Equivalent Circuits_1
Problem 1
For the simple equivalent circuit of a 0,017 m2 PV cell, the reverse saturation current, I0, equals
4×10-11 A and at an irradiance of 1000 W/m2 the short circuit current, Icc; equals 6,4 A at 25 ºC.
Consider m=1.
Find:
a) Open circuit voltage
b) Load current and output power when the output voltage equals 0,55 V
c) Efficiency of the cell at 0,55 V.
Problem 2
Suppose the equivalent circuit for the PV cell of Problem 1 includes a parallel resistance Rp
equal to 10 Ω. At 25ºC with an output voltage of 0,57 V find:
a) Load current and power delivered to the load
b) Efficiency of the cell
Problem 3
A four module array has two south facing modules exposed to 1000 W/m2 of irradiance and
two west facing modules exposed to an irradiance of 500 W/m2.
At an irradiance of 1000 W/m2 the I-V curve for a single module with its MPP at 4 A, 40 V is
shown below
a) Draw the I-V curve for the 4 module array in these conditions.
b) Compute the output power at the maximum power point of this array.
Problem 4
A 200 W (DC,STC) crystalline silicon PV module has a NOCT of 45 º and a temperature
coefficient for rated power equal to -0,5%/ºC.
a) At an irradiance of 1000 W/m2 and an ambient temperature of 25 ºC estimate the cell
temperature and output power
b) Suppose a heat exchanger cools the module to a temperature equal to 35 ºC. How much
power is now delivered by the module.
Problem 5
The data of a photovoltaic module delivered by the manufacturer is shown in table 1. Table 2
assembles, under the reference irradiance, the open circuit voltage, Voc, as a function of
temperature obtained from the I-V curves as a function of temperature provided by the
manufacturer.
Using the simple model compute:
a)
b)
c)
d)
The efficiency under reference conditions
The fill factor
The efficiency for an irradiance equal to 250 W/m2 and reference temperature
The error in the computation of Voc and the output power for a temperature of 75 ºC
and reference irradiance.
Peak Power
Voltage at Peak Power
Current at Peak Power
Open circuit Voltage
Short Circuit Current
Voltage Temperature coefficient
Current Temperature coefficient
Number of cell in series
length
width
PMP [Wp]
VMP [V]
IMP [A]
Voc [V]
Icc [A]
Voc/ºC [V/K]
Icc/ºC [A/K]
Nºcells
l [m]
w [m]
Table 1
170
36
4,72
44,2
5
-1,60E-01
3,30E-03
72
1,58
0,783
Θ [ºC]
Voc [V]
0
48,5
25
44,2
50
39,5
75
35,0
Table 2