Solar Power Nonsense

I often see people say, "we need to convert to solar energy before the world collapses."  Or something to that effect.  OK, what do we when the sun isn't shining?  Of course the answer is energy storage.  What a minefield of unanswered questions.   I am hoping that Elon Musk gets his proposal for South Australia accepted so we can see how that plays out.  I really hope we do this experiment.   Of course the problem in South Austrailia has to do with wind energy generation.  Their reliance on wind generation has had terrible consequences.  Google it.  But we can compare wind to solar for this study.  I notice that Al Gore is lauding south Australia for its experiment.  The people of South Australia certainly do not appreciate being part of that experiment! 

Let's do the calculations using batteries as the energy storage mechanism, just to show how ridiculous it is.  There are other energy storage mechanisms that will be necessary to lend any credence to this as we will see!  There will have to be some truly remarkable energy storage breakthroughs to break us from traditional power plans.  Not happening yet. 

Just a few calculations.
Let's assume that the average family uses 10 KWHr of energy per day (it is more like 20-30, so I am being generous).
Let's assume the average family is 4 people. 
Let's assume the population of the country is 400 million (really about 360?)

So the average energy we need per day is 100 million familes times 10KWhr, or 10^8 times 10^2 = 10^10KWhr of energy. 
Divide by half if we assume the sun is shining for half the day (a very liberal assumption).   And yes, I know energy usage during the night is less. 
So we will need .5 times10^10 KWhr of energy to cover the US. 

Let's assume Lithium Ion batteries.  I believe they are the most energy efficient today, and the technology that Elon Musk is using. 
From his site for Powerwall  we can figure out that the energy density storage is app 3KWhr/ft^3. 
[14KWhr per powerwall which is 6x29x44 in]
This costs about $8K.  NO provision for inverters/distribution/connection to grid at this time.  We will consider that later.

So, the amount of battery space using Musk's battery tech is (.5times10^10 KWhr) / (3KWhr/ft^3) = .16 times 10^10 ft^3
There are 144.5times10^6 ft^3 per cubic mile.  So this is about 1 cubic mile of batteries, or let's make it 10 feet high, so that is 525 square miles of batteries 10 feet high.
Maybe we should space them out.  You think!  Let's increase this to 5,000 square miles of batteries 10 feet high.  This will leave room for everything else, like buildings, roads, maintenance, ancillary equipment, a spare battery stock, etc.  I seriously doubt this is enough room still, given the efficiency  -not calculated here-  How much heat do you suppose this will generate!!!!!  --we are assuming none here! 

We can also calculate the cost.  $8K per powerwall is listed on the site.  Let's be very generous and say costs will come down by half in the next maybe 10 years - say $4K per powerwall, $4K per 14KWhr.  So this is (10^10KWhr) x ($4K/KWhr) =  4times10^13 $, or 4 billion thousand dollars, or 4 trillion dollars JUST TO BUY the batteries.  And God forbid let us not even consider where we are going to get all the precious metals --- China?  Is there even this much in the world recoverable?  How much  can you use for batteries? 

Let's be generous and distribute them to the 50 states. So we have 100 square miles of batteries in each state.  10 foot high.  Probably more like 1000 square miles in states like CA, NY, TX!  That is bigger than most metro areas - 30x30 miles. 

Now we have the problem of inverters to convert all this DC power to AC.......   And somehow it will have to connect to the existing power grid to assume the generation when there is no sun/no solar.  Of course we have the problem of the varying solar generation during the day, let alone the complete absence at night.  How in the world do you manage this power switching? 

And we have the problem of distribution.  Certainly the conversion to AC from DC will have to be done at the battery site, otherwise the size of the cables to carry DC current [at comparitively low voltages] is simply ridiculous. --It may take all the copper we mine!  And I cannot imagine what the inverter/etc electronics will look like to convert 1000 square miles of a battery farm to AC.  Can you?

We have not considered the generation side of this equation.  How many thousands of square miles of solar panels to generate this power....  I will leave that as an exercise to the reader.  The collection of the DC current from the solar arrays is another problem.  Typically you place very small DC/AC converters next to the arrays so you can do the transmission in AC at much higher voltages. 

Actually, let's do the calculation......   We will have to generate twice the 10^10 KWHr of energy each day, half to power the country and half to charge the batteries to prepare for the night. 
My sources estimate 50 WHrs per sq ft of array averaged over a day and a year and over the US.  Let us assume 100 WHrs to account for advances.  So .1KWhr per sq ft.  We need 2 times 10^10KWhr to run the country and charge our battery farms for use during the night.  So this is (2 times 10^10KWhr) / (.1KWhr/ft^2) of Solar PV area, or 20 times 10^10ft^2, or (20 * 10^10ft^2) / (27.5 * 10^6 ft^2 per mile^2), or about 10,000 sqare miles of array.  If you divide this between the 50 states, this is 200 sq miles of arrays in each state.  Or a 14 mile square array.  Let's assume 100 mile square array since we will have to space them out!!  In each state.  PLUS the 1000 sq miles of batteries!   More like 1000 mile square array in CA, NY, TX, and maybe 10 mile square array in WY for example.  CA is 164,000 sq miles.  So about 1 % of the state's area for batteries and arrays.   HUH!!?? .  Of course you can't put these in Yosemite. 

The advances in technology and the declining costs of all this will certainly improve in the future.  But I think you can see how ridiculous the notion is that we could replace our current power infrastructure with solar -using battery energy storage- anytime in the say, next 50 years?   Where is the breakthrough in energy storage technology we need? 

Solar power generation has its place in niche markets across the world.  There are obvious advantages to solar in very specific applications.  I have played with it at my house, but it is simply not yet cost effective.  EVEN with the free money the government gives you to try to give this a head start it is very questionable.  And make no mistake, the costs of solar are coming down, mostly because the Chinese have captured the market and driven US companies out of business!!!  

But the statement that we just need to convert to solar is ridiculous in the extreme.

This quick study is along the same lines of the one done exhaustively by google some years ago.  See this link for more info.  Here is their basic conclusion.
Even if one were to electrify all of transport, industry, heating and so on, so much renewable generation and balancing/storage equipment would be needed to power it that astronomical new requirements for steel, concrete, copper, glass, carbon fibre, neodymium, shipping and haulage etc etc would appear. All these things are made using mammoth amounts of energy: far from achieving massive energy savings, which most plans for a renewables future rely on implicitly, we would wind up needing far more energy, which would mean even more vast renewables farms and even more materials and energy to make and maintain them and so on. The scale of the building would be like nothing ever attempted by the human race.

Here is another good read, especially about "Battery derangement Syndrome."
Another study.
Interview with Bill Gates.  quote: 

"It’s kind of ironic: Germany, by installing so much rooftop solar, has it that both their coal plants and their rooftop solar are available in the summer, and the price of power during the day actually goes negative—they pay people to take it. Then at night the only source is the coal, and because the energy companies have to recover their capital costs, they either raise the price because they’re not getting any return for the day, or they slowly go bankrupt."