Techniques for Evaluating PanelsLong ago， my buddy Eks observed： "If solar power is so good， why is
there winter？" His excellent engineering judgment notwithstanding，
photovoltaic （PV） panels appear everywhere these days： dark plates
facing the sun from buildings， backyards， and even utility poles.
Common performance numbers concentrate on the big picture with
sweeping assumptions that might well not apply in a specific
location. Although everybody seems to know the "kilowatt per square
meter" value of total insolation，few people can relate that to a
system‘s actual， usable output power.
In this column， I'll start from the other end by modeling and
measuring the characteristics of a small panel. You can use similar
techniques to evaluate larger panels， perhaps to verify a
manufacturer‘s claims or to characterize a panel's actual
performance in your system. After you work through the details， you
should have a much better understanding of how the big picture
looks from your standpoint.
MODELINGFigure 1 presents the classic circuit model of a PV cell： a current
source in parallel with a diode. The component values correspond
roughly to one cell of the panel appearing in Photo 1. Unlike
larger panels made from discrete slices from silicon wafers， this
panel is a flat glass sheet with deposited cells separated by
barely visible vertical stripes.
D1， the 1N914 diode in the model，has a forward voltage and maximum
current reasonably close to those of the panel‘s cells， but it's
obviously unsuited for modeling high-power panels. Achieving a
better match may require tweaking a Spice"ideal diode" model，
rather than using a standard part.
Current source I1 models the cell‘s photocurrent， which varies in a
surprisingly linear manner with incident illumination. The nominal
value is essentially the cell's ISC， the shortcircuit current
produced with 0 V across the output terminals.
The diode‘s forward voltage controls VOC， the cell's opencircuit
voltage. Unlike ISC， VOC doesn‘t vary much with illumination：even
diffuse sunlight can punch the cell's voltage close to its nominal
full-sun value. Even with little power（and， thus， current） behind
VOC at dawn or dusk， inadvertent contact with a high-voltage
panel‘s output can flatten you right out.
Shunt resistor RSH adjusts the slope of the current-voltage curve
near the short-circuit current limit， while series resistor RS
affects the slope near the open-circuit voltage. You can calculate
those values from measurements or use an eyeballometric
curve-fitting process. Both resistors represent parasitic losses
within the panel that depend largely on its chemistry and
construction.
The family of curves in Figure 2 simulates several values of RS
along with the output of the actual panel in Photo 1 scaled to a
single-cell VOC. The RS = 1.5-Ωcurve seems to be a reasonable
match，although further fiddling with RSH and D1 might improve the
fit.
A silicon-based PV cell has a VOC near 500 to 700 mV and an ISC
that， for a given technology， varies linearly with the cell's
surface area. Larger panels use cells wired in series for higher
output voltage and in parallel for higher output current.
Just as in the real world， modeling multiple-cell panels involves
little more than copying and pasting single-cell models in series
or parallel. However， if parts of your realworld panel can be
shaded from the sun， then your panel model must incorporate bypass
diodes and vary the current sources across the array.
You can create a more complex piecewise-linear model of each cell
with either a mathematical black-box table or curve-fitted
combinations of diodes and resistors. Spice simulations may run
slowly with a pure look-up table source， but figuring the values of
stacked diode-resistor pairs rapidly turns into a fierce
mathematical exercise that isn‘t relevant here.
Before you spend a great deal of effort modeling a specific cell or
panel， however， remember that real-world performance depends
strongly on illumination and temperature. It's generally better to
verify that your design works with an approximately correct source
than to get distracted by the third or fourth decimal place of an
incomplete model.
Remember that the standard model represents only the DC response，
which may turn out to be a serious omission for switching power
converters or grid-connected systems. We‘ll investigate that later.
TEST SETUPIt's relatively simple to measure the fundamental DC properties of
a PV panel： record the output voltage and current as functions of a
variable load. Getting well-calibrated values requires a known
illumination， but we civilians can slide by with the standard sun
found above any backyard lab. It should come as no surprise that
all values vary nonlinearly with temperature， so recording the
panel temperature is vital.
For obvious reasons， I was unwilling to buy a commercial PV panel
for this column， but I had the 11-cell panel in Photo 1 in my parts
heap. It came from a surplus supplier with only two specifications：
the 5″ × 6″ physical size and a 7.4 V at 170 mA rating. The rear
surface has aluminum contacts covered with transparent plastic
insulation that must be scraped off to make contact. Soldering
anything to aluminum is difficult， particularly atop a glass
substrate， so I had to find another connection method.
The panel‘s low-current rating suggested simply gluing connectors
to it with carbon-based wire glue， but the resistance turned out to
be 15 to 20 Ω per contact. I popped those off and discovered that
the glue left an impervious， completely insulating layer atop the
aluminum. Perhaps there's a strange chemical reaction going on？
After several other fruitless experiments， I folded copper fabric
adhesive tape to produce a metallic connection on both sides，
clamped it under a 0.1875″ quick-disconnect tab，and epoxied the
entire affair to the panel. Photo 2 shows the resulting joint，
which is surprisingly durable and has a resistance well below the
resolution of any of my meters.
I machined two openings for the contacts in an aluminum sheet，
spread a thin layer of Bondo body filler on the panel，and squished
it in place. The aluminum backing adds mechanical rigidity，
provides a convenient heatsink， and simplifies mounting the entire
affair to a scrap of plywood. While Bondo isn‘t a true thermal
epoxy， it's good enough for this application.
I also epoxied a small brass tube to the center of the aluminum
sheet and inserted a thermocouple to measure the temperature. The
reading from the rear of the aluminum sheet is within a few degrees
Fahrenheit of the value reported by my noncontact IR thermometer
for the panel‘s front surface in full sun.
The two 50-Ω power resistors on either side of the panel enable me
to raise its temperature well above ambient，which isn't something
you want in a normal application. I also tucked a foam sheet behind
the panel to reduce the effect of breezes.
The instrumentation consists of three multimeters attached to the
plywood base， one apiece for panel voltage，current， and
temperature. Each of my multimeters has a different current-sensing
resistor， so I picked the meter with a 1-Ω resistor for the
panel-current job.
My parts heap also disgorged a pair of big panel-mount
potentiometers that I glued to the plywood； they‘re barely visible
to the left of the yellow meter in Photo 1. This definitely won‘t
work for higher-power panels， as pots have a very low power
dissipation rating. On the other hand， this panel is good for 1 W，
tops， and those pots were well past their bestused- by date. Later
on， I'll show you how to build a variable load the right way， but
this will suffice for now.
I wired a 3-kΩ potentiometer in series with a 300-Ωpotentiometer，
both connected as variable resistors， to get enough resolution over
the entire current range. The panel‘s VOC was 8.3 V in full sun，
but 2.5 mA through the potentiometers at maximum resistance dropped
it to 8 V； I disconnected the potentiometers to get the true VOC.
The larger potentiometer covered the range up to 25 mA and the
smaller one went to nearly ISC. I shorted the potentiometers to
measure the output current limited by the meter's 1-Ω internal
resistance.
With all of that wired up， I sat on the front steps of our house，
aimed the panel directly at the sun， and started recording data.
POWER PRODUCTION
The purple curve arcing downward from the upper left of Figure 3
represents the panel‘s performance at about 80°F， before it warmed
up in the sun. The data points are about 10 mA apart up to 100 mA，
then every 25 mA above that， so there are relatively few points in
the left half of the curve.
Although the ISC and VOC points are easy to measure， the panel
delivers no power to the load at either point. The humped purple
curve plots the panel's power output calculated by multiplying the
panel‘s terminal voltage and current at each point. This clearly
shows that the maximum power output occurs near 5 V at about 125
mA.
That's just over 600 mW， far less than you‘d estimate by simply
multiplying the only two numbers in the panel's specs： 7.4 V and
170 mA. Those are evidently the panel‘s nominal VOC and ISC， not
its peak output.
The other curves in Figure 3 show the effect of temperature. The
panel stabilized at about 105°F in full sun with a breezy ambient
of 75°F， producing the blue curve. Applying 24 V to the power
resistors boosted the panel to 138°F to produce the green curve.
Both VOC and ISC change with temperature， although the details
differ. As with all such things， careful measurements trump
preconceptions. Because the voltage decreases with increasing
temperature， the maximum output power also decreases：
unfortunately， hot panels produce less power than cold panels.
Panels produce their highest voltage when they‘re coldest，a
situation that generally occurs just before dawn. If you're working
with multiple panels in series， the early dawn output voltage may
be much higher than you expect from the nominal rating.
The green power curve in Figure 3 shows that the panel produces 0.5
W （4.8 V and 110 mA） at the sort of temperature you‘d expect from a
weatherproof installation. To extract that power from the panel，
however， the load must draw 110 mA at 4.8 V， not whatever voltage
or current might be required for， say， optimal battery charging or
an instrument's power supply.
SIMPLE BATTERY CHARGINGOld-school PV battery chargers simply soaked up whatever current
the panel could produce at whatever terminal voltage the batteries
supported. As you‘ve seen in my previous columns， proper battery
charging requires more than random trickle charging， so a dumb
charger （or none at all）trades off complexity for battery lifetime
and performance.
This panel‘s output suggests it could charge a four-cell NiMH
battery pack. A fully charged cell runs about 1.5 V， so the final
charge current at 6 V would be 60 mA in full sun at 138°F. To
prevent overcharging， the cells should have a capacity of about an
order of magnitude larger. Contemporary low-end AAA NiMH cells run
about 750 mAh，with some claiming upwards of 1000 mAh。
With a quartet of 750-mAh cells discharged to the usual 900 mV/cell
endpoint， the panel will produce 120 mA at 3.6 V and charge the
pack at an initial C/6 rate.
Unfortunately， that rate won‘t last while the battery pack voltage
increases and it certainly doesn't apply all day unless the panel
tracks the sun. In fact， this solar panel would take two or three
days to fully charge a four-cell AAA pack， which is probably not
what you were expecting.
Because the panel‘s output is fully devoted to charging the cells，
there's no power "left over" to run anything else. You could swap a
pair of four-cell packs between the solar charger and your gadget，
but only if a pack lasts two or three days in normal use. A few
cloudy days can put an end to that schedule，though， because there‘s
just not enough energy available.
But it gets worse.
EFFICIENCYThat kilowatt per square meter of solar energy that everybody
quotes should come with a few asterisks： the utterly absorbing
surface must be perpendicular to the sunlight. A square meter of
solar PV panel doesn't produce anything close to a kilowatt.
The primary problem is the conversion efficiency： not all photons
falling on the panel turn into electrical current. A good rule of
thumb for packaged panels seems to be around 10% to 15%， with
higher efficiencies priced exponentially higher.
The panel in Photo 1 measures about 0.02 m2 and should absorb about
20 W when perpendicular to the full sun. Figure 3 shows that it
produces about 0.6 W at best， for an overall efficiency around 3%.
Perhaps it was a surplus panel for good reason.
I had no problem tracking the sun with my test setup， but that
doesn‘t work for larger installations. Obviously， if the panel
isn't perpendicular to the sun， it won‘t absorb as much energy and
its output will drop. Check the references and run the numbers for
your location； you may lose 10% to 30% of the incoming energy.
I also own a Powertraveller Powerm&111nkey solar
eXplorer，primarily because I chanced upon a $100 rebate that
brought the price down to my level. The basic Powerm&111nkey
consists of a 2.2-Ah lithium battery inside a small plastic case；an
assortment of connectors that match many common phones， PDAs，
cameras， and other electronic gadgets； and a wall-wart charger.
An internal 5-V DC/DC converter produces a constant output voltage
that‘s compatible with most gadgets， so， in theory， the
Powerm&111nkey can recharge your gadget when you're far from an
AC outlet. Even if it can‘t produce a full charge， you may be able
to make one last phone call.
The "Solar" option adds the folding solar panel in Photo 3，which is
supposed to charge the Powerm&111nkey battery from ordinary
sunlight. I had my doubts about this from the start and some
measurements confirmed my suspicions.
The "Outdoor" traces in Figure 4 show the output of the
Powerm&111nkey panel during a day with thin， high clouds. I
have no way to measure the actual insolation， but it was a
typically sunny day in these parts. The peak power output is 900 mW
with the panel perpendicular to the sun. Moving the panel indoors，
behind two panes of 1950s-era glass， cut the power output in half.
You can see where this is going. The Powerm&111nkey can produce
2.2 Ah at 5 V, for a total of 11 Wh。 Assuming 75% charging
efficiency， you must inject 900 mW for 16 h to reach full charge.
If the panel is inside your window， then plan on over 32 h. If you
only get 5 h of usable sunlight per day， then a full charge will
take three or six days.
The instruction manual alludes to this situation： "6 hrs of
sunlight will charge powerm&111nkey-eXplorer by one third."
On the other hand， the Powerm&111nkey solar panel is far more
efficient than my larger surplus panel. With an active area of
about 0.007 m2， the panel should absorb 7 W in full sunlight. It
actually produces 900 mW for an efficiency of nearly 13%.
That‘s pretty good， but you need more than four times the panel
area to recharge the Powerm&111nkey in a day. Perhaps it's no
surprise that they named their larger model Powergorilla？
CONTACT RELEASELogging data by hand makes perfect sense when you‘re first
experimenting with a gadget， but it gets really tedious really
quickly. In my next column， I'll take a look at the analog
circuitry required to automate the process， along with a bit of
firmware to get rid of the paperwork, too.
Ed Nisley is an EE and author in Poughkeepsie，NY. Contact him at
ed.nisley@ieee.org with "Circuit Cellar" in the subject to avoid
spam filters.
PROJECT FILESTo download the additional file, go to
ftp://ftp.circuitcellar.com/pub/Circuit_Cellar/2009/223.
RESOURCESJ. Bachiochi, "Collecting Solar Energy,"Circuit Cellar 209, 2007.
R. Campbell, "A Circuit-based Photovoltaic Array Model for Power
System Studies,"
www.ee.washington.edu/research/sesame/publication/Conference/2007/Campbell_PWL_PV_Model_NAPS2007.pdf.
K. Chapman, "Solar Panel Monitor,"Circuit Cellar 185, 2005.
S. Ciarcia, "Solar-Powering the Circuit Cellar," Circuit Cellar
209, 210,and 211, 2007.
T. Kerekes, "High Frequency Analysis and Modelling of
Transformerless PV Inverter Systems,"
www.iet.aau.dk/~tak/personal/phd_proj_descr.htm.
C. Landau, "Optimum Operation of Solar Panels,"
www.macslab.com/optsolar.html.
Linear Technology Corp., "Switcher-CAD III,"
www.linear.com/designtools/software/switchercad.jsp.
G. Martin, "Living and Working Off the Grid," Circuit Cellar 216
and 218,2008.
New York State Energy Research and Development Authority,
www.powernaturally.org/default.asp.
E. Nisley, "Battery Capacity: Charge,"Circuit Cellar 201, 2008.
---, "Battery Capacity: Discharge,"Circuit Cellar 199, 2007.
---, "Real-World NiMH Charging,"Circuit Cellar 221, 2008.
Wikipedia, "Maximum power point tracking,"
http://en.wikipedia.org/wiki/Maximum_power_point_tracker.
SOURCESSurplus solar panels
All Electronics Corp., www.allelectronics.com
The Electronics Goldmine, www.goldmine-elec.com
Wire glue
Anders Products | www.wireglue.us
Bondo body filler
Bondo Corp.
www.3m.com/us/auto_marine_aero/bondo/catalog_browsec9d6.html?parNbr=26gnuplot
gnuplot
www.gnuplot.info
Powerm&111nkey solar eXplorer
Powertraveller
https://powertraveller.com/iwantsome/primatepower/powerm&111nkey-explorer/
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