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Solar Energy
Photovoltaic cell generator
Determination of the current x voltage characteristic curve of a PV cell
1. Ideal Photovoltaic Generator
Figure 1. Ideal photovoltaic generator (in blue) discharging through a finite resistance.
The simplest way to describe
a photovoltaic generator is to depict it as an ideal current source, which
produces a current (IF)
aproximately proportional to the incident light power, in parallell with
a diode, as shown in Figure 1. If the solar cell terminals are connected
by an external load resistor RL,
part of the current produced by solar radiation will flow through the resistor
(external current I) and the other part will flow
through the diode (diode current ID).
The external current I is thus given by
Figure 1 also shows that,
for the ideal photovoltaic generator, the voltage
V applied on the
resistor is equal to the voltage on the diode VD:
The diode is a non-linear
conducting element which current x voltage curve is given, in a general
way, by
(eq. 3)Using (eq. 2) in (eq. 3), and this result in (eq. 1), we obtain the function that describes the I x V characteristic curve of the ideal photovoltaic generator (Figure 2):
(eq. 4)
Figure 2. I x V characteristic curve of the ideal photovoltaic generator
The fact that we have drawn an I x V graph should not give us the wrong impression that the voltage (or the current) is a variable that can be independently varied; as a matter of fact, the independent variables in the situation of Figure 1 are the incident light power and the external resistance RL. This situation is found in the experimental determination of the I x V characteristic curve, where the load resistance RL is varied, maintaining a constant light intensity, and the values of the (I,V) pair that correspond to each tested value of resistance are measured and plotted in a graph where RL do not appear explicitly.
Truly, the external current
I
and the external voltage
V are related, in (eq. 4), by
allowing to eliminate
one of them from (eq. 4) and to write the other as function of RL,
for constant light intensity. This is a transcendental function that can
be determined as shown in Figure 2. For each value of resistance there
corresponds a (I,V)
pair over the characteristic curve, the coordinates of the point where
the curve is intercepted by the I
= V / RL
straight line.
The values ISC of the short-circuit current (RL = 0) and VOC of the open circuit voltage (RL = ¥), which correspond to the points where the characteristic curve intercepts the V= 0 and the I= 0 axes, respectively, are shown bellow:
a) Ideal photovoltaic
generator in open circuit
(eq. 6)
b) Ideal photovoltaic generator
in short- circuit
Go to>>>:
Real
photovoltaic generator
Figure 3a. Ideal photovoltaic generator in open circuit
When the generator is disconnected from any external load, the external current I is null and the entire photovoltaic current generated by the incident radiation circulates back through the diode. If we make I = 0 in (eq. 4) we obtain the open circuit voltage of the generator:
(eq. 6)b) Ideal photovoltaic generator in short-circuit
Figure 3b. Ideal photovoltaic generator in short-circuit
When the generator is short-circuited (terminals connected by a zero resistance external load), the entire photovoltaic current IF generated by the incident radiation circulates back externally. In this case the diode's current and voltage are both null. The external voltage is V = 0, and the short-circuit external current equals the photovoltaic current IF
Figura 4. Real photovoltaic generator discharging through finite resistance
There are two effects that should be considered for a more realistic description of a photovoltaic generator: i) the internal resistance of the generator and of the contacts, represented by a resistor RS in series with the generator (since it opposes to the external circulation of the current); and ii) the resistive current through the semiconductor crystal, represented as a resistor RP in parallell with the diode (since it offers an alternative mechanism for the internal circulation of the current).
The equation that relates
the external current I to the voltage V
across the load resistor is still obtained from the diode's I(V) function
(eq. 3), but now the relations between I and ID
(eq. 1) and between V and VD
(eq. 2) are given respectively by
and
If we substitute (eq.
8) and (eq. 9) into (eq. 3) and use the Ohm's relation between IP
e VD, we obtain
(eq.
10)
The differences between
(eq. 10) and the ideal case function (eq. 4) are two: the exponent in the
real case is multiplied by a factor (1 + RS/RL)
and there is a subtracted parcel from the current that depends on the inverse
of the internal parallell resistance RP.
In most cases this parcel, that represents the resistive back current,
is much smaller than the diode current and can be neglected. In which respects
to the other effect, RS
is also small, and it will not became noticeable unless we use RL
values as small as RS.
Figure 5. Effect of current and voltage meters on an ideal photovoltaic generator discharging through a finite resistance
Figure 5 shows the effect of the measuring instruments (ammeter A and voltmeter V) on the circuit formed by an ideal photovoltaic generator discharging through an external resistance, which modifies the relations of the external voltage V and current I with the diode's voltage VD and current ID. As it may be seen by comparison with Figure 4, the effect of the ammeter's resistance RA is identical to the effect of the internal series resistance RS and the effect of the voltmeter's resistance RV is the same as the effect of the internal parallell resistance RP.
Leaving aside the issue of
the accuracy of simultaneous measurements of current and voltage (see
Practices in Electrical Measurements), the effect of the meters may
be included in (eq. 10) by using effective RS
e RP values.
The independent variables in the situation of Figure 1 are the incident light power and the external resistance RL. The experimental determination of the I x V curve consists in varying the external resistance RL and measuring the current and voltage for each value of resistance, maintaining a constant light intensity. This can be made with different light intensity conditions, thus obtaining the I x V curves that correspond to each light intensity.
In the following there are
links for a procedure for performing and discussing the experiment, for
a simulator that allows one to perform virtual experiments, and for a remote
experiment, where the real parameters of the photocell curve determination
experiment are remotely controlled and measured via Internet.
1) Experiment procedure
See "Práticas
Básicas em Medidas Elétricas: Gerador Fotovoltaico" for a procedure
for determination of the I x V curves , for local or remot,
real or virtual experiments.
VB program >> "fotovolt.exe"
The above link will download
a VB program with which you can simulate the experimental deterrmination
of the I x V curve of a photovoltaic generator.
http://193.175.144.216/online-experiment/solarzelle/solarzelle.html
The above link will take you to a real experiment of determination of the I x V curve of a photovoltaic generator, housed in the laboratory of the Applied Physics Department of Jülich Division of Fachhochshule Aachen (http://www.juelich.fh-aachen.de/fachbereiche/physik/). The experiment set-up consists in a photocell iluminated by a lamp, both connected to a measuring and control circuit which allows the following actions to be remotely made:
The upper panel shows the present image of the photocell illuminated by the lamp as seen by a video camera, and a figure of a control panel with the present values of the 4 variables defined above. Note that, although it cointains some buttons, the upper panel only show values and do not allow to change any parameter. To remotely change the values of the experiment's independent variables, the voltage applied on the lamp (Lampenspannung) and the countervoltage (Gegenspannung), one has to introduce the desired values in the corresponding text boxes of the lower panel. For this, one should observe that:
