Sunflower a Turd Blossom?

The EnergyInnovations Sunflower-250 has received a fair amount of press lately as a concentrator-photovoltaic system.

http://www.energyinnovations.com/sunflower250.html

After taking a look at the description and artist's impression I was certainly curious. There are several obvious problems. First, the artist's impression shows that the mirrors are self-shading each other, reducing the available irradiance. I also had serious concerns that the system, being horizontally mounted, would have inferior performance outside of the summer solar noon.

I decided to model the system at solar noon on June 21st and December 21st in Pasadena, CA -- latitude 35^ North. This corresponds with the sun being at 10.5^ and 57.5^ to the horizontal on the summer and winter solstice, respectively.

I made the following assumptions about the system:

1. It consists of 25, 254 x 254 mm flat Aluminium mirrors, tightly packed. This corresponds to a total horizontal area of 1.613 m^2.
   
2. The collector was slightly larger than an individual mirror, at 280 x 280 mm. This corresponds to an area ratio between the mirrors and collector of 20.56 times.
3. Incident radiation was 1000 W/m^2 for both dates.
4. Aluminium has a broadband reflectance of 0.9 over the solar spectrum. No anti-reflection coating is used, due to coat, broad-band nature of the light, and the high variation in incident angle.
   

With an area of 1.613 m^2 and irradiance of 1000 W/m^2 the mirrors, if totally flat, will see 1586 W on the summer solstice and 866 W on the winter solstice. After simulation in Zemax, I found the actual power on the collector to be 1224 W for the summer and 804 W for the winter. Given their claim of 200 W output, assuming 1000 W/m^2 irradiance, discounting atmospheric scattering, on the best hour of the best day of the year the PV unit would have to have an efficiency of 16.4 % to achieve this. The actual insolation is more like 850 W/m^2 for the Pasadena region at that time.

The summer configuration has a ratio of 0.77 between the power on the mirrors and that on the collector, giving an overall concentration ratio of 15.86 x. This is well below the 25 x quoted by EnergyInnovations. It is possible to increase the concentration ratio by shrinking the collector to 254 x 254 mm, but at the expense of about 10 % of the overall power. The following image shows the irradiance map on the collector, with the red box measuring 254 x 254 mm (the size of one mirror). At solar noon in the summer, the sun is nearly directly overhead and the unit does a good job of evenly illuminating the collector.


In the winter, the system does better: the ratio is 0.93. This is an interesting result, but it can be explained by examining the mirror configuration. Here is a rendering of the system in its winter configuration:

As you can see, while there is significant shading of the rear mirrors, the overall shape of the system is no longer particularly flat. Instead it forms a curve, to catch more of the sun's rays, improving the overall performance. This result was somewhat surprising.

However, this is not necessarily a positive result. For one thing, the horizontal angle greatly decreases the irradiance available in the winter. For example, a flat plate PV system set at 35^ to the horizontal would see 1470 W on the summer solstice and 1490 W on the winter at the given 1000 W/m^2 intensity. At high angles of incidence, the horizontal layout only has a narrow cross-section to the sun, greatly reducing winter performance. Worse, due to the high angles, the presented cross-section of a mirror looks less like a rectangle and more like a trapezoid. The narrow cross-section results in uneven irradiance on the collector:

As you can see, a large part of the collector isn't receiving light. This is a fundemental issue with the use of flat mirrors. Partial shading of solar cells tends to decrease the performance of the unit as a whole, by creating a leakage current in the shading region. When electron-hole pairs aren't being actively created, the dispersion layer between the p and n-doped semiconductors is not as strong. The following journal article goes into some detail on the performance issues:

http://www3.interscience.wiley.com/cgi-bin/abstract/104543523/ABSTRACT

Note that the unit will have the same problem in the morning and early evening. This uneven illumination of the PV unit will probably shorten its lifespan, although they have added a fan to try and reduce the temperature gradients.

Of course, this totally ignores the effect of diffuse light, which as I noted before, cannot be effectively concentrated by mirrors. Clouds, smog, haze; all will have a ruinous effect on the performance of this system. Note that in EnergyInnovations' Frequently Asked Questions, there isn't a single mention of the world cloud.

After doing this analysis, I can't help but be cynical. It seems to me that this device is being designed to maximize its peak power output (W_p) rating, not its annual capacity factor (kWh/year). The system will suffer from performance losses due to cloud cover, the horizontal layout, and current leakage from uneven photovoltaic irradiance. Why would someone design a system optimized for peak output? Aside from the obvious marketing value, there is another reason if you are familiar with California solar subsidies. California's PV subsidy program has a loophole in it big enough to drive the governator's Hummer through: the subsidy is paid out at $2.80 per peak Watt. The actual annual power production is not considered, because net metering is not required. This has lead to a number of absurd installations on homes, like where the panels are installed on North facing roofs or in the shadow of a large tree. This is in stark contrast to German subsidies, which are for the real power produced. The big question would seem to be, will the new Million roofs program fix this loophole? So far, I haven't been able to find out.