354
I ph refers to the photocurrent (A), I D refers to the diode current (A), I 0 refers to the
inverse saturation current (A), A refers to the diode constant, q refers to the charge
of the electron (1.6 × 10
−9
C), K refers to Boltzmann’s constant, T refers to the cell
temperature (°C), R s refers to the series resistance (ohm), R sh refers to the shunt
resistance (Ohm), I refers to the cell current (A), and V refers to the cell voltage (V).
The output current of the PV cell using the diode model can be described as follows:
I I
I
I
V IR
R
§
©
¨
·
¹
¸
pv
D
D
s
sh
1
2
(16.10)
where
I
I
V IR
a V
D
s
T
1
0 1
1
1
1
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
exp
(16.11)
I
I
V IR
a V
D
s
T
2
0 2
2
2
1
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
exp
(16.12)
I 01 and I 02 are the reverse saturation currents of diode 1 and diode 2, respectively,
and V T1 and V T2 are the thermal voltages of the respective diodes. The diode idealist
constants are represented by a 1 and a 2 . The simplified model of the photovoltaic
(PV) system model is presented below:
v
V
cKT q
oc
oc
=
/
(16.13)
P
V
cKT q
V
cKT q
V
nKT q
V
V
max
/
ln
/
.
/
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
oc
oc
oc
oc
o
0 72
1
1
c c
SC
sc
I
V
G
G
T
T
I
G
G
oc
y
§
©
¨
¨
¨
¨
·
¹
¸
¸
¸
¸
§
©
¨
¨
¨ ¨
·
¹
¸
¸
¸ ¸
§
©
¨
·
¹
¸
0
0
0
0
0
1 E ln
§ §
©
¨
·
¹
¸
a
(16.14)
where ν oc refers to the normalized value of the open-circuit voltage V oc related to the
thermal voltage V t = nkT/q, K refers to Boltzmann’s constant, n refers to the idealist
factor (1 < n < 2), T refers to the temperature of the photovoltaic (PV) module in
Kelvin, α refers to the factor responsible for all the nonlinear effects on which the
photocurrent depends, q refers to the electron charge, γ refers to the factor representing all the nonlinear temperature-voltage effects, while β refers to a photovoltaic
(PV) module technology-specific dimensionless coefficient. Equation (16.14) only
represents the maximum energy output of a single photovoltaic (PV) module while
a real system consists of several photovoltaic (PV) modules connected in series and
in parallel. Therefore, the equation of total power output for an array with N s cells
connected in series and N p cells connected in parallel with power P M for each module would be for PV panel
16 Sustainable Cities and Communities
I ph refers to the photocurrent (A), I D refers to the diode current (A), I 0 refers to the
inverse saturation current (A), A refers to the diode constant, q refers to the charge
of the electron (1.6 × 10
−9
C), K refers to Boltzmann’s constant, T refers to the cell
temperature (°C), R s refers to the series resistance (ohm), R sh refers to the shunt
resistance (Ohm), I refers to the cell current (A), and V refers to the cell voltage (V).
The output current of the PV cell using the diode model can be described as follows:
I I
I
I
V IR
R
§
©
¨
·
¹
¸
pv
D
D
s
sh
1
2
(16.10)
where
I
I
V IR
a V
D
s
T
1
0 1
1
1
1
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
exp
(16.11)
I
I
V IR
a V
D
s
T
2
0 2
2
2
1
§
©
¨
·
¹
¸
ª
¬
«
«
º
¼
»
»
exp
(16.12)
I 01 and I 02 are the reverse saturation currents of diode 1 and diode 2, respectively,
and V T1 and V T2 are the thermal voltages of the respective diodes. The diode idealist
constants are represented by a 1 and a 2 . The simplified model of the photovoltaic
(PV) system model is presented below:
v
V
cKT q
oc
oc
=
/
(16.13)
P
V
cKT q
V
cKT q
V
nKT q
V
V
max
/
ln
/
.
/
§
©
¨
·
¹
¸
§
©
¨
·
¹
¸
oc
oc
oc
oc
o
0 72
1
1
c c
SC
sc
I
V
G
G
T
T
I
G
G
oc
y
§
©
¨
¨
¨
¨
·
¹
¸
¸
¸
¸
§
©
¨
¨
¨ ¨
·
¹
¸
¸
¸ ¸
§
©
¨
·
¹
¸
0
0
0
0
0
1 E ln
§ §
©
¨
·
¹
¸
a
(16.14)
where ν oc refers to the normalized value of the open-circuit voltage V oc related to the
thermal voltage V t = nkT/q, K refers to Boltzmann’s constant, n refers to the idealist
factor (1 < n < 2), T refers to the temperature of the photovoltaic (PV) module in
Kelvin, α refers to the factor responsible for all the nonlinear effects on which the
photocurrent depends, q refers to the electron charge, γ refers to the factor representing all the nonlinear temperature-voltage effects, while β refers to a photovoltaic
(PV) module technology-specific dimensionless coefficient. Equation (16.14) only
represents the maximum energy output of a single photovoltaic (PV) module while
a real system consists of several photovoltaic (PV) modules connected in series and
in parallel. Therefore, the equation of total power output for an array with N s cells
connected in series and N p cells connected in parallel with power P M for each module would be for PV panel
16 Sustainable Cities and Communities