Sunday, February 24, 2008

The economics of an iterated V-panel

This post is a follow on to a post from last week. Now that I’ve learned that my international patent application has been published, I can discuss a second idea for building a solar panel with more mirrors than cells. The idea is still patent pending, but it is now in “the public domain” by virtue of its publication.

This idea, fittingly enough builds on the first idea. On several occasions I’ve posted entries on a V-shaped panel design, where the cells are oriented at 45 degrees to the panel cover (rather than parallel) and a mirror is placed opposite the cells. In this case, I iterate the design, by replacing each of the solar cells in the row of solar cells (now at a 45 degree angle to the panel cover) with a rotated cell and mirror pair. The result is a design that used ½ the solar cells by area as a standard panel—a significant savings as I will show.

Unfortunately if mounted in a fixed position the design only collects an equivalent amount of sunlight from ½ the sky. Perfect if the only place you can mount the panel is on the east or west side of a wall, building, mountain or other obstruction (where the panel would in any case not get light from the other half the sky).

But one can also mount the panel on a solar tracking system (1-axis) and have the panel produce power optimally all day. This design offers a trade-off, more power per $ invested in panels over a shorter portion of the day, or all day with the added expense of using solar tracking systems. For people already planning to use solar tracking systems, this design offers clear benefits.

Now let’s look at the economics. To begin with I make the same simple assumptions as before: 1) one square meter = 10 square feet and intercepts 1000 W of sunlight. 2) Solar panels “cost” $3.50 per W (producer wholesale price) and half this cost is due to solar cells ($1.75/W). 3) Mirrors cost $2.50 per square foot. I assume the mirrors reflect 100% of the light for simplicity, but then provide a $/W figure for a 90% reflective mirror in []. Except for the perfect mirror assumption, I believe these are conservative estimates.

So on a square foot basis, 100 W of sunlight hit a solar panel. I then look at two cases: case 1) solar cells are 10% efficient meaning the panel produces 10W per sq. ft.; case 2) solar cells are 20% efficient meaning the panel produces 20W per sq. ft.

Case 1) the cost of a square foot of standard design panel is $17.50 (10W x $1.75/W). With my cell & mirror design, I use 0.5 sq. ft. of solar cell ($17.5 x 0.5 = $8.75) and 1.3 sq. ft. of mirror ($2.5 x 1.3 = $3.25) per sq. ft. of panel. So my design costs $12 to produce the same 10W per sq. ft. which comes to $1.2/W…a 31% savings!
[For a 90% reflective mirror the cost is $1.28W, a 27% savings]

Case 2) the cost of a square foot of standard design panel is $35 (20W x $1.75/W). With my cell & mirror design, I use 0.5 sq. ft. of solar cell ($35 x 0.5 = $17.50) and 1.3 sq. ft. of mirror ($2.5 x 1.3 = $3.25) per sq. ft. of panel. So my design costs $20.75 to produce 20W per sq. ft. which comes to $1.04/W…a 41% savings!
[For a 90% reflective mirror the cost is $1.11W, a 37% savings]

Besides reducing the $ cost of solar, these designs use less silicon which should lead to a shorter EROI (the time it takes for the panel to generate as much energy as was used to produce it) since it takes a lot more energy to produce solar cells than a mirror (or a solar tracker).

If no additional savings can be achieved (I believe additional savings exist) in the “balance of panel” costs, then total panel savings of 15-20% are easily achievable using this design if solar cells are assumed to make up half the price of the solar panel.

While this design is a little more complex (because of the iterative nature of it) than the prior design, it is still relatively straightforward. As far as I’m aware, any known solar cell technology can be used.

Edit 2/25/08: I just discovered that my US patent application published here. The US patent format is slighly easier for me to read.


At 9:51 AM, Anonymous Anonymous said...

Hi there Daniel. You've got some interesting ideas. You may also want to consider non-imaging curved optics, like this one. In stead of a pipe you'd have a strip op PV cells in a vertical position. PV area required would be even less and a sun-faced collector would have a very high and consistent output during the day. The optics also capture diffuse light quite nicely like your booster mirror design.

Maybe something cheap like mylar could be used for the reflective area?

Another idea would be a hybrid pv/thermal water system using such a design.

At 1:16 PM, Blogger Daniel said...

Thanks for the comment and compliment anon. I like how your mind works.

I am familiar with the solargenix design. I like it. And an invention much like the vertical PV cell that you refer to was granted to one Anthony Finkl of Sarasota FL (US patent 5,538,563) in 1996.

I am a big believer in cheap mylar mirrors as you will see if you search my blog for "solar distiller".


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