Photovoltaic cell (solar cell) intensity and output curve

 Hi,

For my A-Level physics coursework, I will be investigating the effect
of light intensity on the power, voltage and current outputs of a solar
cell.

Are there any formulae to describe thse relationships, I serched but I
could only find the formulae for IV curve. What is the significance of
the IV curve?

Thanks

  1337usr@gmail.com wrote:

The I-V curve describes the amount of current that a solar cell will
produce at a given voltage. Thus, the operating voltage and current of
the cell is determined by the characteristics of the load. Obviously, a
load with resistance R will operate at the point on the I-V curve where
V = IR. This point can be found by plotting a line from the origin with
slope 1/R on the I-V curve -- the point where the line intersects the
I-V curve tells you the operating voltage and current.

Since the I-V curve is nonlinear, the power output is maximum at a
single point on the curve. This point is called the maximum power point
and can be found from the product of voltage and current at each point
on the I-V curve to produce a P-V (power vs. voltage) curve. Clearly, it
is best to always operate the solar cell at the maximum power point in
order to extract the most energy -- look up "maximum power point
tracker" to see how that is done.

As for the effects of light intensity, strictly speaking there are no
formulae to describe these relationships -- to calculate them explicitly
requires the solution of a system of partial differential equations.
Subject to certain assumptions, though, they simplify to a couple of
approximations that are quite good, provided the light intensity is not
too low ("high level injection" in semiconductor physics terms). I don't
want to do your homework for you, but for various reasons even if you
find these equations yourself you will probably not recognize them as
the ones you need, so here goes:

Isc = Iscref * (G / Gref)
Voc = (k * T / q) * ln (Isc / I0 + 1)

where

Isc = short-circuit current
Voc = open-circuit voltage
G = light intensity for which Isc is desired
Gref = reference light intensity
Iscref = short-circuit current at reference light intensity Gref
I0 = dark saturation current
T = absolute temperature
k = Boltzmann's constant
q = electronic charge

I'll leave it to you to interpret the equations and find reasonable
values for I0.

These only tell you how current and voltage change at the *endpoints* of
the I-V curve (i.e., the open-circuit voltage and short-circuit
current). The points in between, which include the maximum power point,
can only be determined (a) by solving the aforementioned partial
differential equations, (b) experimentally, or (c) using an empirical
model. Therefore, in order to determine how the power output of a solar
cell changes with light intensity you need to use one of these methods.
Several empirical models have been developed for this, and I encourage
you to seek them out (hint: check the publications section of the NREL
web site).

Good luck with your project!

 Thank you very much, you got me started on the project. =)

R.H. Allen wrote:

 Here is the spec sheet from a BP3160 panel. Look for other spec sheets
for their curves. I couldn't find any that are scaled really well.
Make sure you get the whole link.

http://www.bp.com/liveassets/bp_internet/solar/bp_solar_north_america/STAGING/local_assets/downloads_pdfs/pq/product_data_sheet_bp_3160b_03_4022_1_en.pdf

 
Angrist, Chapter 5, Photovoltaic Generators, the equation for solar
cell current is
I = Is - I0 {exp [eV/(kT)] -1}
where Is is the short circuit current (often written Isc), I0 is the
dark or saturation current, V is the voltage across the junciton, k is
Boltzmann's constant, e is the charge on an electron (sometimes written
as q ), and T is the absoulte temperature of the junction. The equation
following the - sign is sometimes called the rectifier or diode
equation, and usually is written as I0 {exp [ eV / ( mkT ) ] - 1 } to
include a "diode quality factor "m" that is between 1 and 2. If you
analyze the equation you will see that in effect there is a current (
Is, that is dependent on light intensity as explained by Mr. Allen)
that is created in the solar cell. If the output is shorted, thereby
forcing the voltage to zero, this is the current that will flow into
the short circuit. If the voltage is allowed to increase to non-zero
values, then some of this current is shunted through the internal diode
according to the diode equation. If the voltage is allowed to increase
to Voc (open circuit voltage) then all the current must flow through
the internal diode since no external current can flow in an open
circuit. For all other values of voltage between zero and Voc the
external load current will be between Isc and zero. This is fine for
ideal solar cells, but in real life there is always some finite shunt
resistance in parallel with the diode junction, and some series
resistance in the circuit ahead of the point where an actual load can
be connected. These two resistors will affect the shape of the I-V
curve, with the shunt resistance primarily affecting the slope of the
curve near Isc, and the series resistance mostly adding to the slope of
the curve near Voc. Of course both resistors actually affect the I-V
curve at all points, and manufacturers attempt to maximize shunt
resistance and minimize series resistance to the extent possible. The
equations are sometimes normalized for area of the cell, in which case
J is substituted for I in the equation.

This should be a good starting point for your study, good luck.

Bob Butcher



1337usr@gmail.com wrote: