF10ZAT from AICH ITOKEI [47].Water temperatures were measured by a T-type thermocouple and distributed in the secondary system to measure the temperature at the water inlet/outlet.The wind speed was measured with a Testo 400 measuring instrument [46] and a Pitot tube.These devices were periodically calibrated to ensure traceability of measurements.All instruments were synchronised and all data were captured every 10 (s).Table 2 shows the characteristics of the measuring instruments used in the tests (see Figure 9).Any sources of error in the experiments conducted need to be taken into account to estimate the overall uncertainty associated with the measurements and to then detect inferences from the experimental results.An uncertainty analysis was performed for this reason.Li, et al. [48] identified the different sources of error that can influence the uncertainties of experimental parameters, such as the methodology of the experiments, the calibration of the test rig, the random fluctuation of the instruments used, and the accuracy of observation.The root mean square method was used to determine the measurement uncertainties [49]: where e R is the overall uncertainty associated with the measurement, f is the given function of the measurement, and e 1 , e 2 ,..., e n are the measurement uncertainties of the related measured parameters.Table 3 shows the uncertainties of the parameters used in this study.Some authors consider experiments to be of high precision for uncertainties when below 2% [50] or 3% [48].According to the results shown in Table 3, the experiments can be considered as highly accurate.

Test Conditions
The experimental test campaigns carried out took into account several considerations, such as various longitudinal tilt angles, various wind speeds, various thermal powers, the same electrical efficiency, similar ambient temperatures, the same water flow rate, and the same duration of each test.These considerations are described below.

Longitudinal Tilt Angle
In order to generate a broad image of the energy analysis presented in this study, six cities were selected according to the following criteria: (i) The cities are located in the Northern Hemisphere.There are several reasons for focusing this study on this hemisphere: (a) Ninety percent of the world's population is concentrated in the Northern Hemisphere [51].(b) The Northern Hemisphere has the largest building roof area, which is the ideal location for energy production in cities.In the European Union, there is a total roof area of residential buildings of about 19 billion (m 2 ) [52].(ii) There is high beam incident solar irradiance in the chosen city.This is one of the conditions that had to be met for this type of technology to be cost-effective.The So-larGis software [53] uses data from 19 high-precision satellites for its simulations and provides maps with a rigorous, systematic approach of different parts of the world.
Figure 10 shows a map of the direct normal solar irradiation all over world.(iii) There are different climate zones with quite different latitudes.In [24], they propose the choice of study locations with a difference of about 6 ( • ) latitude starting at latitudes of 36 ( • ) up to 60 ( • ).In our study, locations higher than 40 ( • ) latitude are not considered due to the value of the incident direct solar irradiance.
Table 4 shows the geographic characteristics of the cities under study.(iv) The optimal longitudinal tilt angle of the secondary system demonstrated in [24] is used to define the longitudinal tilt angle at each chosen location.This angle coincides with the latitude of the location.

Wind Speed
A wind tunnel was used to provide different wind speeds.The wind speeds chosen depend on the characteristics of the wind tunnel.Five different wind speeds (around 0 (m/s), 1.05 (m/s), 2.55 (m/s), 4.99 (m/s), and 10.03 (m/s)) were investigated.

Water Flow Rate
During the tests, the water flow rate remained around 0.5 (L/min) to simulate thermosyphon operation.

Ambient Temperature
Ambient temperature is a parameter that influences the results.The ambient temperature at the start of each test ranged from 19.00 ( • C) to 20.70 ( • C).

Duration of Each Test
Each test used a longitudinal tilt angle, dissipated thermal power, and five wind speeds.The duration of each test was five hours.A total of seventy hours were spent on the research.Each test was carried out on a different day.

Thermal Power
Depending on the PV cell mode of operation, a significant part of the absorbed solar irradiance may not be converted into electricity and is, therefore, completely dissipated as heat.This internal heat source can be expressed according to the following equation [55]: where Q th is the internal heat source (W), I t is the total absorbed solar irradiance for the PV system (W/m 2 ), A PV is the total area of the PV system (m 2 ), and η e is the electrical efficiency of the PV system.Part of the heat Q th is transferred by conduction to the wall of the flat tube, according to Fourier's law of conduction [56]: where k is the thermal conductivity of the flat tube (W/m • K), A AC is the area of the flat tube (m 2 ), T PV is the temperature of the PV cells ( • K), T AC is the temperature of the flat tube ( • K), and δ AC is the wall thickness of the flat tube (m).In this study, k = 50 (W/m • K).The heat is transferred by convection to the working fluid through the wall of the flat tube, according to Newton's Law of Cooling [56]: where h i is the heat transfer coefficient of the wall of the flat tube (W/m 2• K), A AC is the area of the flat tube (m 2 ), T AC is the surface temperature of the wall of the of the flat tube, and T w is the working fluid temperature.h i can be determined using the following equation [57]: where k w is the thermal conductivity of the working fluid (W/m • K), D h is the hydraulic diameter of the flat tube (m), R ew is the Reynolds number of the working fluid, and P rw is the Prandtl number of the working fluid.Part of the heat Q th is transferred by convection (Q convPV ) and radiation (Q radPV ) to the environment.According to the Stefan-Boltzmann law [56], where σ is the Stefan-Boltzmann constant which is equal to 5.67 • 10 −8 (W/m 2 K 4 ), ε PV is the emittance of the PV system, A PV is the total area of the PV system (m 2 ), T PV is the temperature of the PV cells ( o K), and T amb is the ambient temperature ( o K).In this study, ε PV = 0.9 [57].According to Newton's Law of Cooling [56], where h PV is the heat transfer coefficient of the PV system (W/m 2• K), A PV is the total area of the PV system (m 2 ), T PV is the temperature of the PV cells ( • K), and T amb is the ambient temperature ( • K).The heat losses of the flat tube are considered negligible due to the insulation consisting of a glass wool filling 100 (mm) thick.Figure 12 shows a simplified heat transfer scheme.

Electrical Efficiency
The electrical efficiency of a photovoltaic cell depends on its operating temperature [58]: where η e is the electrical efficiency of the PV system at the operating temperature (dimensionless), η re f is the electrical efficiency of the PV system at 25 ( • C) and a solar irradiance of 1000 (W/m 2 ) (dimensionless), β re f is the temperature coefficient at 25 ), and T re f is the reference temperature of 25 ( • C) ( • C).The parameters η re f and β re f are provided by the PV cell manufacturer, 0.209 and 0.0035 ( • C −1 ), respectively.

Thermal Energy Chosen for the Test
The thermal power not converted into electricity by the PV system (see Equation ( 5)) depends on the solar irradiance and electrical efficiency of the PV system, which in turn depend on the ambient temperature and solar irradiance.These parameters depend on the location, day, and time chosen (see Figure 11).Therefore, the choice of thermal energy not converted into electricity by the PV system depends on multiple parameters.The thermal power not converted into electricity by the PV system chosen was 300 and 400 (W).These values were chosen for the following reasons: (i) The concentration factor of the LCPV system is 10.41.To determine this value, the parameters of the primary reflector system shown in Table 1 and the dimensions of the prototype were used.With the incident solar irradiance at the Cairo and Almeria locations, a thermal power not converted into electricity by the PV system of approximately 300 (W) is obtained.(ii) The choice of 300 (W) allows the Medellin, Bangkok, Morelia, and Karachi locations to increase the LCPV concentration factor in future studies.(iii) The choice of 400 (W) allows all locations under study to be able to increase the LCPV concentration factor in future studies.
Figures 13 and 14 show the results of the average water temperature in the flat tube obtained in the tests, the ambient temperature at which the test was performed, and the average temperature of the PV system obtained using Equations ( 6)- (10).From the test, T w and Q conv are obtained, and by means of Equations ( 8) and ( 7), T AC is obtained.Once T AC is known, by means of Equation ( 6), T PV is obtained.On the other hand, once T PV is known, Q radPV can be determined by Equation (9).Q convPV can be obtained by subtracting the losses Q cond and Q radPV from Q th .

Experimental Procedure
Different environmental conditions, such as wind speed and ambient temperature, were recorded.In addition, the thermal power that the photovoltaic cells did not convert into electricity was also recorded.Several longitudinal tilt angles of the secondary system were used in the study.The experimental procedure was carried out according to the following steps: (i) The water was circulated through the cooling system by the pump to simulate thermosyphon operation.The flow meter registered the water flow rate, and a valve was used to keep it constant.(ii) The electrical resistance simulated the energy that the photovoltaic cells do not convert into electricity.An autotransformer was used to ensure that the thermal power remained constant throughout the test.(iii) The test started with a wind speed of 0 (m/s), and every hour the wind speed was increased up to 10.03 (m/s).(iv) The following parameters were measured during the test: the power absorbed by the electrical resistance, the ambient temperature, the water flow rate, the temperature at the water inlet/outlet, and the wind speed.

Assessment Parameters
Two SSLFR configurations were compared for this paper: a base configuration (classical configuration of large-scale LFRs) and a longitudinal tilt configuration.The base configuration (C B ) is characterised by β M = 0 ( • ) and β S = 0 ( • ), and the longitudinal tilt configuration (C S ) is characterised by [24]

Useful Heat Gain
As mentioned above, the part of the absorbed solar irradiance that is not converted into electricity by the PV system is completely dissipated as heat (Q th ).But not all of this heat is used to increase the performance of the system, as there are heat losses.
The useful heat, Q u , can be written as follows [59]: where m is the fluid mass flow rate (kg/s), Cp is the heat capacity of the water (J/kg • C) evaluated at the average temperature, T in is the temperature of the inlet fluid to the secondary system ( • C), and T out is the temperature of the outlet fluid to the secondary system ( • C).This study evaluates the useful heat gain (UHG) due to the longitudinal tilt configuration (C S ) of the secondary system with respect to the base configuration (C B ).To do so, the difference between the useful heat with the configuration studied and the base configuration must be calculated.These values are % useful heat loss, as concerns the base configuration, i.e.,

Thermal Efficiency
The influence of the longitudinal tilt angle of the secondary system is determined by the thermal efficiency (η th ) of the cooling system defined as the ratio between the useful heat and the power not converted into electricity by the photovoltaic cells.
where Q u is the useful heat (W) and Q th is the power not converted into electricity by the PV system (W).

Solar Irradiation Gain Incident on the PV Cells
The beam solar irradiation gain incident on the PV cells can be determined according to the following equation: where H bC S is the beam solar irradiation incident on the PV cells in a longitudinal tilt configuration (kWh), and H bC B is the beam solar irradiation incident on the PV cells in a base configuration (kWh).If H b G is positive, a longitudinal tilt configuration performs better; however, a base configuration performs better if H b G is negative.

Total Useful Energy Gain
In a CPV system, the total useful energy is the sum of electrical energy and thermal energy.To compare the two configurations, the total useful energy gain will be used: where E C S is the total useful energy in a longitudinal tilt configuration (kWh), and E C B is the total useful energy in a base configuration (kWh).

Experimental Results and Discussion
The aim of this section is to estimate the effect of a longitudinal tilt angle for the secondary system of a low-concentration PV system based on a small-scale linear Fresnel reflector and the wind speed on the proposed evaluation indicators: useful heat gain, thermal efficiency, solar irradiation gain incident on the PV cells, and total useful energy gain.Two configurations were analysed for this purpose: a base configuration and a longitudinal tilt configuration.The base configuration (C B ) is the classical configuration of large-scale LFRs and is characterised by β M = 0 ( • ) and β S = 0 ( • ).The longitudinal tilt configuration (C S ) is characterised by the optimal longitudinal tilt angles [24] β M = λ/2 ( • ) and β S = λ ( • ).Experimental tests were carried out for various geographical locations and compared with the longitudinal tilt angle used in large-scale LFRs.
The available flat roof surface of the building was considered to be the same for all studies carried out.Specifically, the dimensions of the flat roof were a width of 78.68 (mm) and a length of 658 (mm).The electrical efficiency of the PV cells was also assumed to be the same for both configurations.In fact, 0.2 was assumed for the two.Moreover, the operating temperature of the PV cells was assumed to be the same in both configurations for the same wind speed.
The useful heat of the secondary system was determined for various longitudinal tilt angles, various powers that the PV cells did not convert into electricity, and various wind speeds.Section 3 shows the dimensions and materials of the prototype under testing.The conditions of the experimental tests conducted were as follows: (i) a range of longitudinal tilt angles from 0 ( • ) to 36.86 ( • ) at intervals of approximately 6 ( • ); (ii) a wind speed range of 0 (m/s) to 10.03 (m/s); (iii) an initial ambient temperature range of 19.00 ( • C) to 20.70 ( • C); (iv) two situations of unconverted electricity power from the PV cells of 300 (W) and 400 (W); and (v) a water flow rate through the cooling system of 0.5 (L/min).The thermal performance of the prototype was examined by monitoring the thermal behaviour while varying the wind speed and the longitudinal tilt angle of the secondary system.
Mathematica™ Computer Algebra System software was used to determine the irradiance incident on the PV system.This software has been used extensively in similar studies [14].In order to be able to analyse how the experimental results affect the SSLFR configuration, the beam solar irradiance incident on the PV system must be determined.Thus, the beam solar irradiance on the horizontal surface of the site under study and, therefore, the specific meteorological conditions must be taken into account.The method proposed by [60] can be used to determine the particular meteorological conditions at a given location.This method uses the PVGIS [54] database to obtain the monthly average beam solar irradiance over horizontal surfaces.The equations used for the calculation of the incident solar irradiation on the PV system are presented in [14].Table 5 shows the beam solar irradiation incident (H b ) on the PV cells for each configuration and city studied.This table also shows the beam solar irradiation incident gain (H b G) with respect to the base configuration (H bC B ).As can be seen in Table 5, the effect of the longitudinal tilt of the secondary system is positive with respect to the incident solar irradiation on the PV cells.

Effect of the Longitudinal Tilt Angle of the Secondary System on Useful Heat
Figure 15 shows the useful heat for the longitudinal tilts under study and the 400 (W) power not converted into electricity by the PV cells.
Figure 15 suggests the following conclusions as concerns the useful heat: (i) Useful heat obviously decreases as the wind speed increases.This effect is more noticeable as the longitudinal tilt angle increases.(ii) When the wind speed is 10.03 (m/s), the useful heat gain (UHG) of the longitudinal tilt configuration is between −21.30% (Medellin) and −33.91% (Almeria) with respect to the base configuration.For this wind speed, there is a noticeable difference in UHG between the lower latitude and higher latitude locations.(iii) If the wind speed is 4.99 (m/s), the UHG is between −17.27% (Medellin) and −18.77% (Almeria).The difference in useful heat gain between the most extreme locations decreases considerably with this wind speed.(iv) When the wind speed is 2.55 (m/s), the useful heat gain in the longitudinal tilt configuration is still lower than in the base configuration.UHG is approximately −8%.
In this case, the difference in useful heat gain between the most extreme locations is negligible.The same is true for a wind speed of 1.05 (m/s).(v) When the wind speed is 0 (m/s), the useful heat gain in the longitudinal tilt configuration is similar to that of the base configuration.(vi) It can be concluded that the presence of wind is detrimental to the longitudinal tilt configuration at all locations as concerns the useful heat.However, it is important to note that this type of technology also generates electricity.Furthermore, according to Table 5, the longitudinal tilt configuration performs better as concerns incident solar irradiation on the PV system.This will be assessed in the study below.Figure 16 shows the useful heat for the longitudinal tilts under study and the power not converted into electricity by the photovoltaic cells of 300 (W). Figure 13 shows similar trends in useful heat as Figure 15.The trends for useful heat gain are also true.

Effect of the Longitudinal Tilt Angle of the Secondary System on Thermal Efficiency
Figure 17 shows the thermal efficiency for the longitudinal tilts under study and the power not converted into electricity by the photovoltaic cells of 400 (W).
Figure 17 suggests the following conclusions: (i) The trend obtained with useful heat (see Figure 15) is also obviously true for thermal efficiency.(ii) The thermal efficiency is always below 0.6.As wind speed increases, this value decreases.This effect is more pronounced as the longitudinal tilt angle increases.(iii) When the wind speed is 1.05 (m/s), the thermal efficiency ranges between 0.5 and 0.4.For wind speeds of 2.55 (m/s), it ranges between 0.4 and 0.3.For wind speeds of 4.99 (m/s) and 10.03 (m/s), the thermal efficiency is between 0.3 and 0.2.This is valid for all locations.The lowest thermal efficiency is obtained in Almeria (location with the highest latitude).Figure 18 shows the thermal efficiency for the longitudinal tilts under study and power not converted into electricity by the photovoltaic cells of 300 (W).The conclusions drawn in Figure 17 are applicable to Figure 18.

Effect of the Longitudinal Tilt Angle of the Secondary System on Total Useful Energy Gain
The total useful energy in the configurations studied is the sum of the electrical energy generated and the useful thermal energy.As shown in Table 5, the incident solar irradiation on the PV system increases with increasing longitudinal tilt angle.This is an important factor in this study.Figure 19 shows the total useful energy gain for the two configurations as a function of two wind speeds.The longitudinal tilt configuration shows the best total useful energy gain in the absence of wind.The lowest latitude location (Medellín) has the smallest increase.On the other hand, for higher latitudes, the total useful energy gain reflects values up to 53%.The longitudinal tilt configuration still performs the best when the wind speed is 10.03 (m/s), except at the lowest latitude location.The total useful energy gain at this wind speed decreases to 25% for the highest latitude location (Almeria).Therefore, it can be concluded that secondary system designs with longitudinal tilt angles perform well at locations with latitudes above 10 ( • ).These results are quite good if the latitude is higher than 24 ( • ) and lower than 37 ( • ).

Effect of Thermal Power on the Electrical Efficiency of the PV System
As the solar irradiance incident on the PV system increases, the nonconverted electricity output increases.Figure 20 shows the electrical efficiency for 300 and 400 (W) with the results obtained in the tests.In this section, the electrical efficiency was determined numerically for 30 and 40 ( • C) ambient temperature.According to Figure 11, the ambient temperature of the studied locations does not exceed 40 ( • C).It can be considered that the losses Q convPV and Q radPV remain constant if the solar irradiance remains constant.According to Mattei et al. [61], if the solar irradiance remains constant, the temperature of the PV system increases in the same proportion as the ambient temperature.Figures 21 and 22 show the electrical efficiency for ambient temperatures of 30 and 40 ( • C), respectively.
Figures 21 and 22 suggest the following conclusions as concerns the electrical efficiency: (i) The electrical efficiency obviously decreases as the ambient temperature increases, since the operating temperature of the PV cell increases.(ii) The increase in wind speed dampens the decrease in electrical efficiency, but not enough to offset the increase in ambient temperature.(iii) Therefore, increasing the ambient temperature decreases the electrical efficiency but increases the thermal efficiency of the system by decreasing the thermal jump between the ambient temperature and the heat source.

Efficiency Comparison between Concentrating and Nonconcentrating PV Systems
In this section, the results obtained above will be applied to compare the NCPV system and the CPV system.The following assumptions were considered in order to compare the two systems: (i) The available roof area of the building was considered to be the same for both technologies.Specifically, the flat roof has a width of 786.88 (mm) and a length of 658 (mm).(ii) According to Figures 20-22, the electrical efficiency varies with incident solar irradiance, ambient temperature, and wind speed.Figure 11 shows how the ambient temperature varies as a function of the time of day at each location under study.Therefore, the electrical efficiency can take a large number of values.The electrical efficiency of PV cells was considered to be the same for both technologies, i.e., 0.18.The operating temperature of the PV cells was also assumed to be the same.It can be considered that the losses Q convPV and Q radPV remain constant if the solar irradiance remains constant.(iii) The NCPV system has a southern orientation and an optimal tilt angle, as determined by the procedure used in [62].(iv) The method proposed by [60] was used to determine solar irradiance for both technologies.
Table 6 shows the optimum tilt angle and the annual solar irradiation incident on the PV cells of the NCPV system at each location under study.Figure 16 shows the solar irradiation gain incident on the PV cells according to the following equation: where H NCPV is the solar irradiation incident on the PV cells in the NCPV system (kWh), and H CPV is the solar irradiation incident on the PV cells in the CPV system (kWh).
As with all NCPV systems, all three solar irradiance components are incident on the PV cells, and the incident solar irradiance will be much higher than in the case of CPV systems, which only use the beam component of the solar irradiance.As shown in Figure 23, the studied configuration always shows better results than the base configuration.With respect to the base configuration (β M = 0 ( • ) and β S = 0 ( • )), the solar irradiation gain is higher than 60%, whereas it is higher than 45% for the longitudinal tilt configuration.The total useful energy in the NCPV system is only electrical energy.In contrast, the total useful energy in the CPV system is the sum of electrical energy and thermal energy.To compare the two technologies, the total useful energy gain must be used: where E NCPV is the total useful energy in the NCPV system (kWh), and E CPV is the total useful energy in the CPV system (kWh).If EG is positive, NCPV systems prove to perform better; however, CPV systems are considered higher-performing if EG is negative.Figure 24 shows the total useful energy gain for the base configuration (β M = 0 ( • ) and β S = 0 ( • )) and for the studied configuration.The total useful energy gain at the lowest latitude location (Medellin) in the absence of wind (see Figure 24a) is in favour of NCPV systems.In contrast, this energy gain is in favour of CPV systems for higher latitudes.As in the rest of the work, the studied configuration shows better results than the base configuration.It is worth noting that this gain is 70% higher at the highest latitude location (Almeria) in the case of CPV systems.Figure 24b shows the effect of wind on the useful energy gain.If the wind speed is 10.03 (m/s), the NCPV systems perform much better.The energy gain of NCPV systems decreases considerably with increasing latitude.

Conclusions
This paper experimentally studied the influence of a longitudinal tilt angle for the secondary system of a small-scale linear Fresnel reflector used in a low-concentrating photovoltaic system based on several evaluation indicators (useful heat gain, thermal efficiency) under various wind speed conditions and in different locations throughout the Northern Hemisphere.Other evaluation indicators were also analysed, such as solar irradiation gain incident on the photovoltaic cells and total useful energy gain.A comparative study between nonconcentrating and low-concentrating photovoltaic systems was also carried out.The experiments to obtain the evaluation indicators were carried out with two configurations: a base configuration and a longitudinal tilt configuration.The base configuration is the classical configuration of large-scale linear Fresnel reflectors and is characterised by β M = 0 ( • ) and β S = 0 ( • ).The basis of the study is the power not converted into electricity by the photovoltaic cells, i.e., the thermal power wasted in a nonconcentrated photovoltaic system.Depending on the dimensions of the prototype used, a resistor simulating the thermal power of 300 and 400 (W) was used.Therefore, this power takes into account the operating temperature of the photovoltaic cells.The longitudinal tilt configuration is characterised by the optimal longitudinal tilt angles [24] β M = λ/2 ( • ) and β S = λ ( • ).The experiments were carried out with five wind speeds (around 0 (m/s), 1.05 (m/s), 2.55 (m/s), 4.99 (m/s), and 10.03 (m/s)), and six cities in the Northern Hemisphere (Medellin, Bangkok, Morelia, Karachi, Cairo, and Almeria).To carry out the research, an experimental platform was designed and built, consisting of the secondary system of a small-scale linear Fresnel reflector, an open-loop wind tunnel, an electrical subsystem, a thermal subsystem, a longitudinal tilt system of the secondary system, and measuring equipment.The following conclusions were drawn: (i) As concerns useful heat production, the longitudinal tilt configuration performs worse as the longitudinal tilt angle and wind speed increase.For example, the following is true for the power not converted into electricity by the photovoltaic cells of 400 (W): (a) When the wind speed is 10.03 (m/s), the useful heat gain shows the worst results, ranging from −21.30% (Medellin) to −33.91% (Almeria).(b) If the wind speed drops below this value, e.g., 4.99 (m/s), the useful heat gain also decreases, resulting in useful heat gains between −17.27% (Medellín) and −18.77% (Almería).(c) For 2.55 (m/s), the useful heat gain is approximately −8%.(d) When the wind speed is 0 (m/s), the useful heat in the longitudinal tilt configuration is similar to that of the base configuration.As wind speed increases, the difference in useful heat gain between lower and higher latitude locations increases.(ii) The thermal efficiency decreased with increasing wind speed and a longitudinal tilt angle.The thermal efficiency was always below 0.6.As wind speed increases, this value decreases.This effect is more pronounced as the longitudinal tilt angle increases.For example, the following is true for the power not converted into electricity by the photovoltaic cells of 400 (W): (a) When the wind speed is 1.05 (m/s), the thermal efficiency ranges between 0.5 and 0.4.(b) For wind speeds of 2.55 (m/s), it ranges between 0.4 and 0.3.(c) For wind speeds of 4.99 (m/s) and 10.03 (m/s), the thermal efficiency is between 0.3 and 0.2.The lowest thermal efficiency is obtained in Almeria (location with the highest latitude).(iii) The total useful energy in a low-concentration photovoltaic system is the sum of the electrical energy generated and the useful thermal energy produced.The longitudinal tilt configuration shows the best increase in total useful energy in the absence of wind.The lowest latitude site (Medellín) has the lowest increase.On the other hand, for higher latitudes, this total useful energy gain takes values up to 53% (Almeria).
The longitudinal tilt configuration remains the best-performing when the wind speed is 10.03 (m/s), except for the lowest latitude location (Medellin).At this wind speed, the total useful energy gain decreases to 25% for the highest latitude location (Almeria).Therefore, it can be concluded that secondary system designs with longitudinal tilt angles perform well at locations with latitudes above 10 ( • ).These results are very good if the latitude is higher than 24 ( • ) and lower than 37 ( • ).It can be concluded that the effect of the longitudinal tilt of the secondary system has a positive effect.
To highlight the importance of this work, the results obtained in the configuration comparison were used to compare a nonconcentrating photovoltaic system and a lowconcentrating photovoltaic system.The following conclusions were drawn: (i) The solar irradiance incident on the photovoltaic cells will be much higher in nonconcentrating photovoltaic technology.This solar irradiance gain is more than 60% with the base configuration and 45% with the longitudinal tilt configuration.(ii) The total useful energy gain at the lowest latitude location (Medellín) is the only location favourable to nonconcentrating photovoltaic systems in the absence of wind.For all other locations, this gain is in favour of low-concentrating photovoltaic systems.It is worth noting that this gain is −70% at the highest latitude location (Almeria).(iii) The nonconcentrating photovoltaic system performs better if the wind speed is 10.03 (m/s).With increasing latitude, the total useful energy gain of the nonconcentrating photovoltaic system decreases considerably.

Figure 1 .
Figure 1.(a) Scheme of the SSLFR.(b) Parameters of the transversal study.(c) Parameters of the longitudinal study

Figure 6 .
Figure 6.Photographs and schematics of the prototype.

Figure 7 .
Figure 7. Photographs of the inclination system.

Figure 8 .
Figure 8. Photograph of the thermal subsystem.

Figure 11 shows
Figure 11 shows some environmental conditions at the locations under study.This figure shows the daily mean temperature and daily normal irradiance with solar tracking for the month of June.The highest solar irradiance values occur in this month.The values shown in Figure 11 are obtained from the PVGIS database [54].

Figure 13 .
Figure 13.Temperatures for power not converted into electricity by the PV cells of 300 (W).

Figure 14 .
Figure 14.Temperatures for power not converted into electricity by the PV cells of 400 (W).

Figure 15 .
Figure 15.Useful heat for power not converted into electricity by the PV cells of 400 (W).

Figure 16 .
Figure 16.Useful heat for power not converted into electricity by the PV cells of 300 (W).

Figure 17 .
Figure 17.Thermal efficiency for power not converted into electricity by the PV cells of 400 (W).

Figure 18 .
Figure 18.Thermal efficiency for power not converted into electricity by the PV cells of 300 (W).

Figure 20
Figure 20 suggests the following conclusions as concerns the electrical efficiency: (i) Electrical efficiency increases as the wind speed increases and as the operating temperature of the PV cell decreases.(ii) Electrical efficiency decreases as the thermal power of the PV system increases and as the incident solar irradiance on the PV system increases.(iii) The difference in electrical efficiency for 300 and 400 (W) decreases with increasing wind speed as the operating temperature of the PV cells decreases.

Figure 23 .
Figure 23.Solar irradiation gain incident on the photovoltaic cells.
T amb Ambient temperature ( • C) T AC Temperature of the flat tube ( • C) T PV Temperature of the PV cells ( • C) T in Temperature of the inlet fluid to the secondary system ( • C) T out Temperature of the outlet fluid to the secondary system ( • C) T re f Reference temperature ( • C) T w Working fluid temperature ( • C) UHG Useful heat gain (dimensionless) W AC Width of the active cooling system (m) W Mi Width of the i − th mirror (m) W PV Width of the PV cells (m) α Absorptivity of the PV cell (dimensionless) β i Angle which mirror i forms with the horizontal ( • C) β M Angle between the mirror axis and the horizontal plane ( • C)β re f Temperature coefficient (1/ • C) β SAngle between the PV system and the horizontal plane ( • C) δ AC Wall thickness of the flat tube (m) η e Electrical efficiency of the PV system (dimensionless) η re f Reference electrical efficiency (dimensionless) η th Thermal efficiency (dimensionless) θ i Angle between the vertical and the line centre point of each mirror with the focal point ( • ) θ l Longitudinal incidence angle ( • C) θ t Transversal incidence angle ( • C) θ t 0 Operation interval ( • C) λ Latitude ( • C) ρ Reflectivity of the primary mirrors (dimensionless) τ e Transmissivity of encapsulant (dimensionless) τ g Transmissivity of glass (dimensionless)

Table 1 .
Optimal design parameters for the primary reflector system.

Table 3 .
Computed uncertainty of performance parameter.

Table 4 .
Cities under study.

Table 5 .
Beam solar irradiation incident on PV cells.

Table 6 .
Results obtained for the NCPV system.
A ACArea of the flat tube (m 2 ) A PV Total area of the PV cells (m 2 ) C p Heat capacity of the water (J/kg • C) CL g Cleanliness factor of the glass (dimensionless) CL m Cleanliness factor of the mirror (dimensionless) D h Hydraulic diameter of the flat tube (m) d i Separation between i − th and i + 1 − th mirrors (m) Solar irradiation incident on the PV cells (kWh) H NCPV Solar irradiation incident on the PV cells (kWh) I t Total absorbed solar irradiance for PV system (W/m 2 ) k Thermal conductivity (W/m • C) L i Position of i − th mirror (m) L AC Length of the active cooling system (m) L M Length of the mirrors (m) L PV Length of the PV system (m) m Fluid mass flow rate (kg/s) N Number of mirrors on each side of the SSLFR P rw Prandtl number of the working fluid (dimensionless)