If I connect my 20V open circuit PV panel to a discharged 20V cap
bank, I assume I get the short circuit current avail from the panel
until the cap charges up closer to 20V? Does this technique harvest as
many or more coulohms from the PV panel as trying to seek a max power
point from the panel? Seems like max current trumps max power when
charging the cap bank? What am I missing here?
Charging up a cap doesnt look like a short cct other than when you
Once the cap voltage rises above 0V it no longer looks like a short
The only way find the max power point of a Solar panel is to do what a
MPPT controller does, which is progressivley load the solar panel with
an ever increasing resistive load, whilst measuring the current draw
and the load voltage.
There are a number of common techniques for doing this , but most
involve a switch mode controller controlled by a small microcontroller
which continuously juggles the effective load on the Solar panel to
maintain max power at varying levels of sunshine.
Someone just answered your question, but someone has found interesting to
use the cap charged at open-circuit voltage as a startup current deliverer
for electrical motors.
This means: high peak power for a while, but low average power (that is what
we have at its maximum with a MPPT circuit)
All right, I _am_ an electrical engineer.
Let's have a little fun. To a first order approximation, a PV panel with
sun shining on it looks like any other "real" power source: It can be
modeled as a voltage source with a series resistance or a current source
with a parallel resistance.
So, remembering that this is all first order approximation stuff, the
open circuit voltage of the panel (no load) gives you the open circuit
voltage; divide this by the short circuit current and you have the
The circuit would then look like:
Sophomore EE201 has the equation for current, assuming that the cap
starts off with 0 charge at t = 0:
I(t) = V/R * (exp(-t/(R*C)).
Voltage on the cap would be:
V(t) = V*(exp(-t/(R*C)) - 1.0)
At t = infinity the current is zero; at t = 0 the current is V/R (your
short circuit current). Let "tau" be R*C; when t = 5*tau, you're pretty
much done. When t = tau, you're about 63% of the way there.
Oh, yeah: "exp(x)" is e raised to the x, where e is 2.718.
The reason that this is a first order model is that there's a ton of
second order effects. Your standard PV panel consists of a whole bunch
of P-N junctions wired up in series and parallel. So, the resistance of
the whole thing looks like the bulk resistance of all the silicon plus
the voltage drops of the P-N junctions, which goes I = Io *
(exp(q*Vd/(eta*K*T) - 1), where q = 1.609e-19 (electron charge), K =
Boltzman's constant, T is the temperature in Kelvin, and Vd = ln(I/Io -
1)*eta*K*T/q. Io is the leakage current the diodes when they're reversed
biased; natch, you've got diodes in parallel and diodes in series, so
life gets even more interesting. Oh, yeah: The diodes themselves are
capacitors, too, and the capacitance goes up as the P-N voltage goes
down. Lots of non-linear fun.
And, if you really want to get nasty, capacitors themselves are rarely
ideal. They have internal resistance at DC (leakage, especially
electrolytics) and odd things can happen when the ripple current into
one gets large. Capacitors have Q and D factors for first order loss
analysis; it gets even more fun when the frequencies begin to climb.
Now, I don't work with PV panels much, other than having fun looking at
the specs on the ones on my roof, so I haven't tried (or needed to) do
any modeling and simulation, but, for rather bigger caps (couple hundred
microfarads) I'd expect the first equation up there to work relatively
well; that is, the current curve you'd get would be within 10%-15% of
reality. For small values, all the nonlinear diode stuff would probably
through that curve right off.
Now, I notice in the EE trade rags that people are starting to talk
about supercapacitors as a storage mechanism. We're talking here about
capacitors with values up in the farads. If that's what you're thinking
about, it's not quite clear to me if just hooking a PV panel up to a
supercap is necessarily the best way to charge said cap. I could be
wrong about this, but typical power sources have max power transfer when
the external load has the same resistance as the internal resistance of
the source. Hence, some kind of switcher that draws the max power from
the PV panel (that is, ISC/2 at Vo/2 or something) and dumps said power
into the cap until the switcher runs out of steam at the higher
voltages, would probably be a better bet than just hooking said cap up
directly across the PV panel; more power in the batter, and faster, too.