Much cheaper photovoltaics part 1
Okay, what you see above is a nice graph of power output vs. irradiance at the panel surface for a typical polycrystalline panel, for 3 different *ambient* temperatures. Amorphous panels are better, with a temp coefficient of 0.0027 or so, but I couldn’t find any for sale to get the price info, so I didn’t use them, although they are usually cheaper than polycrystalline and everything here should work even better with them if you can get ’em.
Okay, so I previously mentioned the fact that it is clearly wrong that tracking systems and mirrors cannot give you more bang for your buck from a photovoltaic panel. Now I worked out the details reasonably well for Minnesota with a spreadsheet, and it looks like it would greatly reduce the price of the system. Incorporating the stuff below I think you could reduce the cost of the actual panels by a factor of 2.8 or even more if you had a lot of space for the reflector, and there is no way the cost of teh reflector and tracking stuff is going to even start to cancel that out, as I’ll go into a little more in part 2. To start explaining observe the graph below, which shows the “direct normal irradiance”(which is the amount of light hitting a surface perpendicular to the sun’s rays) and “diffuse horizontal irradiance”(which is the amount of radiation cominf from the rest of the sky, after having been scattered by clouds etc.), figure 2:
This is January, and the x axis is days.
Again this is all with typical meteorological year data, which is not perfect but gives a reliable idea of what’s going on. Actually I discovered a while back this great software called “system advisor model” from the National solar radiation database people, which I recommend you google and download if you are thinking of installing a photovoltaic system. It simulates stuff like we are doing here but better, except it can’t simulate the precise type of system that we are talking about, which is a concentrating and sun tracking apparatus that uses commodity solar panels we can actually obtain. It’s where I got the handy equations and some numbers for how to account for the temperature of the solar cells though.
So I did it in calc. The system is corrected for the temperature the PV cells will reach, and this is pretty important because they get much less efficient as the temp goes up (and the temp goes up with the irradiance). This is what causes the curve in figure 1. If the panels had the same efficiency at all temperatures the plot would be a straight line, which would be nice, but…. Also, the windspeed is significant, but was too much work to take into account, so I assumed it is always 1 meter per second, which is lower than usual (average in Minneapolis is 4.6 m/s), which means the simulated performance of the system is only under, not over estimated. So it doesn’t invalidate that this system should work at least as well as laid out here.
Basically I was going to try simulating several systems, but it takes quite a bit of time especially since my computer is so slow, so I just did what would, I think give the very best performance : A variable concentration ratio collector. I have a few ideas on the details of how to do this which I’ll post in part 2 of this, and am sure there are much better ideas in the ether, including in the crowd here. But for now let’s look at the potential performance increase such a system would provide, so we know how much there is to gain.
The fact that it can vary it’s concentration ratio within a certain range allows it to acheive high concentration levels when there is little sunlight (which you can see happens sometimes in figure 2) while at the same time not overheating the panels when the sun comes out in full force.
First we want to know what the maximum operating temperature of the solar cells is. I found on the net somewhere that panels are rated for between -40 and +85 degrees c ambient. They might actually be capable of more than that, I bet there is room for experimentation there. The Datasheet of a typical polycrystalline solar panel, the SUN-SV-T180 tells us that the cells of such a panel operates at 26 degrees above ambient at 800 watts of irradiance and 1 meter per second wind velocity (“open rack” presumably, which means it is not mounted on a roof, just free in the air which improves air circulation). From that we can find that the U value between the actual silicon cell and the great outdoors, 30.7 or so.
If the panels are rated to operate at 85 deg c ambient they must be able to accept 800 watts or so at 85 degrees, so their maximum operating temperature is 85 plus 26 degrees, 111 degrees.
So with this info and the climate data, including hourly ambient temperature and solar irradiance values I can make a spreadsheet that simulates the variable concentration ratio collector, for some reason I decided it should be able to concentrate between 3.6 and 14.7, which is a pretty big collector but actually if you reduce it to 8 that is still good and you can make it even less with performance hits, as mentioned below. You can change it in the spreadsheet easily.
I couldn’t get the data out of SAM, so I can’t put them on the same graph, but you can see the difference. Also I would like to put the data for the concentrator on a more detailed graph but calc keeps crashing.
That SUN t180 panel is about the cheapest there is actually obtainable and is $1.69 per watt, $1690 per kW of panels, 12% efficient which translates to $202.8 per square meter.
5 kWh is pretty low useage even for a tinyhouse, and you can see from the graph, the unassisted 0.9 kW (8.1 sq meters) of panels would give you about 78 kWh per month in the limiting month, or 2.6 kWhr per day. So for 5 kW we need 1.92 kW(EDIT: I made a mistake there, tha should read 1.73 kWh arg so the remaining calculations are nor quite right but still same general idea) of panel, or $3244.8, (plus tax and shipping). With the concentrator and tracking system you would get 220 kWh per sq meter of panel in the limiting month for the same size panel so you only need 1/2.83 times as much solar panel (2.86 sq meters).
Also, by the way you can’t see it in the graph, but I checked what would happen with only a max. conc. ratio of 8 and it’s still 1/2.53 the cost. With a solar collector like this you would save (1-1/2.83)*3244.8= $2098. There’s no way a homebrew tracking system and collector made with 2 by 4s, door hinges and $70 actuators and some electronics is going to cost that. Another bonus of this system is that you have a more even distribution of solar input, which would reduce battery cost too. That would be another interesting thing to do with calc. Actually calc is too slow. I can’t believe how much time I spent on this so sorry if I seem like I’m rushing.
I haven’t figured out exactly the best way to make such a thing, but tune in next time for some ideas, and also some actuators and stuff about mirror configurations so maybe y’all can think of something even better.
Improvements in the system could be made by using amorphous panels and maybe and even bigger max. concentration ratio. Also, including the wind speed might give substantial gains. I wonder about using a fan or something, a big, slow moving fan might actually give you a substantial net energy gain after the electricity it uses. As you can see from figure 1, there is not much point in trying to operate the panel at higher irradiance values, though, because you actually end up with *less* power above about 3500 watts/m2 or so due to increased temps.
Here is the spreadsheet: