Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 210
But the main purpose of this box is to point out the following. Full
overhead sunshine bathes the ground in about 1,000 W/m 2 . 55 So if
you could contrive to keep the sun directly overhead for 5 hours,
you’d get 5 kWh of solar energy for each square meter on the ground.
Therefore, if your site is listed as getting 5 kWh/m 2 /day, it’s the
equivalent amount you’d get from 5 hours of direct overhead sun. 56
What actually happens is that the day is longer than 5 hours, but
for much of the day the sun is at a lower angle so that the panel
is not directly illuminated, <strong>and</strong> weather can also interfere. This
leads to a concept of full-sun-equivalent-hours. A site getting an
annual average of 5.4 kWh/m 2 /day might be said to get 5.4 hours of
full-sun-equivalent each day. It’s a pretty useful metric.
55: It’s 1,360 W/m 2 at the top of the atmosphere,
<strong>and</strong> the atmosphere blocks/scatters
some of the wavelengths outside the visible
part of the spectrum.
56: This equivalence relies on the convenient
fact that full overhead sun is about
1,000 W/m 2 . It would not work otherwise.
Box 13.2 leads to a crucial bit of underst<strong>and</strong>ing on characterizing a PV
system. Panels are rated on what they would deliver when illuminated by 57: The 1,000 W/m 2 is reasonable, but a
1,000 W/m 2 at a temperature of 25 ◦ C. 57 So the measure in kWh/m 2 /day, photovoltaic panel in full sun will be about
or full-sun-equivalent hours tells you effectively what fraction of a day
the panel will operate at its rated capacity.
Example 13.4.1 A 250 W panel at a location getting 4.8 kWh/m 2 /day,
or 4.8 full-sun-equivalent hours, is basically operating at 250 W for
4.8 hours out of every 24, or 20% of the time. So the panel delivers an
average powerof50W,not250W. 58
The 250 W rating is referred to as “peak” Watts, sometimes denoted
250 W p . Panels are sold this way, <strong>and</strong> now cost about $0.50/W p .
30–40 ◦ C hotter than its surroundings (it
gets hot!), so it would have to be very cold
outside to meet the specification of 25 ◦ C
panel temperature. Solar panel performance
wanes when hot, <strong>and</strong> will only reach 85–
90% of rated capacity in typical conditions.
58: We would need to apply a de-rating of
0.85 to 0.9 to account for typical PV temperatures
in the sun, bringing the panel to
about 45 W average power.
A 30-year study by the National Renewable <strong>Energy</strong> Lab [88] initiated in [88]: National Renewable <strong>Energy</strong> Lab (1994),
Solar Radiation Data Manual for Flat-Plate <strong>and</strong>
1960 characterized solar potential across the U.S. <strong>and</strong> produced detailed
Concentrating Collectors
statistics on what each location might expect to collect each month for
panels in different orientations. Table 13.2 is a subset of the complete
data for St. Louis, Missouri. 59 All cases in Table 13.2 correspond to a
panel facing south, at various tilts (including flat, at 0 ◦ <strong>and</strong> vertical at
90 ◦ ; other tilts are relative to the site latitude of θ ≈ 39 ◦ ). From this, we
see that tilting the panel at the site latitude delivers an annual average of
4.8 kWh/m 2 /day, matching the graphic expectation from Figure 13.11.
Also shown is the monthly breakdown <strong>and</strong> how different tilts translate
to performance. We will visit this table again in Section 13.6 to help us
establish an appropriate size for a residential installation.
59: . . . a fairly typical solar location in the
U.S.
south
0 o
θ–15 o
θ
θ+15 o
90 o
Figure 13.14: Panel tilts for Table 13.2, for
θ 39 ◦ .
Angle
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
0 ◦ 2.2 2.9 3.9 5.0 5.9 6.4 6.4 5.7 4.6 3.5 2.3 1.8 4.2
θ − 15 ◦ 3.2 3.8 4.6 5.4 5.9 6.3 6.3 6.0 5.3 4.5 3.2 2.7 4.8
θ 3.6 4.2 4.7 5.3 5.6 5.8 5.9 5.7 5.3 4.8 3.5 3.1 4.8
θ + 15 ◦ 3.8 4.3 4.6 4.9 4.9 5.0 5.1 5.2 5.1 4.8 3.7 3.3 4.6
90 ◦ 3.5 3.7 3.4 3.1 2.6 2.4 2.6 3.0 3.5 3.8 3.2 3.0 3.2
Table 13.2: Solar exposure (kWh/m 2 /day)
for a south-facing panel in St. Louis, MO,
at various panel tilts (θ is latitude, which
happens to be 39 ◦ for St. Louis). 0 ◦ means
a panel lying flat, pointing straight up (like
on a flat roof), <strong>and</strong> 90 ◦ means vertical, like
on a (south-facing) wall (see Figure 13.14).
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.