
Where are we on the actual math of solar power? - randomnumber314
I&#x27;ve seen several articles and threads lately that make claims of solar energy matching or surpassing that of more traditional (coal, gas) energy.<p>What&#x27;s the &quot;simple verdict&quot; on it--is there simple math?
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CyberFonic
As an approximation solar flux is about 1kW / m^2. Last time I looked the
efficiency of panels was about 20% so we can generate about 200W / m^2 for at
most 6 hours a day. The USA power usage / day is 4^15 W.hr.

As 1km^2 = 1,000,000 m^2. So taking the power usage, we divide by solar flux,
by number of hours of high solar input, by 200 W / m^2, by area conversion,
and get approx 3,000,000 km^2. Since the USA is 10,000,000 km^2, we would need
to cover 1/3 of the country with solar panels to generate enough electricity,
mostly down south where the sun shines the most. Alaska would be spared.

Since we use power 24 hours a day and can only expect to generate at peak rate
for 6 hours, we need to store the power in batteries. Not to mention that not
every day is sunny. It sometimes rains, panels get covered in dust and need
cleaning, stuff breaks down, etc.

A Tesla PowerWall stores approx 120KWhr / m^3. So 4^15 / 120^3 = 33^9 m^3 just
for the batteries, not including cabling, racking, etc. To get an idea of how
this compares, Trump Tower in Chicago is approx 80,000 m^3. So we'd need
400,000 of them to house the batteries and this only for one day's worth of
power.

Of course, none of the foregoing considers the power required to make the
solar panels, the mounting hardware, the batteries, the housing and new power-
lines. The math just gets more complicated. But if you were to consider every
step from beach sand to working solar panels you will find that the lifetime
energy produced by solar panels is less than that which was used to produce
them in the first place. I read an article to this effect once, but can't find
it. Google is your friend if you are interested to research further.

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verite
The USA power usage is actually closer to 4x10^15 W-hr per year, not per day.
Source:
[http://www.eia.gov/state/seds/sep_sum/html/pdf/sum_btu_1.pdf](http://www.eia.gov/state/seds/sep_sum/html/pdf/sum_btu_1.pdf)
; 1 btu is 10^3 joules so 10^5 tbtu = 10^19 j ~= 4x10^15 W*hr. So your land
coverage requirement is off by a factor of a few hundred.

For battery space, the same factor of a few hundred still applies. Also I'm
not sure where you looked up the volume of the Trump tower but wikipedia
claims a floor area of 240,000 m^2 and I doubt people can walk in an area a
foot tall. With a more realistic ceiling height of 3m, you'd be off by another
factor of 10 there.

\--> Closer to 1/1000 of land area for coverage and 100 trump towers for
storage.

Your claim on it taking more energy to make a solar panel than it produces is
likely untrue, but I don't have enough scientific background to quantitatively
refute it.
([http://www.nrel.gov/docs/fy99osti/24619.pdf](http://www.nrel.gov/docs/fy99osti/24619.pdf)
claims a breakeven period of 2-4 years)

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vectorwhat
From your document it seems that the researchers ignored the most energy
intensive part of the process!

From your document:

"Purifying and crystallizing the silicon are the most energy-consumptive parts
of the solar-cell manufacturing process."

"To calculate payback, Dutch researcher Erik Alsema reviewed previous energy
analyses and did not “charge” for the energy that originally went into
crystalizing microelectronics scrap."

The way I understand it, the calculations don't charge the most expensive part
of the process by arguing that, being scrap of the semi-conductor business,
its already been paid.

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vectorwhat
I'd like to see the math myself. I have the suspicion that there's funny math
involved, like when the nuclear industry forgets the cost of warehousing
nuclear waste for 100 000 years.

My most pressing question is how the capital costs are factored in. China
built a huge PV capacity and arguably that made the price of panels collapse.
Also, the semiconductor industry had been indirectly subsidizing the PV
industry by upgrading their old fabs.

I also really don't understand how PV can be cheaper than Concentrated Solar
Power < literally just a bunch of mirrors aimed at a normal thermal plant.

Lot's of funny numbers, lots of questions, few open source gitted models
available to play with.

