353
T a refers to the ambient temperature in °C, G t refers to the solar irradiance in a
tilted module plane (W/m
2
), and NOCT refers to the standard operating cell temperature in Celsius (°C) degree. The total irradiance in the solar cell, considering both
standard and diffuse solar irradiance, can be estimated by the following equation:
I I R I R
I I R
t
b b
d d
b
d
r
(16.4)
The solar cell is essentially a P-N junction semiconductor able to produce
electricity via the PV effect, which is interconnected in a series-parallel configuration
to form a photovoltaic (PV) cell [22, 35, 36]. Besides, to improve the efficiency of the
resulting photovoltaic (PV) cell, graphene is integrated into the PV module [15, 37, 38].
Using a standard single diode, as depicted in Fig. 16.2, for a cell with N s seriesconnected arrays and N p parallel-connected arrays, the cell current must be related
to the cell voltage as
I N I
I
q V IR
AKTN
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
ª
¬
«
«
º
¼
»
»
p
p h
r s
s
s
exp
1
(16.5)
where
I
I
T
T
E
AK T T
rs
rr
r
G
r
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
3
1 1
exp
(16.6)
In Eqs. (16.5) and (16.6), q refers to the electron charge (1.6 × 10
−9
C), K refers
to Boltzmann’s constant, A refers to the diode idealist factor, and T refers to the cell
temperature (K). IR s refers to the cell reverse saturation current at T, T r refers to the
cell referred temperature, I rr refers to the reverse saturation current at T r , and E G
refers to the bandgap energy of the semiconductor used in the cell. The photocurrent
I ph varies with the cell’s temperature and radiation as follows:
I
I
k T T
S
i
ph
SCR
r
ª
¬
«
º
¼
»
100
(16.7)
I SCR refers to the cell short-circuit current at the reference temperature and irradiance, k i refers to the short-circuit current temperature coefficient, and S refers to the
solar irradiance (mW/cm
2
). The I–V characteristics of the photovoltaic (PV) cell can
be derived using a single-diode model which includes an additional shunt resistance
concurrent with the optimal shunt diode model as follows:
I I
I
ph
D
(16.8)
I I
I
q V R I
AKT
V R I
R
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
ph
s
s
sh
0
1
exp
(16.9)
Methods and Materials
T a refers to the ambient temperature in °C, G t refers to the solar irradiance in a
tilted module plane (W/m
2
), and NOCT refers to the standard operating cell temperature in Celsius (°C) degree. The total irradiance in the solar cell, considering both
standard and diffuse solar irradiance, can be estimated by the following equation:
I I R I R
I I R
t
b b
d d
b
d
r
(16.4)
The solar cell is essentially a P-N junction semiconductor able to produce
electricity via the PV effect, which is interconnected in a series-parallel configuration
to form a photovoltaic (PV) cell [22, 35, 36]. Besides, to improve the efficiency of the
resulting photovoltaic (PV) cell, graphene is integrated into the PV module [15, 37, 38].
Using a standard single diode, as depicted in Fig. 16.2, for a cell with N s seriesconnected arrays and N p parallel-connected arrays, the cell current must be related
to the cell voltage as
I N I
I
q V IR
AKTN
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
ª
¬
«
«
º
¼
»
»
p
p h
r s
s
s
exp
1
(16.5)
where
I
I
T
T
E
AK T T
rs
rr
r
G
r
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
3
1 1
exp
(16.6)
In Eqs. (16.5) and (16.6), q refers to the electron charge (1.6 × 10
−9
C), K refers
to Boltzmann’s constant, A refers to the diode idealist factor, and T refers to the cell
temperature (K). IR s refers to the cell reverse saturation current at T, T r refers to the
cell referred temperature, I rr refers to the reverse saturation current at T r , and E G
refers to the bandgap energy of the semiconductor used in the cell. The photocurrent
I ph varies with the cell’s temperature and radiation as follows:
I
I
k T T
S
i
ph
SCR
r
ª
¬
«
º
¼
»
100
(16.7)
I SCR refers to the cell short-circuit current at the reference temperature and irradiance, k i refers to the short-circuit current temperature coefficient, and S refers to the
solar irradiance (mW/cm
2
). The I–V characteristics of the photovoltaic (PV) cell can
be derived using a single-diode model which includes an additional shunt resistance
concurrent with the optimal shunt diode model as follows:
I I
I
ph
D
(16.8)
I I
I
q V R I
AKT
V R I
R
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
ph
s
s
sh
0
1
exp
(16.9)
Methods and Materials