Welcome to the PV-online course on grid connected PV-systems,
this chapter is called "Electric characteristics of a solar cell".
In this particular teaching unit we will deal with the influence
of temperature and irradiance on the J-V-characteristic of a solar cell.
To understand how a change in temperature or irradiance affects
the electrical behavior of a solar cell, let's look at both effects separately.
Let's start with the irradiance
and its influence on the short circuit current density.
In an ideal solar cell without losses, all incident photons
with sufficient energy generate electron-hole pairs.
If the number of photons doubles,
the number of electron-hole pairs also doubles.
Therefor, for the ideal solar cell, there is a linear relationship
between the photocurrent and the irradiance.
Since the short-circuit current corresponds to the photocurrent,
the short-circuit current density also increases linearly with the irradiance.
We indicate this linear relationship here by a constant c0.
As you can see,
a change in irradiance also affects the open circuit voltage.
With increasing irradiance, the open-circuit voltage
also increases, but less than the short-circuit current.
Let's examine this effect in more detail.
At the beginning of this chapter we derived an equation
for the open circuit voltage for the ideal solar cell.
We have seen that the open circuit voltage depends on the temperature voltage
and on the logarithm of the photocurrent divided by the reverse saturation current.
We assume that ONLY the irradiance changes, not the temperature.
The temperature voltage
and the reverse saturation current density
are not influenced by the irradiance.
The photocurrent, however, as we have
just seen, is proportional to the irradiance.
For the open-circuit voltage, therefore, there is a logarithmic dependence
on the irradiance, which we represent here with the constant c1.
Let us now also look at the influence of irradiance on efficiency.
In the first teaching unit of this chapter,
we defined the efficiency of a solar cell as follows.
So, the efficiency is linearly related
to the short circuit current and the open circuit voltage.
For simplicity, we assume that the fill factor remains constant
as the irradiance changes.
We have just shown that the short-circuit current
increases proportionally with irradiance and the open-circuit voltage
increases proportionally with the logarithm of the irradiance.
Let's put these relations into the formula for the efficiency.
This term can be simplified.
We can eliminate the irradiance
and summarize all the constants in a constant c2.
So we see, that the efficiency of a solar cell
is proportional to the logarithm of the irradiance.
What is the significance of this relationship
for the behavior of a solar cell?
To answer this question, we plot the efficiency against the irradiance.
According to the relationship just derived, we get a logarithmic curve.
The curve shown here relates
to a constant cell temperature of 25 °C.
It was calculated using the single-diode model for a commercial solar module.
In the data sheet of the solar module, the efficiency is given as 19.6%.
We can see that this efficiency is only reached at an irradiation of 1000 W/m².
In central Europe, this corresponds to the irradiation
at midday on a clear summer day.
As the irradiance decreases,
the efficiency drops significantly.
For the operation of solar systems, this behavior can be significant
if low irradiance values are frequently present.
For example, the frequency of irradiation
below 300 W/m²
in Cologne (Germany) is 30%.
Now let's look at what happens when the temperature
of the solar cell increases.
First, we will look at the effect on the short circuit current.
In the diagram shown here, you can see the JV-curve
at different cell temperatures Note that these do not correspond
to the ambient temperature, since a solar cell usually heats up
during operation and is therefore usually warmer than the ambient.
We can see that the short circuit
current increases slightly as the cell temperature increases.
But what is the reason for this?
Well, it is because the band gap E_G of the semiconductor material becomes smaller
with increasing temperature due to the oscillations of the crystal lattice.
As a result, photons with a little lower energy
can also be absorbed and lift electrons into the conduction band.
Therefore, the number of charge carriers
increases and the short-circuit current
increases linearly.
In contrast to the irradiance, however, a doubling of the temperature
does not lead to a doubling of the short-circuit current.
The dependence of the short-circuit current on the temperature
is described by the temperature coefficient alpha.
For a crystalline silicon solar cell, it is about 0.02 mA/cm² per degree K.
Usually, alpha is related to the short-circuit current at STC conditions
- that is 1000 W/m² and 25 °C cell temperature -
and is given in % per K.
Typical values of alpha in silicon are 0.05%/K.
The short-circuit current at
any other temperature can be calculated using the following formula.
Note that the temperature coefficient
alpha applies only to the short-circuit current.
A linear dependence on temperature can also be determinedfor the MPP current,
but this results in a different temperature coefficient.
Let us now
look at the influence of the temperature on the open-circuit voltage.
We can see in the diagram that the temperature has a much stronger
effect on the open-circuit voltage than it has on the short-circuit current.
Let's take a look
at what this is.
If we consider the formula for the open circuit voltage,
at first glance we might think that the open circuit voltage increases
with increasing temperature due to the temperature voltage .
But this is not the case, which is due
to the reverse saturation current density.
The reverse saturation current density describes
the current generated by thermally generated electron-hole pairs.
It increases exponentially with increasing temperature.
As a result, V_oc decreases as the temperature T increases.
Just as with the short circuit current,
a linear dependence on temperature can be derived for the open-circuit voltage.
This dependence again is described by a temperature coefficient.
For the open-circuit voltage, it is denoted by Beta.
Beta indicates the change in open-circuit voltage per degree Kelvin.
Beta is also
usually related to the open-circuit voltage
at STC and given in %/K.
Since the open-circuit voltage decreases
with increasing temperature, beta always has a negative value.
Typical values for silicon solar cells are about minus 2.2 mV/K
or minus 0.035%/K.
Again, note that the temperature coefficient
refers only to the open-circuit voltage.
A linear relationship can also be established for the MPP voltage,
but here a different coefficient would result.
Due to the strong drop of the open-circuit voltage
with increasing temperature, the power in the MPP also decreases.
A temperature coefficient can also be specified for the MPP power.
For silicon solar cells, this is about minus 0.4 to minus 0.5 %/K.
With a temperature increase of 10°, the power of a solar module
thus decreases by about 4-5% of the nominal power.
We can use the temperature coefficients to calculate the short-circuit current
and open-circuit voltage at any operating conditions.
If the short-circuit current is known for a certain
cell temperature T_1 and irradiance E_1,
the following equation can be used to calculate the short-circuit current
I_2 at a different temperature T_2 and irradiance E_2.
The dependence on the temperature is
described by the temperature coefficient alpha,
the dependence on irradiance is linear.
Similarly, the open-circuit voltage
can be calculated for any conditions
if the open-circuit voltage
U_oc1 is known at temperature T1 and irradiance E1.
Here the dependence on temperature is described
by the temperature coefficient beta.
For the irradiance we had found a logarithmic influence.
This influence is additionally
modulated by the dimensionless correction factor Zeta.
Zeta is about 0.06 or 6% for crystalline solar cells.
These equations will play a significant role later, as we need to
consider the system performance at different outdoor temperatures
when designing an inverter for a system.
Finally, let us consider the influence
of the temperature on the efficiency of a solar cell.
In the diagram shown here, the influences of temperature
and irradiance on the efficiency are illustrated.
Due to the linear decrease of the MPP power,
the efficiency also decreases linearly with the temperature.
It can be seen that at high irradiance the influence of temperature on efficiency
is predominant, while at low irradiance the influence of irradiance is stronger.
We summarize: With increasing irradiance, I_sc increases
proportionally and V_oc increases logarithmically.
With increasing temperature, I_sc increases slightly, while the V_oc
drops sharply.
Overall, a higher irradiance leads to a higher efficiency
and a higher temperature to a lower efficiency.
I thank you for your attention.