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International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
“CHARACTERIZATION OF CONCENTRATED
LIGHT BEAMS WITH APPLICATIONS TO
SOLAR CONCENTRATORS”
Part B:
“Radiometric methods”
Antonio Parretta
ENEA – Bologna
OUTLINE
1.
2.
The Double Cavity Radiometer:
i)
Theory
ii)
Practical realization
iii)
Calibration
iv)
Applications
Introduction to radiometers for solar concentrators with
cylindrical receivers
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DOUBLE-CAVITY RADIOMETER (DCR)(1)
The optical model
(1)Patented
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Radiometer with two coupled integrating spheres
P0
sphere 1
photodetector
m
in
to voltmeter
or lock-in
sphere 2
Pm
Pin
c
i
Pc(r)
Pi
j
G2
G1
Pc(l)
Pj
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
The optical model
Energy conservation law applied to sphere 1:
N1
P0  Pc
P

(r )
i
 Pw 1
i 1
N1
P0  G 2  S c 
G
1
 S i  (1  R i )  G 1  S w 1  (1  R w 1 )
i 1
Energy conservation law applied to sphere 2:
N2
(l )
c
P

P
j
 Pw 2
j 1
N2
G1  S c 
G
2
 S j  (1  R j )  G 2  S w 2  (1  R w 2 )
j 1
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
The optical model
Irradiance into sphere 1:
N2
P0  [  S j  (1  R j )  S w 2  (1  R w 2 )]
G1 
j 1
N1
N2
[  S i  (1  R i )  S w 1  (1  R w 1 )]  [  S j  (1  R j )  S w 2  (1  R w 2 )]  S c
i 1
j 1
Irradiance into sphere 2:
G 2  G1 
Sc
 ...
N2
[  S j  (1  R j )  S w 2  (1  R w 2 )]
j 1
... 
P0  S c
N1
N2
[  S i  (1  R i )  S w 1  (1  R w 1 )]  [  S j  (1  R j )  S w 2  (1  R w 2 )]  S c
i 1
j 1
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
2
2
The optical model
Power at input “in”:
P0  G 0  S in
Irradiance incident on the photodetector “m”:
Gm 
G 0  S in  S c
N1
N2
[  S i  (1  R i )  S w 1  (1  R w 1 )]  [  S j  (1  R j )  S w 2  (1  R w 2 )]  S c
i 1
j 1
Radiant power on the photodetector “m”:
Pm  G 2  S m  ...
... 
G 0  S in  S c  S m
N1
N2
[  S i  (1  R i )  S w 1  (1  R w 1 )]  [  S j  (1  R j )  S w 2  (1  R w 2 )]  S c
i 1
j 1
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
2
2
The optical model
We define the following Attenuation Factors:
i)
f1  G 0 / G1
f 1  G 0 / G 1  ...
N1
N2
[  S i (1  R i )  S w 1 (1  R w 1 )]  [  S j (1  R j )  S w 2 (1  R w 2 )]  S c
... 
i 1
j 1
N2
S in  [  S j (1  R j )  S w 2 (1  R w 2 )]
j 1
ii) f 2  G 1 / G 2
N2
[  S j (1  R j )  S w 2 (1  R w 2 )]
f 2  G1 / G 2 
j 1
Sc
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
2
The optical model
iii)
f A  G 0 / G 2  f1  f 2
G
Attenuation factor for the irradiance
(flux density measurements)
N1
N2
[  S i (1  R i )  S w 1 (1  R w 1 )]  [  S j (1  R j )  S w 2 (1  R w 2 )]  S c
fA 
G
iv)
i 1
j 1
S in  S c
f A  P0 / Pm  f A  S in / S m
P
N1
G
Attenuation factor for the power
(power measurements)
N2
[  S i (1  R i )  S w 1 (1  R w 1 )]  [  S j (1  R j )  S w 2 (1  R w 2 )]  S c
fA 
P
2
i 1
j 1
Sm  Sc
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
2
The optical model
Attenuation Factors:
i) f  G / G 
1
0
1

ii) f  G / G 
2
1
2
iii) f
G
A

iv) f P 
A

i


i

i
2
j
j
Sc
j
 Sc
2

S in  S c

j
S in  

 Sc
j
Sm  Sc
 Sc
N1
i
 [  S i (1  R i )  S w 1 (1  R w 1 )]
i 1
2

N2
j
 [  S j (1  R j )  S w 2 (1  R w 2 )]
j 1
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Modelling of a prototype of DCR
sp
cl
of
win
wof
is1
is2
wc
wm
pr
m
rad1
We model the radiometer for measurements of the total power incident on the
concentration cell SunPower HECO252, used as photovoltaic receiver in the
concentrating system PhoCUS operating at ENEA Research Centre of Portici.
C-Module of the PhoCUS Project
C-Module
Assembled
SunPower
HECO252 cell
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Modelling of SP cell and optical fibre
SP-HECO252 cell
SS frame Glass window
DCR
window
Optical fibre
SP-HECO252 cell
Absorber
Surface area
(mm2)
Emissivity [7]
Reflectance
(%)
SP cell:
Central region
Sm1 = 156
_
Rm1 = 4
SP cell:
Copper frame
Sm2 = 69
Copper scraped
0.64
Rm2 = 36
Optical fibre:
Glass window
Sof1 = 7.1
_
Rof1 = 4
Optical fibre:
SS frame
Sof2 = 12.5
Stainless steel
Sheet polished
0.07
Rof2 = 93
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
The optical model (prototype)
P0
Sin
Sm
Pin
G1
Sc
Pm
Pc(r)
G2
Pc(l)
Sphere diameter, d = 5 cm;
input window area, Sin = 1.1 × 1.1 = 1.21 cm2;
photodetector window area, Sm = 1.5 × 1.5 = 2.25 cm2;
optical fiber head area, Sof = 0.196 cm2.
Sof
Variable quantities:
aperture area, Sc = 0.1÷2.0 cm2;
wall reflectance, Rw = 92÷99%.
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Pof
The optical model (prototype)
G 0  S in  S c  S m
Pm 
f
P
A

i

 P0 / Pm 
j

 Sc
i
2

j
 Sc
2
ScSm

i
 [ S in  S c  S w1 (1  R w )]

j
 [ S m 1 (1  R m 1 )  S m 2 (1  R m 2 )  S of 1 (1  R of 1 )  S of 2 (1  R of 2 )  ...
...  S c  S w 2 (1  R w )]
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Attenuation factor for power
200
2
Sin = 1.21 cm
2
Sm1 = 1.56 cm ; Rm1 = 4%
Attenuation factor, fA
P
2
Sm2 = 0.69 cm ; Rm2 = 93%
150
Rw92%
Rw93%
Rw94%
Rw95%
Rw96%
Rw97%
Rw98%
Rw99%
2
Sfo1 = 0.071 cm ; Rfo1 = 4%
2
Sfo2 = 0.125 cm ; Rfo2 = 84%
100
50
0
0,0
0,5
1,0
1,5
2,0
2
Intermediate aperture area, Sc (cm )
Attenuation factor of the DCR radiometer, calculated as function of the
intermediate aperture area, Sc, for some values of the wall reflectance, Rw.
DOUBLE-CAVITY RADIOMETER (DCR)
Ray tracing
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Ray tracing (prototype)
Ray tracing by TracePro
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DOUBLE-CAVITY RADIOMETER (DCR)
The thermal model
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Thermal model
Heat generated on the SunPower cell:
Q out  Pm  [1   ( C m ) ]  Pm  R m  Pm  [1   ( C m )  R m ]
Q out 
0 . 1  C in  S in  S c  S m

i

j
 Sc
2
 [1   ( C m )  R m ]
where:
G 0 (W / cm )  C in ( suns ) / 10
2
C m ( suns )  C in ( suns ) / f
G
A

C in  S in  S c

i

j
 Sc
2
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Efficiency of SP-HECO252 cell
26
25
SP-HECO252 cell
C=30X
Efficiency (%)
24
23
22
21
20
0,0
0,5
1,0
1,5
2,0
2,5
log10 (C)
 ( C )  20 . 481  6 . 6063  log C  2 . 1524  (log C )
2
Efficiency versus concentration
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Efficiency of SP-HECO252 cell
26
Efficiency,  (%)
25
24
2
Sc = 0.1 cm
2
Sc = 0.2 cm
2
Sc = 0.5 cm
2
Sc = 1 cm
2
Sc = 2 cm
23
Sin = 1.21 cm
Rw = 99%
2
22
2,0
2,5
3,0
3,5
4,0
log Cin (suns)
Efficiency of SP-HECO252 cell versus concentrationat at input of DCR
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Generated Heat
3
Heat, Qout (W)
2
Sc=2.0
Sc=1.0
Sc=0.5
Sc=0.2
Sc=0.1
2
Sin = 1.21 cm
Rw = 99%
1
0
0
50
100
150
200
250
Concentration, Cin (suns)
Heat generated on the SP-HECO252 cell of DCR vs. light concentration
(medium) at input, for different Sco values.
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Generated Heat
20
18
16
2
Sin = 1.21 cm
Rw = 99%
Heat, Qout (W)
14
12
10
8
Sc=2.0
Sc=1.0
Sc=0.5
Sc=0.2
Sc=0.1
6
4
2
0
0
1000
2000
3000
4000
5000
Concentration, Cin (suns)
Heat generated on the SP-HECO252 cell of DCR vs. light concentration (high)
at input, for different Sco values. The curves are truncated at Gm = 200 suns.
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DOUBLE-CAVITY RADIOMETER (DCR) (1)
Manufacturing of the prototype
(1) Patented
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
Schematic 2of the DCR gauge head
1
(t)
(w1)
(w4)
(si1)
z
(b1)
y
(si2)
Vertical section
(fco)
x
(fco)
(w3)
1
(si1)
(b3) (si2)
3
y
(b2)
Horizontal
section
x
z
2
(w2)
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
General scheme of DCR
fc
(pa)
(Pe)
(fo)
Spectrometer
(tr)
(rd)
(rd)
(v)
(ins)
(rd)
(ra)
Control Module
T (°C)
P (risc.)
Touchscreen
Isc
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DCR-1 Radiometer
Output to the
optical fibre
Input of
light
ECO-VIDE (Roma)
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DCR-1 Radiometer
slit
SunPower
cell
ECO-VIDE (Roma)
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DCR-1 Radiometer
Input of light
insert
Window for
SP cell
inserts
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DCR-1 Radiometer
Input of light
auxiliary
window
insert
Window
for SP cell
inserts
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006
DCR-1 Radiometer
baffle 1
baffle 3
baffle 2
Ist International School on Concentrated Photovoltaics, Ferrara 2-6 September 2006