Bragging rights

Cariboocoot

Re: Bragging rights

westbranch wrote: »

Or use a virtual array with each part set at a different orientation to the sun.

Virtual tracking.
Yes, that is what I would do. Panels on the porch roof would catch early morning light and start charging sooner which would improve the performance.

I don't have to worry about that unless the Mrs. buys even more electric kitchen gadgets.

Lee Dodge

Re: Bragging rights

AuricTech wrote: »

I found a table (Table 3 in this article) that displays the effects of elevation on insolation at a given latitude (in the case of the linked table, latitude 38.95N). If I'm reading it correctly, then insolation at an elevation of 1000 meters should be close to (insolation at sea level)/.89 . Doing the calculation doesn't quite give the results in the table, which leads me to believe that there's some rounding-induced errors, but it does come close (dividing global insolation at sea level [556.1 watts/m^2] by .89 = 624.8 watts/m^2, while the table gives global insolation at 1000 meters as 614.9 watts/m^2).

Is this the basic process by which you calculated your derating factor?

You raise an interesting point about the effect of elevation on solar insolation, and provide a good reference. However, you are not treating the effect of relative air optical depth at zenith correctly. That is clear, because using your formula, dividing the insolation at sea level by the optical depth would lead to infinite solar insolation when the optical depth goes to zero, i.e., at the outer edge of the atmosphere!

The actual relationship is:
I = I0 * exp(-sigma * c * l)
where
I = insolation at any optical depth (W/m^2)
I0 = insolation at zero optical depth, i.e., outside the atmosphere (W/m^2)
sigma = scattering and absorption coeff.
c = concentration
l = path length
In this case, cl = optical depth

From the data in the Table 4 that you referenced, you can solve for I0 = 1062 W/m^2, and sigma = 0.8934. Plugging these into the equation above, you can duplicate the data in Table 4 pretty closely,

Altitude, Rel. Optical Path, Direct Radiation, Value from Eqn.
(m) (-) (W/m^2) (W/m^2)
0 1 435.9 434.6
10 0.999 436.3 435.0
1000 0.89 482.0 479.5
2000 0.78 528.1 529.0
3000 0.69 573.8 573.3
4000 0.60 618.4 621.3
5000 0.53 661.4 661.4
space 0.00 ? 1062

The formula is not exact because the optical depth is at the zenith, while Table 4 data are for insolation levels at 38.95N.