Journal of Japan Solar Energy Society, 50（3）, 71-76（2024）

https://doi.org/10.24632/jses.50.3_71••••••••••••••••••••••••••••••••••••••••••••
Research Paper
研究論文
研究論文

Assessment of the Tilt Effect and the Truncation
Assessment of the Tilt Effect and the
Effect on the energy collection performance ofTruncation Effect on the energy collection performance of the MultiPro-CPCs
the MultiPro-CPCs in Tokyoin Tokyo*1‡Aïssatou MBOUP
Atsushi AKISAWA*1
*2
*2
*1‡
*2
*2
Aïssatou MBOUP
Atsushi
AKISAWA*1
Ramón PUJOL-NADAL
Víctor MARTÍNEZ-MOLL
Ramón
PUJOL-NADAL
Víctor MARTÍNEZ-MOLL
Abstract
Although compound parabolic concentrators (CPCs) are widely used for solar concentration, they only have one
degree of freedom in the design of their acceptance angle. To overcome this limitation, a new type of concentrator
called MultiPro-CPCs has been developed. These three-dimensional concentrators have multiple compound parabolic
profiles, combined with elliptical and rectangular receivers, enabling them to have multiple directional acceptanceangles. In this study, the tilt effect, and the truncation effect on the energy collection performance of the MultiProCPCs in Tokyo is presented with a comparison to the three-dimensional CPC through ray tracing simulation. The
MultiPro-CPCs with an elliptical receiver showed the highest performances, up to twice the collected energy perreceiver area of the 3DCPC. Moreover, all truncated MultiPro-CPCs show higher peak performance compared to the
non-truncated 3DCPC. The outcomes show the MultiPro-CPCs as better options in the field of concentration when
considering high-cost receivers and concentrator height limits.
Keywords: Compound Parabolic Concentrator, Elliptical receiver, Rectangular receiver, Truncation, Tilt
rays(3). The shapes created by rotating the CPC curve around an

1．
．Introduction

axis are called three-dimensional CPC (3DCPC) and the ones
created by translating the CPC curve in a direction are called two-

The amount of energy that falls on the Earth in just one hour

dimensional CPC (2DCPC). It has been also proven that theof sunlight surpasses the energy consumption of the entire worldenergy concentration ratio of the 3DCPC is found to be thefor a whole year(1). Therefore, an efficient use of all this solar

square of the one of the 2DCPC (4). Two-dimensional and three-energy can solve the problems of energy access and energy

dimensional solar concentrators are used for heat generation(5-7),

securitytechnologies.

thermodynamic power generation(8,9) and photovoltaic power

Nevertheless, solar installations require significant land areas

generation(10,11). Since the sun’s position changes with time,

and tracking systems to achieve high temperatures due to their

momently tracking technologies are still used to concentrate thedependency on the momently movement of the sun. To overcome

solar rays with high energy collection ratios.

withenvironment-friendly

solar

these efficiency limits, solar concentration using mirrors or

To overcome these limits, the author previously developed thelenses to concentrate the solar rays on a receiver is shown as a

MultiPro-CPCs(12) which are non-momently tracking three-solution. The compound parabolic concentrator (CPC)(2)

dimensional solar concentrators. This appellation comes from thedesigned by Winston et al. and consisting of a combination offact that the MultiPro-CPCs have a CPC profile at any diagonal

two parabolic mirrors, is a core technology in the field of solar

cross-section and changeable receiver shapes. In this previous

concentrator. The CPC has the function of advancing obliquely

study, multiple CPC profiles with different directional

incident rays to the receiver, but it has only 1 degree of freedom

acceptance angles, and elliptical and rectangular receiver shapes

in designing the half acceptance angle at which it can receive

are assumed. Based on simulations considering solar incidence*1 Graduate School of Bio-Applications and Systems Engineering,Tokyo University of Agriculture and Technology, Nakacho 2-24-16,
Koganei, Tokyo 184-8588, Japan‡e-mail: dadamboup@hotmail.fr*2 Industrial Engineering and Construction Department, University of
the Balearic Islands, Carretera de Valldemossa km 7.5, Palma, Illes
Balears, Spain
Received: February 13, 2024, Accepted: April 3, 2024

and axial angles, it has been demonstrated that the MultiProCPCs can achieve an optical concentration ratio which can be up
to 10 times higher compared to the conventional CPCs when
their receiver major length is equal(12). Furthermore, assuming amirror reflectance of 95%, the highest optical efficiency of 95%
occurs when both the longitudinal and transversal incidence－ 71 －

Aïssatou MBOUP, Atsushi AKISAWA, Ramón PUJOL-NADAL and Víctor MARTÍNEZ-MOLL

angles are 0°, meaning the emitter is directly above theconcentrator. In MultiPro-CPCs, the efficiency decreases when
the directional incidence angles increase. Compared toconventional CPCs, MultiPro-CPCs have moderate filtering,
especially in the longitudinal direction. In addition, MultiProCPCs with rectangular receivers, capture wider oblique
incidences than MultiPro-CPCs with elliptical receivers(12).
Nevertheless, the energy collection performance in a specificlocation during a specific period is yet to be clarified.
The objective of this study is to complement the assessment of
the MultiPro-CPCs, spatiotemporal raytracing simulations inTokyo in 2022. The assessment index is the energy collection perreceiver area obtained through optical simulation. Moreover, thetilt effect and the truncation effect on the energy collection
performance of the MultiPro-CPCs are presented.
NomenclatureDγ [mm]Diameter of the aperture of the CPC at a profiledγ [mm]Diameter of the receiver of the CPC at a profilefγ [mm]Focus length of the CPC at a profile

H [mm]Height of the CPC

Mγ [-]

Point of the receiver at γtγ [°]

Angular parameter of the receiver at γ

x [mm]

x-axis coordinate

y [mm]

y-axis coordinate

αγ [°]

Half acceptance angle of the CPC at a profile

α0° [°]

Longitudinal direction half acceptance angle

α90° [°]

Transverse direction half acceptance angle

γ [°]Angle between a profile plane and the east-west

from 0 to 90° and truncated at 3/4 and 1/2 of their heights H. In
total, 3 types of concentrator are compared when truncated andnot truncated: the MultiPro-ECPC with an elliptical receiver, theMultiPro-RCPC with a rectangular receiver, and the 3DCPC witha circular receiver and the same α0°, d0° and H value as theMultiPro-CPCs. The geometric concentration ratio represents themagnification factor at which a concentrator can concentratesolar energy without losses, assuming that the emitter ispositioned directly on top of the concentrator. It is obtained by
dividing the aperture area by the receiver area. Fig. 2 shows the
3DCPC, the MultiPro-ECPC, the MultiPro-RCPC, theirtruncated derivatives when α0°=15° and α90°=10° and thetruncation settings. Here too, all heights of the concentrators andthe longitudinal receiver diameters are equalized. Concerning thegeometric concentration ratio, the maximum value is 22.0 which
is obtained with the non-truncated MultiPro-ECPC when α0°=15°
and the minimum value of 1.76 is obtained with the truncated
3DCPC when α0°=45°. In Fig. 3, the variation of the receiver area
ratio normalized to the receiver area of the 3DCPC for each shapeand axial half acceptance angle combination is represented. The
conventional 3DCPC has a fixed circular receiver area due to thefixation of the longitudinal receiver diameter to 50 mm. It isnoticeable that the receiver area of the MultiPro-CPCs decreases
with α0° and increases with α90°. Furthermore, the MultiProRCPCs have the second-largest receiver area for each case andup to 10 times less receiver area compared to the 3DCPCs.
N･DAγdiag [°]

B

A’

･f

H

M$

OR
γ

$ $" °

B’

･

! !°

+

d

Value of γ at the diagonal plane of the rectangle

iag
"d #$

M!

$" °

(a) Profile shape(b) Receiver shapes
Fig. 1 Structure of the MultiPro-CPCs．Design Method of the MultiPro-CPCs
2．
The MultiPro-CPCs are new kinds of three-dimensional
concentrators having a compound parabolic concentrator (CPC)
shape at each profile with multiple acceptance angles in all
directions and elliptical or rectangular receivers as shown in Fig.
1. Here, γ represents the angle between the profile plane and thelongitudinal direction, αγ the half acceptance angle, Dγ theaperture diameter, dγ the receiver diameter, and H theconcentrator height. The point Mγ represents a position on thereceiver at γ. The MultiPro-CPCs can be reproduced by using theformulas and by following the steps mentioned in the previous
study(12). In this study, the longitudinal direction (γ=0°)
corresponds to the East-West direction and the transverse
direction (γ=90°) to the North-South. The half acceptance angle
in the longitudinal direction is set to 15° and 45°, and the half
acceptance angle in the transversal direction to 10°, and allreceiver major axes are equalized. Here, in addition to their
original size, the shapes are tilted from the horizontal every 15°
Journal of Japan Solar Energy Society! #! °･α

directionγ－ 72 －(a) 3DCPC(b) MultiPro-ECPCzTilt(c) MultiPro-RCPCSun

Elevation
East
Longitudinal
directionx

Azimuthy
North
Transversal
direction(d) tilt settings
Fig. 2 Compared solar concentrators and tilt settings
Vol.50, No.3, 2024

Assessment of the Tilt Effect and the Truncation Effecton the energy collection performance of the MultiPro-CPCs in Tokyo

3．
．Simulation Method: Raytracingfrom a plane surface with an intensity of 1 kW/m2. The light ismonochromatic with a wavelength of 550 nm. The ray tracing

The raytracing simulation software used in the simulation isTracePro which is based on the Monte Carlo ray tracing
method(13). As for the concentration device, the reflectance of themirror is set to 95% and the absorptance of the receive to 100%.
Concerning the emitter, 140000 rays are launched from a planesurface with an intensity of 1 kW/m2. The light is monochromaticwith a wavelength of 550 nm. The ray tracing simulations aredone in Tokyo throughout the year 2022. For each month, the 1st
and the 15th are simulated. In the simulation, all concentrators

α0° = 15°α90° = 10°

are tilted from the horizontal every 15° from 0° to 90°. The
evaluation index is the collected energy per receiver area

80
60
40
20

60
40
20

tilt 30°

160

tilt 15°

120
100
80
60
40
20
0

140
120

tilt 60°

tilt 45°20(b) MultiPro-ECPC
tilt 30°

160

tilt 15°

120
100
80
60
40
20
0

9/
1
10
/1
11
/1
12
/1

40

Dates [-]

Energy/Receiver Area [MJ/m2]

tilt 75°

tilt 15°

60

0

140
120

Dates [-]

tilt 90°tilt 75°

tilt 60°

tilt 45°

tilt 30°

tilt 15°

100
80
60
40
20
0

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

Energy/Receiver Area [MJ/m2]

tilt 90°tilt 60°

tilt 30°80

Dates [-]

140

tilt 75°

tilt 45°100(b) MultiPro-ECPC
160

tilt 90°

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

tilt 45°

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

tilt 60°

7/
1

5/
1

4/
1

3/
1

1/
1

Dates [-](a) 3DCPC
Energy/Receiver Area [MJ/m2]

tilt 75°

tilt 15°

0

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

Energy/Receiver Area [MJ/m2]

tilt 90°tilt 30°80

Dates [-]

140

tilt 45°100(a) 3DCPC and a flat receiver160

tilt 60°

120

2/
1

0

tilt 75°

8/
1

100

tilt 90°

140

6/
1

160

tilt 60°
tilt 15°

Energy/Receiver Area [MJ/m2]

tilt 75°
tilt 30°

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

Energy/Receiver Area [MJ/m2]

120

tilt 90°tilt 45°
no mirror no tilt

α0° = 45°
α90° = 30°

receiver (Note: for 3DCPCs, α0°=α90°)

cost receiver. Concerning the emitter, 140000 rays are launched140

α0° = 45°
α90° = 20°

Fig. 3 Variation of the receiver area normalized to the flat

[MJ/m2] which is an important driver when considering a high-160

α0° = 45°
α90° = 10°

Dates [-](c) MultiPro-RCPC(c) MultiPro-RCPC

Fig. 4 Annual variation of the energy per receiver area for the

Fig. 5 Annual variation of the energy per receiver area for thetilted shapes with α=α0°=15° and α90° =10°

tilted shapes with α=α0°=45° and α90° =10°

Vol.50. No.3

－ 73 －

太陽エネルギーAïssatou MBOUP, Atsushi AKISAWA, Ramón PUJOL-NADAL and Víctor MARTÍNEZ-MOLL

simulations are done in Tokyo throughout the year 2022. For
each month, the 1st and the 15th are simulated. In the simulation,
all concentrators are tilted from the horizontal every 15° from 0°
to 90°. The evaluation index is the collected energy per receiverarea [MJ/m2] which is an important driver when considering ahigh-cost receiver.
From the ray tracing simulations, the energy passing theaperture and absorbed by the receiver is obtained. The collectedenergy per receiver area is calculated by dividing the absorbed
energy per the receiver area. In addition, the contribution of theMultiPro-CPCs is also assessed through the normalization of its
performance to the mirrorless receiver performance.

basis. It is noticeable that the performance of the concentrators
mainly results from a collection during the 2 hours around noon
when α0°=15°. That period of collection increases to 7 hours
between 9 a.m. and 3 p.m. when α0°=45°, with a drastic decrease
from 43 times to 10 times the normalized intensity obtained. Ona daily basis and on an hourly basis, the MultiPro-CPCs generally
show a better performance compared to the 3DCPC. Especially,
when α=α0°=45°, the MultiPro-ECPC obtains up to 10 times
more energy per receiver area compared to the receiver-only caseand up to twice more compared to the 3DCPC.
These trends reveal that the variation of the directional
acceptance angles and the use of slender receiver shapes
compared to the circular receiver have a leverage effect in termsof collected energy per receiver area.

4．
．Results and Discussion

Journal of Japan Solar Energy Society

Normalized hourly energy perreceiver area [-]Fig. 6 Total annual energy per receiver area normalized to themirrorless receiver performance
45
40
35
30
25
20
15
10
5
0

3DCPC
MultiPro-ECPC
MultiPro-RCPC

7

8

9

10 11 12 13 14 15 16 17 18
Time [h](a) α=α0°=15° and α90° =10°
Normalized hourly energy perreceiver area [-]4.1 Effect of the tilt
Fig. 4 and Fig. 5 respectively show the annual variation of thecollected energy per receiver area for the tilted shapes when α0°=15° and when α0°=45° and a mirrorless flat receiver. The
mirrorless flat receiver maintains its collected energy perreceiver area between 10 and 32 MJ/m2 with a peak in June andJuly. It is noticeable that when α0° =15°, 30° tilt, 45° tilt, 60° tilt,
and 75° tilt correspond to common peak energy collection perreceiver area obtained during 2 periods in the year for each tilt.
For 90° tilt and 15° tilt, the peak values are only obtained withthe 3DCPCs with α0°=45°, respectively between May 15th andAugust 1st, and between November 15th and January 15th. This isbecause these periods of the year correspond to solar elevation
angles at Tokyo that vary between α0° and α0°±25°(14). Therefore,
according to their acceptance range, the concentrators can collectin a larger or a smaller period. Nevertheless, the intensity will be
proportional to their concentration ratio. This also explains the
60% decrease in the peak values of the 3DCPCs from the rangeof 100 MJ/m2/day to 40 MJ/m2/day when α increases. In contrast,
the peak values of the MultiPro-CPCs decrease by about 43%
from the range of 143 MJ/m2/day to 80 MJ/m2/day when α
increases. Compared to 3DCPCs, the MultiPro-ECPCs show up
to 50% higher peak values, followed by the MultiPro-RCPCs.
The maximum energy per receiver area of 143 MJ/m2. is obtainedon December 15th by the MultiPro-ECPC with α0°=15°.
Nevertheless, the MultiPro-CPCs show a necessity of 4 tilt
angles throughout the year, whereas the 3DCPCs only need 2 tilt
angles except when α0° = 15°.
Fig. 6 represents the total annual energy per receiver area
obtained with the 24 simulated days normalized to the mirrorlessreceiver performance. The MultiPro-ECPC with a total collectedenergy per receiver area of 2997.0 MJ/m2 when α0° = 15° obtains
5.8 times more energy per receiver area compared to the receiveronly case and 1.2 times more compared to the 3DCPC. In
addition, when α0°=45°, the MultiPro-ECPC still obtains 3.3
times more energy per receiver area compared to the receiveronly case and 1.8 times more compared to the 3DCPC.
In Fig. 7, the energy per receiver area on January 1st for eachshape at 30° tilt normalized to the mirrorless receiver
performance on the same day is further analyzed on an hourly

45
40
35
30
25
20
15
10
5
0

3DCPC
MultiPro-ECPC
MultiPro-RCPC

7

8

9

10 11 12 13 14 15 16 17 18
Time [h](b) α=α0°=45° and α90° =10°

Fig. 7 Comparison of the hourly energy per receiver area at 30°
tilt normalized to the mirrorless receiver performance on Jan 1st
4.2 Effect of the truncation－ 74 －

Fig. 8 and Fig. 9 respectively show the annual variation of
Vol.50, No.3, 2024

Assessment of the Tilt Effect and the Truncation Effecton the energy collection performance of the MultiPro-CPCs in Tokyo

the collected energy per receiver area for all shapes when theirheights are equal to H, 3H/4, and H/2 when α0°=15° and when
α0°=45°. It is noticeable that with the 75° tilt setting used, energy
collection is only possible between March 15th and September
15th. This is also due to the fact that in that period of the year, thesolar elevation angle at Tokyo varies between 50° and 77°(14).
For each height, compared to 3DCPCs, the MultiPro-ECPCs
show up to 50% higher peak values, followed by the MultiProRCPCs. In addition, when α0°=15°, except for the MultiProECPC, the truncation of the concentrator from H to 3H/4 does
not change the collection intensity at peak. In the same case, the140

CPC 3H:4
H/4

160

CPC H

Energy/Receiver Area [MJ/m2]

CPC H:2
H/2

120
100
80
60
40
20

100
80
60
40
20

Energy/Receiver Area [MJ/m2]

100
80
60
40
20

RCPC 3H:4
H/4

1

1

1

8/

9/

60
40
20

160

Energy/Receiver Area [MJ/m2]

RCPC H

60
40
20
0

140

1

1

12
/

1

11
/

9/
1

10
/

8/
1

7/
1

6/
1

5/
1

Dates [-]RCPC H/2
H:2

RCPC 3H:4
H/4

RCPC H

120
100
80
60
40
20
0

4/
1

/1

1

7/

80

Dates [-]

80

3/
1

ECPC H(b) MultiPro-ECPC

100

2/
1

ECPC 3H:y4
H/4

100

0

120

1/
1

ECPC H/2
H:2

120

Dates [-]RCPC H/2
H:2

/1

1

6/

140

(b) MultiPro-ECPC

140

12

1

5/

160

ECPC H

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

ECPC 3H:4
H/4

120

160

/1

1

4/

(a) 3DCPC

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

ECPC H/2
H:2

140

11

1

3/

Dates [-]

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

Energy/Receiver Area [MJ/m2]

160

10

1

2/

0

(a) 3DCPC

Energy/Receiver Area [MJ/m2]

CPC H

120

Dates [-]

0

CPC 3H:4
H/4

1/

0

CPC H/2
H:2

140

1/1
1/15
2/1
2/15
3/1
3/15
4/1
4/15
5/1
5/15
6/1
6/15
7/1
7/15
8/1
8/15
9/1
9/15
10/1
10/15
11/1
11/15
12/1
12/15

Energy/Receiver Area [MJ/m2]

160

energy collection per receiver area of the MultiPro-ECPC during
the peak period decreases by around 10 MJ/m2 with the height ofthe concentrator.
Furthermore, for all cases when α0°=15°, the truncation of theconcentrator from 3H/4 to H/2 decreases by up to 10 MJ/m2 theenergy collection per receiver area during the peak period. Thisis due to the decrease in concentration ratio caused by thetruncation of the CPC profile which results in smaller apertureareas as shown in Fig. 2. In addition, when α0°=15°, the energy
collection period increases by one month with the truncation. In
contrast, when α0°=45°, for all cases, the truncation of theconcentrator from H to H/2 does not change the collection
performance except in June and mid-July where an

Dates [-](c) MultiPro-RCPC(c) MultiPro-RCPC

Fig. 8 Annual variation of the energy per receiver area for thetruncated shapes tilted at 75° with α=α0°=15° and α90° =10°

Fig. 9 Annual variation of the energy per receiver area for thetruncated shapes tilted at 75° with α=α0°=45° and α90° =10°

Vol.50. No.3

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太陽エネルギーAïssatou MBOUP, Atsushi AKISAWA, Ramón PUJOL-NADAL and Víctor MARTÍNEZ-MOLL

overcollection of up to 10 MJ/m2 is noticeable with the MultiProCPCs. These results indicate that with the increase of α0° from
15° to 45°, less difference in collection performance due totruncation is noticed for each shape. This is due to the wider
range of acceptance provided by the truncation of the CPC profile
shown in Fig. 1 which results in a bigger half acceptance angle
compared to the α0° of origin. Since 45° of half acceptance angle
already covers most of the daily azimuth angle variation(14) insummer, a truncation that further increases the half acceptanceangle does not bring as much increase in the incidence coveragecompared to the case where α0°=15°.
For each combination of α0° and α90°, all truncated MultiProCPCs have up to 50% higher peak values compared to the nontruncated 3DPCs. Nevertheless, the peak periods are the same for
all MultiPro-CPCs, where they increase with α0° for the 3DCPCs.

This study was supported by the Japan Society for the
Promotion of Science (JP22J13486) and by the Doctoral
Program for World-leading Innovative and Smart Education ofTokyo University of Agriculture and Technology.
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5．
．Conclusion

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8)

throughout the year whereas the 3DCPCs need 3 tilt angles when

Y. Han et al, An efficient and low-cost solar-aided lignite drying
power generation system based on cascade utilization of

α0° = 15° and 2 tilt angles when α0° = 45°. Truncated MultiPro-concentrating and non-concentrating solar energy, Energy 289,

CPCs generally outperform non-truncated designs, showing up

129932, 2024.

to 50% more energy per receiver area even when truncated at half9)

their heights. The wider range of acceptance provided by

E. Resendiz et al, Analysis of a small-scale modified beam-downsolar concentrator system for low temperature applications,

truncation results in less difference in collection performance

Renewable Energy 215, 119007, 2023.

with increasing α0°, indicating diminishing returns beyond a10) C. Chen, H. Yang, Solar concentrators filled with liquid for

longitudinal half acceptance angle of 45°. This suggests theenhancement of photocurrent generation and angular responses ofpotential for optimizing CPC designs for enhanced energy

light incidence, Solar Energy 267, 112257, 2023.

collection with smaller heights.

11) V. Oliveto et al., Theoretical investigation of asymmetric light

These outcomes concerning the tilt effect and the truncationinterfaces for increasing optical efficiency of luminescent solar

effect imply that the MultiPro-CPCs may provide newconcentrators via integration of finite element simulation results

possibilities in solar concentration when considering stationary

with Monte Carlo ray tracing, Renew. Energy 218, 119314, 2023.

high-intensity concentration and limited concentrator height.

12) A. Mboup, A. Akisawa, R. Pujol-Nadal, V. Martínez-Moll, Design

In this study, the MultiPro-CPCs are investigated in terms ofand optical performance evaluation of the three-dimensional solar

single unit performance. In the case where the concentrators willconcentrators with multiple compound parabolic profiles, ellipticalbe used in an array format, the units are arranged in a delimited

and rectangular receiver shapes, Energies 17(3), 721, 2024.

area. With the resulting aperture shapes, there will be a spacedoi.org/10.3390/en17030721

between the units, which will decrease the space efficiency at the13) Lambda Research Corporation, Solar Collector Design, andapertures. Therefore, adoption of aperture shapes with straight

Analysis using TracePro, https://www.lambdares.com (Feb. 2024)
14) Casio, Solar elevation Angle calculator, https://keisan.casio.jp

edges for array formats is yet to be discussed.

(Feb. 2024)

Acknowlegments

Journal of Japan Solar Energy Society－ 76 －

Vol.50, No.3, 2024