At the college where I work we have a compitition for tuition between all of the local districts for high school. It is an amazing opportunity where students get to earn up to 12 credits per person per compitition, or around 36 credits (a year!) If they won 1st in each. We award 1st 12credits, 2nd 8 credits and 3rd 4 credits. If you try it is likely you’ll do well as generally there are only 10-12 teams per compitition.

Last year I had everyone make solar ovens from scratch and bake cupcakes. Sounds great, but my supplies used styrofoam for insulation and grow lights to cook them since we have low intensity cloudy weather in February. It was cool but what a PITA. It took me and two students 3 hours to cleanup the mess on our knees vacuuming with a shop vac over 2000ft2. Nope never doing that again! So I immediately changed the compitition so it would be simple, easy to measure and CLEAN.

I designed a system where they would build solar concentrators and bring them finished and we would measure the light and power from solar cells and a light meter to evaluate who concentrated the most power to be crowned the winner.

After talking with my assistant professor I realized that we would need to normalize our numbers, because all solar cells are slightly different in their efficiencies and it wouldn’t be right to test only by light intensity and power ourput, as a student with a 18% solar cell would easily beat a student of a 9% solar cell. We could eliminate the solar pv cell and test just the concentration with the light meter but it tops out at 3x the light of ambient light and could damage the meter with heat generated, so we will need to interpolate the data and normalize it.

To find the effective solar concentration you need to know a few things; the light intensity of the sky around you, the concentrators light gain, the power of the cell before concentration and after concentration. If you had an expensive machine that tests the standard test conditions (stc) of the cells at 1000w/m2 @ 25c, I could just test the before and after and have a known efficiency of the cell. I do not sadly. Knowing that every cell will be off a little bit from each cell will make this much more complicated. So what do we do?

First let’s talk efficiency of pv. The sun ranges in light intensity from 0-2000w/m2 on average from lighted hours in a day. 6am being low intensity at around 150w/m2 to 1500w/m2 in my area. If you add all these up you get a power factor over a day of around 4000w/m2/day. If you have a pv module (panel) that measures 1 meter x 1 meter you will be able to get that 4000w in a day if it is 25c out. How do you measure it in a second or a minute? What if it isnt 25c out? To determine this we need to normalize the data so that every solar cell is equal to each other at any given pont.

  • So first we calculate what the size of the cell is and what fraction of that area is m2. Thats just geometry lxw minus the corner wedges cut out. Then you take what the cell produces at 100% efficiency (area x 1000w) and record what the volts, amps and intensity of the cell to find the power ((vxa) x the area) x current intensity/1000w to give you what you should get at 100%. Then divide the actual power by the theoretical to get the efficiency of the cell.

To find the actual power you take the stc conditions x efficiency x irradince/1000w/m2 to get the watts the cell produces. We are on the right track.

Ok now we have to create an stc of our cell even though it isnt 25c or 1000w/m2, but we do have the efficiency now. Ok, so we need to effectively remove the chemistry of the cell mathematically.

These are monocrystalline pv cells, which have a property that increases the cell voltage when it is colder than 25c and decreases the amperage. They are do the opposite when it is hotter than 25c. They are not proportional to each other by the same amount. The voltage moves roughly 10x the amount that the amperage does. For these solarworld cells (manufacturer) the temp difference is roughly -0.041%/c. So every degree in c it goes down the cell increases in power by .041% of the total power. So we solve for power and remove the temperature coefficient chemistry out of the cell to normalize it to its stc at the given efficiency. Now were in business.

We take this effective stc and we use it to find the true actual power at stc and at concentration. We then calculate the the true effective concentration by dividing the conventrated normalized stc cell power/the actual normalized stc power at the current irriadiance value to determine the percentage of gain in their solar concentrators. We did it!

Best part is I can do this by testing 6 variables, voltage,amps before and after, temp and irriadiance. These tests take about 10 seconds to test and excel does the rest.

I skipped some nitry gritty data and was a bit high level here, but if you care to see the data or my spreadsheet just comment and I’ll post it!

Now who said math isn’t fun?!

Leave a Reply

Notify of