T) system using compound hyperbolic –trumpet, V-trough and compound parabolic concentrators

Journal Pre-proof Numerical investigation of concentrating photovoltaic/thermal (CPV/T) system using Compound Hyperbolic –Trumpet, V-trough and Compound Parabolic Concentrators

Abid Ustaoglu, Umut Ozbey, Hande Torlaklı PII:

S0960-1481(20)30116-6

DOI:

https://doi.org/10.1016/j.renene.2020.01.094

Reference:

RENE 12957

To appear in:

Renewable Energy

Received Date:

08 October 2019

Accepted Date:

21 January 2020

Please cite this article as: Abid Ustaoglu, Umut Ozbey, Hande Torlaklı, Numerical investigation of concentrating photovoltaic/thermal (CPV/T) system using Compound Hyperbolic –Trumpet, Vtrough and Compound Parabolic Concentrators, Renewable Energy (2020), https://doi.org/10.1016 /j.renene.2020.01.094

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Journal Pre-proof Numerical investigation of concentrating photovoltaic/thermal (CPV/T) system using Compound Hyperbolic –Trumpet, V-trough and Compound Parabolic Concentrators Abid Ustaoglu1,*, Umut Ozbey2, Hande Torlaklı2 1Department 2Institute

of Mechanical engineering, Bartin University, Bartin, 74100, Turkey

of Science and Technology, Bartin University, Bartin, 74100, Turkey

*Corresponding author Tel.: +90 378 501 10 00-1689, Fax: +90 378 501 10 21; E mail address: [email protected], [email protected]

1

Journal Pre-proof Abstract A novel configuration of concentrating-photovoltaic system, compound hyperbolic concentrator-trumpet photovoltaic-thermal system (CHCT-PVT), has been proposed to enhance electrical-efficiency by reducing reflector size. CHCT-PVT was compared with the conventional non-imaging concentrators; V-trough-PVT (VT-PVT) and compound parabolic concentrator-PVT (CPC-PVT) systems. 2D-Ray-tracing analysis was carried out to decide energy flux. The numerical investigation was applied to decide the PV-cell-temperature. The electrical performances were determined regarding cell-temperature and solar radiation intensity. The results show that the CHC-PVT system can generate almost the same electrical power with that of CPC and V-trough system at the normal incidence angle, although CHC requires almost half size as V-trough or CPC for same concentration. It will forge ahead CHC for a CPVT using a sun tracking system. The largest electrical-efficiency was achieved for the CHC system. The electrical efficiencies of PVs using CPC, V-trough, and CHC-trumpet are 18.44%, 18.51%, and 18.59%, respectively. CHCT-PVT, the power output was about 42.9% higher than the CPC-PVT and about 58.97% higher than the VT-PVT systems per the reflector unit area. The results indicate that the CHCT-PVT system is a preferable alternative to CPVTs using conventional non-imaging reflectors. CHC may provide more apparent advancement for a CPV-system. Key words: Photovoltaic-thermal; compound parabolic concentrator; V-trough, Compound Hyperbolic concentrator – trumpet; Ray-tracing; uniformity. 1. Introduction Photovoltaic/Thermal (PV/T) system is a solar energy technology that can simultaneously generate electricity through the photovoltaic system and utilizes heat generated in the PV-cell. The thermal energy transfers to heat transfer fluids (HTFs) circulating under the PV-module. Thus, the decrease in electrical-efficiency arisen from high PV-cell-temperature can be minimized, and this thermal energy can be utilized. These can improve overall performance significantly. Recently, researchers have shown an increasing interest in designing a more efficient system to reduce undesirable heat dissipation in a photovoltaic cell. Saeedi et al. [1] carried out an optimization study about PV/T active solar still systems. The results show that the increment of basin area improves the absorbed energy of water from the PV-cell, thereby increasing the energy efficiency as decreasing the PV-cell-temperature. Bianchini et al. [2] conducted experimental measurements, performance evaluation, and economic evaluations of the PV/T system. The cooling of PV can increase the electrical 1

Journal Pre-proof generation by up to 3%. Habibollahzade [3] employed the PV/T system as a roof of the solar chimney power plant and carried out energy, exergy, and exergoeconomic analyses. They indicate that the cell operating temperature should be kept at a lower temperature to achieve high exergy efficiency and power output. Yu et al. [4] conducted an experimental analysis of a micro-channel loop-heat-pipe (MC-LHP) PV/T system. The proposed system improved the condensation and evaporation effect in the LHP, thereby increasing significantly the thermal and electrical-efficiency. Shao et al. [5] analyzed the electrical and thermal performance of the PV/T roof in the summer season. The results state that electricity generation and electricalefficiency increased by 12% and 10.8%, respectively, compared to the PV roof due to the lower cell-temperature in the case of PV/T. Al-Waeli et al. [6] evaluated PV, water-based PV/T, PV/T with PCM, and water coolant systems. The result indicates that the lowest cost of the power generation was achieved in PV/T PCM-water system as 293 $/MJ while the highest cost occurs in the PV system as 478.275 $/MJ. The existing literature in PV/T technologies reveals its promising development and indicates the problem of the high PV-cell-temperature. A simple possible way to improve the power generation of a PV-cell is to concentrate a large area of sunlight into a smaller receiver area of PV by reflector mirrors. The parabolic trough and parabolic dish concentrators are the most common types of concentrators, and they are called the imaging concentrators [7]. These kinds of the concentrators have a high concentration-ratio. However, a high concentration in PV-cells results in heat dissipation, and it even damages the cell and causes a significant reduction in PV performance due to high PVcell-temperature. Additionally, they need a sun tracing system due to their low acceptance angle. Low concentrating non-imaging collectors could be a preferable solution for these problems since they do not require the use of a sun-tracking due to their wide acceptance angle and the relatively low heat they generate. CPCs have been considered as the best static concentrators for solar energy collection [8]. Moreover, they have high optical efficiency and can utilize diffuse solar radiation as well as direct radiation. There have been many applications and novel designs of the CPC system for PV applications. Bahaidarah et al. [9] performed a comparative performance analysis of flat photovoltaic (PV) and symmetric combined parabolic condenser (CPC) photovoltaic systems. To determine the effect of cell-temperature on the performance of PV systems, a flat PV and PV-CPC systems were evaluated. The results show that the maximum power output of the cooled flat PV array was about 49% greater than the power obtained without cooling. Atheaya et al. [10] proposed a new design of a partially covered photovoltaic-thermal -CPC (PVT-CPC) with a glazed and unglazed reverse absorber. The results showed that, although the glazed inverted absorber 2

Journal Pre-proof caused a decrease in the electrical-efficiency by increasing the module temperature at high solar density. Tripathi and Tiwari [11] evaluated N partially covered CPC-PVT, PVT, CPC and flat plate collector (FPC) systems for water and molten salt using energetic and exergetic approach. The electrical-efficiency in the molten salt was lower because of higher PV-cell-temperature. Proell et al. [12] experimentally analyzed standard CPC (S-CPC) and a lowered absorber plane CPC (LA-CPC) on the electrical performance of the PVT system. They indicate that a nonuniform illumination on the PV-cell decreases the electrical-efficiency. Proell et al. [13] carried out another study about the CPC-PVT system. The thermal efficiency of the increased to 34% at the maximum power point while it is only 17% for a flat plate PVT. The electrical-efficiency decreased from 15% to 9% due to the high temperature and non-uniform flux distribution. Tripathi et al. [14] made energy and exergy analysis of a partially covered CPV/T system. They used water and Dimethyl‐Diphenyl silicone fluid (DMDP) to cool down and utilize the celltemperature. The solar cell-temperature was lower for the case of water compared to the DMDP case. Li et al. [15] applied CPC into PV/T system to develop new hybrid roof-top CPV/T system. The results show that any decrease in cell-temperature causes a substantial increase in current and electrical-efficiency. Saini et al. [16] evaluated the electrical and thermal performance of series-connected N partially covered CPC-PVT system for various solar cell material. The results indicate that the minimum gains were obtained for the case of amorphous silicon (a-Si) based solar cells because of the maximum solar cell-temperature. Wang et al. [17] made a performance analysis of a large-scale truncated CPC-PVT system with a configuration of multiple reflection elimination (EMR). EMR-CPC system has higher optical efficiency and uniformity of solar illumination compared to CPC system. Hadavinia and Singh [18] experimentally analyzed the CPC and V-trough system. The results show that the non-cooled CPC generates about 12.44% less power output than the cooled CPC due to the temperature increment of 30.9 ºC. It indicates a temperature reduction of 0.4% per 1ºC reduction. CPC generates a non-uniform illumination on the receiving area for high incidence angles in particular. It causes hot-spots on the PV and increases the cell-temperature. A non-uniform flux distribution can result in an increase in the cell-temperature and decrease in the open-circuit voltage in PV-cells and, consequently, in reduced cell efficiency. Cuevas and Lopez‐Romero [19] stated that the filling factor and yield decrease due to the increase of the non-uniform lighting ratio. Baig, et al. [20] examined the causes of the non-uniform distribution of CPVsystems to understand this effect. They indicate that the performance can be improved by reducing the effect of non-uniform. Franklin and Coventry [21] stated that the systems under non-uniform distribution experienced a decrease in open-circuit voltage and efficiency. Non3

Journal Pre-proof uniform temperature distribution in the solar cell causes the heat transfer in the cell to be affected, while a negative temperature coefficient reduces thermal performance [22]. Uniform heat distribution is essential not only for efficiency but also for ensuring long-term cell and concentrator reliability [23]. Considering a flat-plate reflector in a CPV application is the simplest way to achieve uniform illumination. V-trough includes two flat plate reflectors and has been considered as the best one in terms of uniformity of solar illumination [24]. V-trough may provide advantages with reduced complexity, increased uniformity of solar illumination and lower manufacturing cost [25]. Mosalam et al. [26] evaluated a V-trough concentrator on a photovoltaic system with two-axis solar tracing in a hot desert climate. For a concentration-ratio of 1.6, V-trough can generate 40% higher cell power than the cell without a concentrator. Singh et al. [25] carried out an experimental study about the low concentrating line axis concentrator photovoltaic system. The experimental data shows that the V-trough system can provide more uniform illumination and achieved about 17.2% higher electrical power output than the CPC system. Wang et al. [27] analyzed the performance of a photovoltaic-solar water disinfection system using V-trough. The results show that V-trough concentrators improve the power generation of the system significantly. This improvement becomes about 63% in the maximum case. Baig et al. [28] made an experimental analysis of V-trough PV/T. 35% improvement was achieved in the power output compared to a conventional PV. Elminshawy et al. [29] experimentally investigated V-Trough PV system combined with a heat exchanger cooling system. The surface temperature of the PV-module decrease from 72.5 ºC to about 39 ºC. A maximum power improvement of 28.3% was achieved for the case of a mass flow rate of 0.04 kg/s. V-trough concentrator may require more reflector area to achieve same concentration-ration with CPC. CPC and V-trough concentrators have been considered for the integration of PV applications in many studies. These concentrators can be operated with judicial efficiency, can exploit diffuse radiation as well as a direct one. However, they may have some problems for CPV applications, including non-uniform illumination, hot-spot generation, high PV-celltemperature for CPC. Moreover, they require a larger area of the reflector and have unwieldy sizes for both systems. Along with the CPC and V-trough, several other concentrators fall into the group of the non-imaging concentrator, and one of them is Compound Hyperbolic Concentrator (CHC). It can be defined by the surface of revolution whose cross-sectional profile is determined by two hyperbola geometry. CHC geometry requires much less reflector size to attain equal collection efficiency with a CPC [30]. It is a novel approach using the compound hyperbolic concentrator in a concentrating4

Journal Pre-proof photovoltaic application. Moreover, there is no study about the comparison of the CHC-PVT system with that of CPC and V-trough in terms of energy flux distribution, the PV-celltemperature and their effect on the performance parameters of CPV including electricalefficiency, power generation, current and voltage output. In this study, a numerical model was established for the evaluation of concentrating-photovoltaics. Three different non-imaging concentrators, CPC, V-trough and CHC-trumpet types were investigated to decide on the optimum design for a CPV application. The solar energy flux distribution was evaluated by using a Ray-tracing Model written in FORTRAN. In order to determine the PV-celltemperature, control volume method was applied into the systems. The PV-cell-temperature was evaluated as a function of the incident angles. The electrical efficiencies and power output of CPV-systems were determined regarding the incident angle and the PV-cell-temperature. The present study aims to make a comparison of CPV geometries to decide on an optimum design geometry and proposes a new type of CPVT-system. It will provide advantages for the CPV applications to achieve a cost-effective design and improved performance. 2. Analysis model 2.1. V-trough concentrator V-trough geometry is compounded of two flat plate reflectors. Therefore, they have advantages of easy manufacturing and requires low-cost.

Figure 1. 2-D geometry of V-trough Concentration -PV system The cross-sectional geometry of V-trough concentrator is shown in Fig. 1. In this study, V-trough concentrator is considered to have a design in which a solar ray came with the normal incident angle at the edge of reflector reaches the full center of PV length Aa, and the other rays scatter the half part of the PV which is close to the reflector. The maximum acceptance angle 5

Journal Pre-proof max of the V-trough concentrator can be calculated by the following equation [31].  max  2  

(1)

where  is the acceptance angle of the concentrator. The length of V-trough reflector h can be calculated with the following equation. h

Aa cos 2 2 sin

(2)

The concentration-ratio is an important parameter and can be described as the ratio of the aperture area of the concentrator to the receiving area. The following equation can represent the concentration-ratio Cvt of a V-trough concentrator. Cvt 

Aa 2  2 Ac tan   1

(3)

2.2. Compound Parabolic Concentrator CPC compounds of two parabolic concentrators and they are placed on the focus point of each other. A CPC can concentrate all radiation pass through the reflector aperture within the acceptance angle to the receiving area [8].

Figure 2. 2-D geometry of Compound Parabolic Concentration (CPC)-PV system The cross-sectional geometry of a CPC is given in Fig. 2. The geometry of a CPC can be formed by using the following equation [8].

y

x2 2 s (1  sin  max )

(4)

where s represents the cross-sectional length of receiver. The concentration-ratio of a full CPC can be obtained by the following equation [8]. 6

Journal Pre-proof Ccpc 

Ac 1  Aa sin  max

(5)

In order to obtain a cross-sectional geometry of a CPC, a parabola should be rotated depending on the acceptance angle. The coordinates of a CPC can be obtained by resolving the equations depending on the acceptance angle, as seen in the following equation [32].

xN  ( s   ) cos 2  max 

x 2 sin  max 2 s (1  sin  max )

yN  ( s   )sin  max cos  max 

(6)

x 2 cos  max 2s(1  sin  max )

where  value changes from 0 to the aperture length, L to alternate the reflector size. 2.3. Compound Hyperbolic Concentrator-Trumpet A trumpet type geometry is a particular type of CHC. The cross-sectional geometry of a trumpet type non-imaging concentrator is shown in Fig 3.

Figure 3. 2-D geometry of Compound Hyperbolic Concentration (CHC)-PV system CHC uses a virtual focus that can cause multiple reflections to arrive the solar rays at an angle close to the acceptance angle before reaching the receiver. CHC reflector can have an unlimited length as an ideal concentrator. Therefore, the size of the CHC has to limit to certain dimensions [33]. The curve of trumpet type concentration can be calculated by the following formula. 2   s   4x y   2  1  2 tan    s 

0.5

(7)

The concentration-ratio of CHC Trumpet type concentrator can be obtained by the following 7

Journal Pre-proof equation [34]. Cchc 

2c Ac 1   2a Aa sin  max

(8)

where 2a is the length of receiver and 2c is the length between imaginary focal points. The coordinates of x-axis can be calculated by the following equation

s  s(1  sin  )  C ( x2 )     sin  2  2sin  

(9)

where  value is changed between 0 ≤  ≤ /2 in order to attain 2-D geometry. When  becomes /2, x coordinate of point C and hence the length of aperture L can be obtained. 3. Analysis method 3.1. Thermal modelling of PV-module

Figure 4 Energy balance of PVT system with copper pipe The solar radiation within the visible and near-infrared region is converted into electricity in accordance with the characteristic of PV and its performance. The rest of the energy is converted into heat. This heat removes through the convection and radiation from the upper and lower part of the PV-module, as seen in Figure 4. In order to decide the celltemperature and the temperature distribution on PV, a numerical analysis was carried out by using the finite volume method.

8

Journal Pre-proof

Fig. 5. Different characteristic regions on the PV component The solar radiation on the aperture of the concentrator divided into 5000 rays. The 2-D size of PV-module was considered having a thickness of 0.02 m and a width of 0.1 m. PV-cell was divided into 2000 elements, and the solar radiation reaching each element on the upper boundary of PV was decided using the Ray-tracing method (Fig. 5). The ray-tracing analysis written in FORTRAN was validated with experimental evaluation and verified by comparing our results to the studies carried out in the literature [35,36]. In order to facilitate the evaluation; the following assumptions have been made 

Two-dimensional (2D) thermal model was considered since the 2D cross-section shows a similar characteristic along with the reflector length.



PV-cell was considered having a specific-heat capacity, cPV of 677 J/kg.K and a density,

PV of 2330 kg/m3. They are independent of the temperature variation. 

The glass and EVA layers on PV-cell were taken into account in the calculation of optical performance.



PV-module was considered having an average conductivity, kPV of 40 W/mK.



The mass flow rate within the copper pipe is considered uniform.



The optical properties of PV, including reflectivity, transmissivity and absorptivity, were independent of the temperature.



Internal reflections within the transparent layers of the PV were neglected.



Radiative heat loss from the backside of the PV-module was not taken into account



Emissivity  of PV-cell was independent of the wavelength and the surface temperature.



PV-panel has the direct heat transfer into ambient, sky and working fluids.



The view factor was considered to be unity.



Incident solar radiation was assumed to be 1000 W/m2.



Diffuse radiation effect was not taking into account.

The overall energy balance on PV-module can be written as follows.

9

Journal Pre-proof

 PV cPV

dTPV  opt qs   hrad Tsky  TPV   hconv1 (Tamb  TPV )  hconv 2 (T fluid  TPV ) dt   2TPV ( x, y )  2TPV ( x, y )   k pv     Eelec 2 2  x  y  

(10)

opt indicates the optical efficiency of CPV-system and can be calculated as a function of the reflectivity of the reflector, transmissivity of the glass-cover and the absorptivity of the PV-cell. qs represents the incident solar insolation coming to the tilted surface. It was decided in accordance with the incident angle of solar radiation. Different energy balance was applied for different areas in PV as its borders are indicated in Fig. 5. The discretization equation is derived by integration of Eq.10 over the control volume and over the time interval from t to t+t as in the following [37]. e n t t

 PV cPV   w s

 t

T t xy  t

t t n e

 t

   T   s w  x  k x  xyt 

t t n e

   T  

    y  k y  yxt t

s w

t t n e



(11)

   S xyt t

s w

The full implicit method was considered for the evaluation of the control volume. Thus, the weighting factor f was considered to be one after the integration over control volume and time in the following equation [37]. c

 k (T  T ) k (T  T )   k (T  TP ) k S (TP  TS )   xy P W TP  TP0   f  e E  w P y   N N    x      x  t  x w   x s     x e n 

(12)

 k (T  T ) k (T  T )   k (T  T ) k S (T  T )   e  w   y   N  x   S xy  x  w   x s     x e   x n

1  f  

0 E

0 P

0 P

0 W

0 N

0 P

0 P

0 S

The source term S states two parts (Sc+SpT). One is the coefficient of the temperature Sp, and the other one is constant part Sc. Identifying the values as in the followings can simplify the equation for the numerical analysis [37].

aE  ke

y ,  x e

aP0   c

aW  kw

y ,  x  w

aN  kn

x ,  y n

xy 0 0 , b  Sc xy  aPTp , t

aS  k s

x  y  s

(13) (14)

a p  aE  aN  aS  a 0p  S p xy

(15)

Sc  opt qs  Eelec  hconv1T f  hconv 2Tamb   hrad Tsky

(16)

S P  hconv1  hconv 2   hrad

(17) 10

Journal Pre-proof Where the radiative heat transfer coefficient hrad can be calculated by the following equation [38] 2 2 hrad  TPV  Tsky TPV  Tsky 

(18)

Identifying above parameters, the following equations is obtained [37].

aPTP  aETE  aW TW  aN TN  aS TS  b

(19)

The over-relaxation process was applied into the equation by introducing of relaxation factor  as in the following [37]

 a T  b 0 TP  TP0    nb nb  TP  aP  

(20)

3.2. Electrical modelling of PV-module The temperature affects all parameter in PV-cell characteristic. Its effect mainly appears on the open-circuit voltage, VOC and dark-saturation-current, Io of PV-cell. The current-density of a PV-cell can be described by [39]

J  J SC  J 0  eV

aVT

 1

(21)

where JSC and JO are the silicon short-circuit current and the dark-saturation densities, respectively. V is the output voltage of the module. a is diode ideality-factor. The thermal voltage of a cell, VT can be calculated by the following equation [40]

VT 

kboltzTPV q

(22)

where q is the charge of an electron (1.602×10−19 C), k is the Boltzmann constant (1.3806×10−23 J/K), Tcell is cell-temperature. The current value generated by PV-cell can be calculated as follows [41]

I PV 

J SC APV G  J 0 APV  eV 1000

aVT

 1

(23)

Rearranging of Eq. 11, the following can be obtained [41]

I PV  I L  I D  I L  I 0  eV

aVT

 1

(24)

where IL is called light-generated current and becomes identical with the short-circuit current for an ideal solar cell. The ID is the current of the diode. The dark-saturation-current, I0 as a function of short-circuit current can be calculated as in the following [41].

I 0  I SC

e

VOC aVT



1

(25) 11

Journal Pre-proof There are some losses arisen from the resistance in current flowing in the electrodes and silicon. Incorporating with series resistance, the current of PV-panel can be presented by [42]

  V  IRS I PV  I L  I 0 exp   aVT 

    1  

(26)

In this equation, the temperature variation is not taken into account. This model includes five unknown parameters including IL, I0, a, Rs and Rsh. The current-voltage (I-V) curve for a single junction PV-module under standard test condition using a single diode equivalent circuit can be described by following equation [43].

I PV  I L  I D  I p

(27)

This equation can be detailed as in the following equation [44]

  V  IRS I PV  I L  I 0 exp   aVT 

  V  IRS   1  RSH  

(28)

where RS is the series resistance of the PV-cell. The parallel resistance RSH can be considered having an infinity value to be ignored. When the effect of temperature is considered in the shortcircuit current and without taking into account the series resistance in the current flowing in the electrodes and silicon, the following model can be obtained [41].

I PV  I SC,ref 1  K i T 

  V I SC G  exp  Gref exp VOC / (aVT )   1   aVT

    1  

(29)

where the first term of the equation is can be described as light-generated current regarding the solar irradiation and cell-temperature. It is assumed as equal to the short-circuit current ISC for ideal cases [45]. I L  I SC 

G  ISC,ref  Ki ISC,ref T  Gref

(30)

where T indicates the difference between the cell-temperature and the reference temperature of the PV-cell. The short-circuit current ISC,ref is obtained by multiplying of the reference value of short-circuit current-density, JSC,ref with PV area (JSC,ref=36.1 mA.cm-2) [46]. Ki is the temperature coefficient of the short-circuit current (Ki=0.0035/K) [41]. VOC can be calculated by

J  I  VOC  aVT ln  SC  1  aVT ln  SC  1  J0   I0 

(31)

where the dark-saturation densities, JO is 10-12 A.cm-2 [41,47] and the ideality-factor , a is considered as 1.5 [44] for the silicon-based solar cell. 12

Journal Pre-proof The following equation expresses the electrical-efficiency of PV depending on celltemperature [48].

elec  ref [1   ref (TPV  Tref )]

(32)

where ref is the electrical-efficiency of the PV-cell at the reference temperature Tref. By considering the incident radiation depending on the optical performance, the electrical energy output Eelec can be calculated by





Eelec  qsopt ref 1   ref TPV  Tref    

(33)

ref is the temperature coefficient and given by the following equation

 ref 

1 T0  Tref

(34)

where T0 is the maximum working temperature of the PV-module when elec drops to zero [49]. The temperature can increase up to 270ºC for crystal silicon solar cell [48]. Thus, the temperature coefficient varies between 0.002 and 0.0045, depending on the disposition of PV. This value increases up to 0.0063 [50–52]. Figure 6 shows the flow chart of the PV power output and electrical-efficiency as a function of optical performance and PV-cell-temperature.

Figure 6. Flow chart of the numerical model for Ray-tracing and electrical performance 4. Results and Discussion 4.1. Optical performance of CPVs 13

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Table 1 demonstrates the design parameters of the concentrators. The length of AB in CPC, V-trough and CHC-trumpet geometries indicates the PV length. The length of CB shows the length of one side of the reflectors h in 2D cross-section. The length of CPV meant the length of the system in the z-axis. It was defined to determine the incident power. Table 1. Geometrical design parameters of CPC, V-trough and CHC-trumpet Parameter CPC V-trough CHC-Trumpet 31 21 Acceptance angle  Maximum Acceptance angle θmax 31 41 54 10 Trough angle  Concentration-ratio C 1.94 1.94 1.94 Length of PV-cell (m) 0.1 0.1 0.1 Length of CPV (m) 1.64 1.64 1.64 Length of reflector h (m) 0.251 0.27 0.147 Surface area of reflector Ar (m2) 0.824 0.887 0.483 0.9 0.9 0.9 Reflectivity of reflector r Transmissivity of glass cover τc 0.92 0.92 0.92 Transmissivity of EVA τc 0.9 0.9 0.9 0.95 0.95 0.95 Absorptivity of PV PV Figure 7 shows the optical efficiency of the PV-CPV, V-trough and CHC-trumpet type concentrators. CPC cannot utilize the radiation out of the maximum acceptance angle of 31º while the V-trough and CHC-trumpet types can concentrate the radiation until the incident angle of 41º and about 54º, respectively. CPC and V-trough show similar performances up to the incident angle of 21º, and then, there is a reduction in the optical efficiency of the V-trough system. The optical efficiency of the PV-CHC-trumpet system gradually decreases until its

Optical efficiency th

acceptance angle.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 0.0

CPC V-trough CHC-trumpet

0

10

20 30 40 Incident angle 

50

60

Figure 7. Optical efficiency of the PV-CPV, V-trough and CHC-trumpet type concentrator 14

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4.2. Energy flux distribution on PV surface The solar illumination infrequently reveals a uniform illumination across the receiving area. Therefore, it is quite essential to investigate the flux distribution on the PV to decide the uniformity. The maximum acceptance angles of V-trough and CHC-trumpet geometries are much broader than CPC. It indicates that these geometries will collect more energy in the absence of a solar tracking system. Figure 8 illustrates the energy flux distribution on PV of CPC, V-trough and CHCtrumpet concentrators. CPC has uniform illumination only for the incident angle which is close to normal incident. When the incident angle gets close to the maximum acceptance angle, the solar radiation proceeds to concentrate into a smaller area, thereby increasing the heat flux. This condensed heat flux can cause hot-spots and a temperature increase in the PV-cell. Therefore, CPC geometry may not be preferred in terms of uniformity since a uniform illumination solar radiation is quite crucial for the power output of PV. Around the maximum incident angle, the energy flux can reach up to ten times of the those of V-trough and CHC-trumpet. This much heat flux may shorten the effective life cycle or even damages the PV-cell. On the other hand, V-trough and CHC-trumpet geometries show a quite similar characteristic with a slight change in the heat flux distribution. Most of the radiation concentrates on a more substantial area on the PV-cell. The center area of PV collect much more radiation compared to the edge of the cell; however, the difference is not as much as a CPC. It can be claimed that there are no hot-spots occurs for the case of V-trough and CHCtrumpet. The maximum energy flux of only about 4000 W/m2 occurs for both cases. These geometries may give a significant advantage for the efficiency of CPV-systems due to reasonably uniform illumination of solar radiation.

15

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Figure 8. Solar energy flux on the CPC-PV (a) V-trough-PV (b) and CHC-trumpet-PV (c)

16

Journal Pre-proof 4.3. Temperature distribution in PV-cell Solar cell under the concentrated radiation generates larger currents while it slightly affects the voltage generation. It causes an increase in power output. It is desired to get a uniform solar illumination on PV-cell; however, it could be inevitable that a portion of the solar cell may be illuminated by the excessive light, which generates a large current and heat or rarely is exposed to the radiation. This excessive radiation causes hot-spot thereby increasing the temperature. As is known, the electrical-efficiency is strongly related to PV temperature. Therefore, the cell-temperature is an essential factor to decide the actual performance. The solar radiation reaches to PV-cell depending on the optical performance of the CPVsystem. PV-cell generates electricity regarding its electrical-efficiency. The rest of this energy incline the temperature of the PV-module depending on conductivity, density and specific-heat of the component of the PV-module. A portion of this heat is transferred through the radiation and convection into ambient or copper pipe circulating cooling water. Figure 9 shows temperature distribution on CPC-PV system for various incident angles. In the case of the normal incident angle, the temperature distribution can be assumed mostly uniform while the cooling water circulating in the copper pipe decreases the temperature of PV. Increase in the degree of the incident angle alter the temperature distribution and arise a nonuniform distribution. A hot-spot starts to occur from the incident angle of 15 and that spot tends toward the right side of PV. Increase in the incident angle makes the hot-spot clear and the cooling effect of circulating water decrease. The maximum temperature difference increase from 2.5ºC to more than 7ºC as the incident angle varies from the normal incident to the maximum acceptance angle.

17

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Figure 9. Temperature distribution on CPC-PV system for the incident angle of 0 (a), 5 (b), 10 (c), 15 (d), 20 (e), 25 (f), 28 (g) and 30 18

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Figure 10. Temperature distribution on PV-V-trough system for the incident angle of 0 (a), 5 (b), 10 (c), 15 (d), 20 (e), 25 (f), 30 (g) and 35 19

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Figure 11. Temperature distribution on PV-CHC-trumpet system for the incident angle of 0 (a), 5 (b), 10 (c), 15 (d), 20 (e), 25 (f), 30 (g) and 35 20

Journal Pre-proof Figure 10 shows the temperature distribution for the case of PV-V-trough system. Until the incident angle of 15º temperature distribution is mostly uniform in the upper part of PV while the center temperature of the bottom side of PV decrease due to the cooling fluid. After this angle, the temperature of the temperature difference between the left and right sides of the PV-cell increase, while PV-cell-temperature on the right side decreases. This decrement arises from the reduction of the intensity of solar radiation. The maximum temperature difference decrease from 2.1ºC to 0.5 ºC. Figure 11 illustrates the temperature distribution for PV-CHCtrumpet system. This system also shows a quite similar characteristic with V-trough system. The upper part of PV is mostly uniform up to the incident angle 20º then the difference starts to increase. The maximum temperature difference decreases about from 2ºC to 1.2 ºC from the normal incident to incident angle of 35º, respectively. The results indicate that V-trough and

Hot Spots Temperature on PV (K)

Average temperature of PV (K)

CHC-trumpet have a quite uniform illumination and temperature distribution compare to CPC.

a

310 308 306 304 302 300

CPC-PVT V-trough-PVT CHC-PVT

298 296

0

10 20 30 Incident angle 

40

b

310 308 306 304 302 300

CPC-PVT V-trough-PVT CHC-PVT

298 296

0

10 20 Incident angle 

30

40

Fig. 12. Average (a) and hot-spot (b) temperatures of PV adapted with CPC, V-trough and CHC-trumpet system The hot-spots and average temperatures of PV was illustrated for all concentrators in 21

Journal Pre-proof Fig. 12. The average temperature of PVs for CPC and V-trough is almost identical and remains around a temperature of 304 K up to the incident angle of 20º, and then it remains stable for CPC while that of V-trough decreases due to lower energy collection. The average temperature of CHC-trumpet gradually decreases by increasing of incident angle. The hot-spots temperatures are quite essential to decide non-uniformity. As seen in Fig. 12b, the highest temperature occurs for the case of CPC then followed by V-trough and CHC-trumpet. This case changes after the incident angle of 27º, then the temperature of V-trough decreases under that of CHC. After the incident angle of 20º, the temperature of CPC increases significantly as that of V-trough decrease until the incident angle of 40º. 4.4. Electrical performance of PV-cell The temperature increase and non-uniform illumination on PV-cell have an adverse effect on the solar cell efficiency as well as the VOC. Therefore, solar irradiation and cell-temperature are critical issues for the performance characteristic of a photovoltaic system. In this study, an ideal single diode model as a function of cell-temperature and solar irradiation was considered to evaluate the CPV-systems. The model requires the light-generated current (IL), saturationcurrent (IO), and ideality-factor (a). The solar irradiation on the PV-cell (G) was calculated through the ray-tracing analysis. Gref was considered to be 1000 W/m2. The cell-temperature was taken into account to calculate the IL and IO. Eventually, the current of the system can be obtained for the voltage variation. A single solar cell having a size of 100mmx100mm was adapted to concentrators. Figure 13 illustrates the I-V curves of the CPVT-systems. In Fig.13a, the normal incidence angle was considered. The most extensive incidence radiation was achieved for the case of Vtrough to be 1375.5 W/m2. It is followed by CPC (1358 W/m2) and CHC (1351.1 W/m2) cases, respectively. The ISC values were about 5.02 A, 5.08 A and 4.99 A for CPC, V-trough and CHC cases. The largest ISC achieved in the case of V-trough. However, the difference between the CPV-systems is insignificant. The VOC values were 0.95 V for all cases. For the incidence angle of 10º, the solar intensity slightly decreases for the cases of CPC and V-trough while the reduction reaches to about 12.5% for the CHC-PVT. The ISC values become about 5.014 A, 4.99 A and 4.35 A for CPC, V-trough and CHC cases. CPC and V-trough systems show very similar values. This reduction in the CHC arisen from the lower solar energy collection at this incidence angle. The optical efficiency of the systems enlightens about the characteristics of the systems regarding the incidence angle. The solar intensity for CPC, V-trough and CHC at 22

Journal Pre-proof the incidence angle of 20º reduced by 6.9%, 11.8% and 28.9 % compared to the cases at the normal incidence angle (Fig. 13c). The short-circuit currents become 4.67 A, 4.47 A, and 3.52 A for CPC, V-trough and CHC at this incidence angle. The reduction in the ISC is strongly related to solar intensity. The temperature effect on the VOC is quite minimal for these systems due to the slight variation of cell-temperature. A significant reduction of about 58.7% occurs at 30º for the case of V-trough compare to the normal incidence angle. For the case of CPC-PVT system, the reduction in the ISC is only 16.6% from 0º to 30º. The short-circuit currents become 4.23 A, 2.17 A and 2.55 A for CPC, V-trough and CHC, respectively (Fig. 13d). 6

Current I (A)

5

b

o

0

V-trough CPC

6 o

5

CHC

4

Current I (A)

a

3 2

CPC V-trough

0 0.0

3 2 2

CPC-PVT (1358 W/m ) 2 V-trough-PVT (1375.5 W/m ) 2 CHC-PVT (1351.1 W/m )

0.2

0.4

0.6

1

0.8

0 0.0

1.0

CPC-PVT (1354.13 W/m ) 2 V-trough-PVT (1350.6 W/m ) 2 CHC-PVT (1182.3 W/m )

0.2

Voltage (V)

Current I (A)

d

6 o

20

5

V-trough CHC

3 2

0 0.0

0.4

0.6

1.0

o

30 CPC

4 3

CHC

2

V-trough 2

CPC-PVT (1264.32 W/m ) 2 V-trough-PVT (1212.92 W/m ) 2 CHC-PVT (960.62 W/m )

0.2

0.8

6

2

1

0.6

5

CPC

4

0.4

Voltage (V)

Current I (A)

c

CHC

4

2

1

10

1 0.8

1.0

Voltage (V)

0 0.0

CPC-PVT (1131.5 W/m ) 2 V-trough-PVT (597.65 W/m ) 2 CHC-PVT (699.92 W/m )

0.2

0.4

0.6

0.8

1.0

Voltage (V)

Fig. 13. Current-Voltage (I-V) curves of CPC-PVT, V-trough-PVT and CHC-PVT systems for normal incidence angle (a) 10º (b), 20º (c), and 30º(d) incidence angles Figure 14 shows the P-V curves of the CPVT. The maximum power point of the CPVT-system was achieved at the voltage around 0.83-0.84. In Fig. 14a, the P-V curves at the normal incidence angle are illustrated. All system systems show a quite similar characteristic. The maximum power, Pmax of the CPC, V-trough and CHC-PVT systems become 4.01 W, 4.05 W 23

Journal Pre-proof and 3.98 W, respectively. While the incidence angle increases, the electrical output of the systems decrease due to the less incidence radiation, this reduction is quite low for the case of CPC. Until the incidence angle of 10º, Pmax of the CPC-PVT system remains stable (4 W). Vtrough and CHC system reduced by 1.97% and 13% and become 3.97 W and 3.46 W, respectively (Fig. 14b). CHC-PVT system is the most influenced one from the increase of incidence angle. The difference between the CPC and V-trough becomes apparent at the incidence angle of 20º. Pmax values of 3.73 W, 3.56 W and 2.79 W are obtained for the case of CPC, V-trough and CHC-PVT systems, respectively. The maximum power output of V-trough suddenly decreases by 58% while that of CHC decreased by 49.3% for the incidence angle of 30º compared to the normal incidence angle, and becomes 1.7 W and 2.02 W, respectively. In the case of CPC, the maximum power becomes 3.41 with a reduction of 14.9% compared to the normal incidence. 5

Power P (W)

4

b

o

2

CPC-PVT (1358 W/m ) 2 V-trough-PVT (1375.5 W/m ) 2 CHC-PVT (1351.1 W/m )

0

V-trough

3 2 1 0 0.0

5 4

CPC CHC

Power P (W)

a

2

CPC-PVT (1354.13 W/m ) 2 V-trough-PVT (1350.6 W/m ) 2 CHC-PVT (1182.3 W/m ) CPC

V-trough

3

CHC

2 1

0.2

0.4

0.6

0.8

0 0.0

1.0

0.2

Voltage (V) 5

Power P (W)

4

2

o

CPC-PVT (1264.32 W/m ) 2 V-trough-PVT (1212.92 W/m ) 2 CHC-PVT (960.62 W/m )

3

CPC

d

20

5 4

V-trough CHC

2

0.6

0.2

0.4

0.8

2

1.0

0.6

0.8

30

3 CPC

2

0 0.0

1.0

o

CPC-PVT (1131.5 W/m ) 2 V-trough-PVT (597.65 W/m ) 2 CHC-PVT (699.92 W/m )

CHC V-trough

1

1 0 0.0

0.4

Voltage (V)

Power P (W)

c

o

10

0.2

0.4

0.6

0.8

1.0

Voltage (V)

Voltage (V)

Fig. 14. Power-Voltage (P-V) curves of CPC-PVT, V-trough-PVT and CHC-PVT systems for normal incidence angle (a) 10º (b), 20º (c), and 30º(d) incidence angles The effect of the temperature can be seen more apparently for electrical-efficiency calculation. 24

Journal Pre-proof In order to investigate the temperature effect on the cell performance, a photovoltaic system having an electrical-efficiency (ref) of 19% was selected. The reference temperature and the temperature coefficient were taken to be 298 K and 0.0041, respectively. Total of five modules constitutes each CPVT-system. The highest temperature was set as a PV-cell-temperature since the final temperature of the PV is affected mostly by the highest temperature. Thus, the effect of hot-spots can be indicated. The analysis was carried out using the FORTRAN program. Figure 15 shows the electrical efficiencies of CPVTs. The electrical-efficiency of the PV slightly changes up to the incident angle of 25º for CPC case and then decreases. The efficiency of the PV for CHC-trumpet case is higher than that of CPC and V-trough, and it improves as the incident angle gets close to the maximum acceptance angle. The average efficiencies of the PVs for CPC, V-trough and CHC-trumpet cases are 18.41%, 18.62% and 18.65% within their acceptance angle, respectively. Within the incident angle of 23.45º, which is the declination angle, the electrical efficiencies are about 18.44%, 18.51% and 18.59%, for PV-CPC, PV-Vtrough and PV-CHC systems, respectively. The differences between the electrical-efficiency of the PV using CHC and those of the others are getting more significant as the incidence angle increases. PV with CHC-trumpet shows a significant advantage at the incident angle of 20º. The electrical efficiencies of PV systems using V-trough and CHC concentrators become identical to be about 18.69% at the incidence angle of 26.76º. After this angle, the most substantial efficiency was achieved for PV with V-trough one due to its low cell-temperature. The solar radiation density is low for higher incident angles. Thus, the cell-temperature

Electrical Efficiency elec

decreases.

0.190

CPC V-trough CHC

0.188 0.186 0.184 0.182

0

10 20 30 Incident angle 

40

Fig. 15. Electrical-efficiency of CPC, V-trough and CHC-PVT systems as a function of celltemperature and incidence angle Consequently, PV with CHC reflector shows a better performance compared to the other system 25

Journal Pre-proof in term of electrical-efficiency. However; it is vital to investigate the electrical power output to decide the actual improvement potential of concentrator systems. The aperture area is calculated to be about 0.318 m2 for each CPVT module. A total of five modules constitute a CPVT panel (Fig. 16). Thus, each CPVT panel has an aperture area of 1.592 m2 and a PV-panel area of 0.82 m2. Figure 16 illustrates the cross-sectional geometry of the concentrators with the same concentration-ratio to provide an insight into the size characterization.

Fig. 16. Cross-sectional geometry of CPC-PVT, V-trough-PVT and CHC-PVT panels Figure 17 shows the electrical power output of panels. Their electrical power generations become 205.5 W, 208.4 W and 204.8 W for normal incidence angle in the case of CPC-PVT, VT-PVT and CHC-PVT systems, respectively. All systems have quite similar power generation value and electrical performance for this incidence angle. CHC-PVT system may provide substantial advantages for a CPVT using the sun tracing system since it can provide similar power generation with almost halve reflector material. CPC and V-trough system generate quite similar power generation with slight difference until the incidence angle of 10º. At this level, the average values are 205.4 W, 206.9 W and 192.7 W for CPC, V-trough and CHC. After 10º, the difference between the power generation of both system increases. CPC shows superior performance with an only slight reduction in the power generation up to the acceptance angle of 31º. The power generation of V-trough system decreases slightly up to the acceptance angle of 21º. Then, the reduction becomes rapid up to the incidence angle of 40º in which the power generation becomes zero. On the other hand, the electrical power generation 26

Journal Pre-proof for CHC-trumpet gradually decreases, and it continues even after the incident angle of 40º due to its larger acceptance angle. It may take an advantage in the early morning, late afternoon hours and annual energy collection. The average power generation until 23.45º becomes about 197.45 W, 191.16 W and 165.6 W CPC-PVT, VT-PVT and CHC-PVT systems, respectively. Although the PV with the CPC system has lower electrical-efficiency than the others, its power generation is quite large compared to the CHC system due to higher energy collection capacity of the CPC. On the other hand, in order to achieve that much high energy collection, CPC requires almost two times more reflector material. The share of the PV price in the capital cost is getting decrease with the technological development. Thus, the price of the reflector becomes upfront in the total amount.

Power Output (W)

Therefore, it is essential to consider the reflector area used in the CPVT-systems.

225 200 175 150 125 100 75 50 25 0

CPC V-trough CHC-Trumpet

0

5

10 15 20 25 30 35 40 Incident angle 

Fig. 17. Electrical power output of CPC-PVT, V-trough-PVT and CHC-PVT panels as a function of reflector area The analyzed concentrators with the same concentration-ratio requires different reflector sizes. Therefore, further evaluation may be required to make a reasonable comparison among CPVT panels. CHC-trumpet reflector needs almost as half-size as that of V-trough or CPC system to attain similar concentration. In order to take into account of reflector size, the power output of photovoltaic panel per reflector surface area was calculated as illustrated in Fig. 18. The power outputs within the incident angle of 23.45º for the CPC-PVT, VT-PVT and CHCT-PVT systems were 47.9 kW, 43.7 kW and 68.5 kW, respectively. The V-trough has about 10% lower power generation compared to the CPC-PVT system. In the case of CHCT-PVT, the power output was about 42.9% higher than the CPC-PVT and about 58.97% higher than the VT-PVT systems per the reflector unit area. CHC-PVT system shows significantly better performance compare to 27

Journal Pre-proof the other CPV-panels when the performance is considered per reflector area. It is followed by the CPC system with stable power output until the maximum acceptance angle. V-trough needs the largest reflector area compared to the others. Therefore, it has the lowest performance per reflector area. It is not an actual power output; however, this is important to show the performance depending on the reflector size. The results indicate that CHC-trumpet system generates the cheapest energy. CHC-trumpet concentrator may be worthy of considering in the

Power Output (W/m2)

concentrating-photovoltaic applications.

90 80 70 60 50 40 30 20 10 0

CPC V-trough CHC-Trumpet

0

5

10 15 20 25 30 35 40 Incident angle 

Fig. 18. Electrical power output of PV-CPC, V-trough and CHC-trumpet panels per reflector surface area 5. Conclusion A novel configuration of a concentrating-photovoltaic system, compound hyperbolic concentrator-trumpet type- photovoltaic-thermal system (CHCT-PVT), was considered to improve the electrical-efficiency by reducing the size of the reflector. The system was compared to the PVT system combined with the conventional concentrators, Compound parabolic (CPC), V-trough. In order to decide the electrical-efficiency and power output, the temperature effect was taken into account. 2D Ray-tracing analysis was carried out to decide the energy flux on the PV-cell of CPVT-systems. A numerical model was applied to decide the temperature of 2DPV-cell. The electrical performance parameters including; power, current, voltage, short-circuit current and open circuit voltages were considered for the evaluation by taking into account the solar irradiation and cell-temperature. The followings points summarize the study. 1. CPC provides the uniform illumination only around the normal incident angle of solar rays. On the other hand, V-trough and CHC-trumpet geometries show a quite similar characteristic with reasonably uniform illuminations. 28

Journal Pre-proof 2. All system can provide similar power, current and voltage for normal incidence angle. Therefore, CHC-PVT system comes to the forefront among the conventional nonimaging geometries due to its less reflector requirement for the same concentration-ratio. 3. The electrical-efficiency is strongly related to the cell-temperature. Even a little increase in cell-temperature has an adverse effect on electrical-efficiency. Therefore, the electrical-efficiency of the PV using the CHC system is higher than that of CPC and Vtrough. 4. CPC and V-trough system generate quite similar power generation with a slight difference. CPC shows a preferable performance with an only slight reduction in the power generation up to the acceptance angle. Their electrical power generations become 205.5 W, 208.4 W and 204.8 W for normal incidence angle in the case of CPC-PVT, VT-PVT and CHC-PVT systems, respectively. 5. In the case of CHCT-PVT, the power output was about 42.9% higher than the CPCPVT and about 58.97% higher than the VT-PVT systems per the reflector unit area. CHC-PVT system shows significantly better performance compare to the other CPVpanels when the performance is considered per reflector area. The results indicate that CHC-trumpet system generates the cheapest energy. 6. This study is an essential start for the evaluation of another type of non-imaging concentrators in the photovoltaic-thermal applications. The experimental analysis can provide advancement of the system more clearly in the real operation condition. CPVsystem can be evaluated to reveal the advancement of CHC for a cheaper solar system instead of CPVT-system. Acknowledgments This present work was developed within the framework of a research project entitled with ‘‘Design, installation and performance evaluation of a novel compound parabolic concentratorphotovoltaic-thermal system (PVT-CPC) (216M051)’’, fully funded by The Scientific and Technological Research Council of Turkey (TUBITAK). The authors would like to thank TUBITAK for the financial support given to the projects. All responsibility for the content of this publication lies with the author. We thank for the support. Nomenclature a

Half-length of receiver on CHC reflector 29

(m)

Journal Pre-proof a

Diode ideality-factor

(-)

Ac

Aperture area of the concentrator

(m2)

Aa

Receiver area of concentrator, absorber surface area

(m2)

APV

PV surface area

(m2)

Ar

Surface area of reflector

(m2)

c

Half-length between imaginary focal points on CHC reflector

(m)

CVT

Concentration-ratio of V-trough

(-)

CCPC

Concentration-ratio of CPC

(-)

CCHC Concentration-ratio of CHC

(-)

cPV

Specific-heat capacity of PV

(kJ·kg-1·K-1)

Eelec

Electrical power of CPV-systems

(W/m2)

G

Solar irradiation

(W/m2)

Gref

Solar irradiation at standard test condition (1000)

(W/m2)

h

Length of one side reflector in 2-D cross-section

(m)

hconv

Convective heat transfer coefficient

(W·m-2·K-1)

hrad

Radiative heat transfer coefficient

(W·m-2·K-1)

IL

Light-generated current

(A)

IO

Dark-saturation-current

(A)

ISC

Short-circuit current

(A)

ISC,ref Light-generated current at standard test conditions

(A)

J

Current-density

(A·cm-2)

JSC

Short-circuit current-density

(A·cm-2)

JO

Dark-saturation density (1x10-12)

(A·cm-2)

kboltz

Boltzmann constant (1.3806×10−23)

(J·K-1)

kPV

Thermal conductivity of PV-cell

(W·m-1·K-1)

Ki

Temperature coefficient of short-circuit current

(K-1)

L

Aperture length of CPV

(m)

s

Receiver length of CPC

(m)

S

Source term states two parts (Sc+SpT).

(W.m-2)

Sc

Constant part of source terms

(W.m-2)

Sp

Coefficient of the temperature

(W.m-2·K-1)

T0

Maximum working temperature of PV-module

(K)

TP

Grid temperature in control volume of PV-cell

(K)

TPV

PV-cell-temperature

(K) 30

Journal Pre-proof Tref

Reference temperature of PV (25 ºC)

(K)

Tamb

Ambient temperature

(K)

Tf

Working fluid temperature

(K)

Tsky

Sky temperature

(K)

qs

Solar insolation

(W·m-2)

q

Charge of an electron (1.602×10−19)

(C)

V

Voltage

(V)

VOC

Open circuit voltage

(V)

VT

Thermal voltage

(V)

Greek letters αPV

Absorptivity of the PV-cell

(-)

βref

Temperature coefficient

(K-1)

δ

Acceptance angle of V-trough reflector

(dgr.)

ε

Emissivity of the PV-cell

(-)

elec

Electrical-efficiency

(-)

opt

Optical efficiency

(-)

ref

Reference efficiency of PV-cell

(-)



Incidence angle

(dgr.)

max

Maximum acceptance angle

(dgr.)

PV

Density of PV-cell

(kg·m-3)

r

Reflectivity of reflector

(-)

σ

Stefan–Boltzmann constant

(W·m-2·K-4)

τc

Transmissivity of glass cover on PV-cell

(-)

τEVA

Transmissivity of glass cover on PV-cell

(-)



Trough angle of V-trough reflector

(dgr.)

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CRediT author statement Abid Ustaoglu: Conceptualization, Methodology, Software, Formal analysis, Investigation, Resources, Writing - Original Draft, Visualization, Supervision, Project administration, Funding acquisition Umut Ozbey: Software, Formal analysis, Resources Hande Torlaklı: Investigation, Resources, Writing - Original Draft

Journal Pre-proof

Declaration of interests ☒ The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. ☐The authors declare the following financial interests/personal relationships which may be considered as potential competing interests:

Journal Pre-proof Highlights  A novel configuration of CPVT system was proposed to enhance the electrical efficiency.  The proposed system, CHCT-PVT was compared to the conventional non-imaging reflectors.  CHCT-PVT needs as half size as that of V-trough or CPC to attain equal concentration ratio.  

The best electrical efficiency was achieved as 18.6% for the case of CHCT-PVT. CHC has 42.9% and 58.9% higher power output than CPC and VT-PVT per unit reflector area.