Energy and Human Ambitions on a Finite Planet, 2021a

13 Solar <strong>Energy</strong> 206
Series combination adds voltages, keeping the same common current.
Parallel combination shares a common (low) voltage but adds
currents. The same power (P IV) obtains either way. But two
problems arise from a parallel combination of cells. First, the ∼0.5 V
voltage is too small to be useful for most devices. Second, the power
lost in connecting wires scales as the square of current, so designing
a system with a large current is asking for trouble. 39
That said, PV installations often combine panels in both series <strong>and</strong>
parallel—like 10 panels in series in parallel to another 10 in series. By
this time, the voltage is plenty high to offset the losses.
39: Making things worse, the voltage drop
in the lines is proportional to current, diminishing
an already small voltage to even
less by the time it gets to its application.
13.4 Insolation
Let’s start our journey from the physics principles we covered in Section
13.2. The sun’s surface is a sweltering 5,770 K, meaning that it emits
σT 4 ≈ 6.3 × 10 7 W/m 2 over its surface. The sun’s radius is about 109
times that of the earth’s, 40 which itself is 6,378 km at the equator.
Multiplying the radiation intensity by the area gives total power output:
4πR 2 ⊙ σT4 ≈ 3.82 × 10 26 W. That’s one bright bulb!
Sunlight spreads out uniformly into a sphere exp<strong>and</strong>ing from the sun. By
the time it reaches Earth, the sphere has a radius equal to the Earth–Sun
distance, which is r ⊕⊙ 1.496 × 10 11 m. 41 Spreading 3.82 × 10 26 Wover
a sphere of area 4πr⊕⊙ 2 computes to 1,360 W/m2 . That’s what we call the
solar constant [4], <strong>and</strong> it’s a number worth committing to memory. 42
Earth intercepts sunlight over the projected area presented to the sun: a
disk of area πR 2 ⊕ . Bright features like clouds <strong>and</strong> snow reflect the light
back to space without being absorbed, <strong>and</strong> even darker surfaces reflect
some of the light. In all, 29.3% of the incoming light is reflected, leaving
960 W/m 2 absorbed by the πR 2 ⊕ projected area of the planet. But now
averaging the 960 W/m 2 input over the 4πR 2 ⊕ surface area of Earth cuts
the number down by a factor of four, 43 to 240 W/m 2 .
High latitude sites suffer more from low sun angles, <strong>and</strong> obviously
cloudier locations will receive less sun at the surface. Taking weather into
account, a decent number for the average amount of power from sunlight
reaching the ground is about 200 W/m 2 . This is called insolation 44 —the
“sol” part of the word stemming from solar.
Solar Flux Context W/m 2
Arriving at Earth 1,360
Full, overhead sun (no clouds) ∼1,000
Absorbed by πR 2 ⊕ 960
Absorbed by 4πR 2 ⊕ 240
Typical insolation, includes weather ∼200
Typical delivered by 15% efficient PV 30
40: Why this convoluted path? Context.
Building from pieces we are more likely
to know/remember better engages our underst<strong>and</strong>ing
<strong>and</strong> ownership of the material.
41: . . . ∼150 million kilometers, or 1 AU
42: See: isn’t it satisfying to know that the
number comes from somewhere? It’s not just
a r<strong>and</strong>om fact, but connects to other pieces.
That’s what the earlier margin note meant
about context.
See Fig. 9.6 (p. 144) for a visual example.
43: We can underst<strong>and</strong> this factor of four as
two separate factor-of-2 effects determining
how much solar power a particular location
receives: one is simply day vs. night: half
the time the sun is not up. The other half
relates to the fact that the sun is not always
overhead, so the amount of light hitting each
square meter of l<strong>and</strong> is reduced when the
sun’s rays are slanting in at an angle.
44: . . . also called global horizontal irradiance
Table 13.1: Summary of solar power densities.
Full overhead sun can be larger than the
global absorbed number because the global
number includes reflection from clouds,
while overhead direct sun corresponds to a
local cloud-free condition.
© 2021 T. W. Murphy, Jr.; Creative Commons Attribution-NonCommercial 4.0 International Lic.;
Freely available at: https://escholarship.org/uc/energy_ambitions.