[robomartin]

Well, I’ll get you started with the math…

Under absolutely ideal conditions, the power output of a solar array is an inverted parabola spanning 12 hours. This means you need 1.5x nominal capacity (integral if parabola is 2/3 area of constant power rectangle).

Of course, now you need batteries to “fill-in” around the parabolic output curve.

This takes care of daytime needs. Double it to cover nights. You have to more than double batteries because you need them 100% of the time during this period.

We are up to 3x nominal steady-state power. It’s a bit worse than that given system and other losses. Call it 4x. If you need 1 GW, you have to build 4 GW.

However, it doesn’t end there. A single cloud formation can cut output by 50%. I see it all the time on my system. Rain? Up to 95%. I’ve seen my 13 kW system go down to 600 W for days with moderate rain. Dirt? 5% or thereabouts, depending on how bad it is. And then there’s the negative temperature coefficient and seasonal realities, which can drop you by up to 25%.

If you do the math (as I have) the reality of solar is shocking. A 10x overbuilding estimate might be way low. I’ve seen plausible calculations calling for multiples of that.

[bryanlarsen]

Sure, you did the math for local solar only.

But if you add in existing hydro + nuclear, a good proportion of wind (which is more consistent and stronger at night), some good long distance interconnects, and a modicum of storage, the number comes out a lot smaller.

Here's the math: https://mitpress.mit.edu/9780262545044/electrify/

It comes up with a 20% overbuild.

[robomartin]

Where is the math? All I see is a link to a book.

Without going too deep: If you need 100% backup for solar, why use solar?

I built a 13 kW array. During recent rains I saw it go down to 600 W peak output. Without 100% backup it would be pointless. I can’t charge electric cars with this, it isn’t enough. I’d have to install a ridiculous amount of storage to to make it viable for a range if use cases. Four years ago, when I installed it, I was idealistic about solar. Four years later I understand the hard-cold reality vs. the fantasy of solar.

[Schroedingersat]

> Without going too deep: If you need 100% backup for solar, why use solar?

In addition to this being a lie, if we pretend it's true then there's a sufficient reason. Solar costs less than the marginal cost of other generation except wind.

[robomartin]

What is a lie? That solar is so unreliable that you need 100% backup or accept shutting down entire buildings or towns?

That is far from a lie.

I just got back from a business trip to Singapore. Among other places, I visited a food production building where we have installed some of our technology for more efficient indoor farming. This building houses some 240 companies. They have a massive solar array sourcing a good deal of their power.

It rained almost constantly for two weeks. That massive array went to nearly zero output during that time.

The only way that building could function was with 100% backup for solar, provided by the grid.

Batteries? The batteries were drained within a day. They could only be replenished by the use of grid power. Once again, 100% backup.

Not sure how you can possibly call it a lie.

This backup can take many forms. Where it makes sense, batteries might be able to help (yet batteries are not magic and they need a reliable power source to charge). A reliable power grid that can provide 100% of the load at any given moment is a must. This grid might be fed by solar (at a different geographic location), wind, hydro, nuclear or burning something. I believe in Singapore's case it is mostly burning gas.

It might seem sensible to think in terms of a wide geographic distribution of solar arrays to supply city A when weather events render the local solar resources unusable. OK, well, at a minimum, then, you need a 100% backup array located elsewhere. Let's call it 1000 km away.

Sounds great. You are betting on the statistical improbability of both arrays being unusable. Weather patterns being what they are, this might be a sensible bet.

What nobody brings into these conversations is: What happens with cities and towns B, C, D, E, F, G, etc.

If both A and C rely on a B's array for weather event mitigation, B's array has to be overbuilt by a massive factor to, at any given time, supply all of A, B and C's power requirements (or combinations thereof). The same become the case for A and C, as they might be required to supply their 1000 km neighbors.

At the end of the day, I think everyone is starting to understand the ways in which solar and wind are unreliable. The idea that mitigation requires 100% backup can't really be disputed at scale.

Put a different way, as I have said elsewhere, one would have to overbuild solar by an obscene multiplier (some have estimated as much as 70x) to achieve the equivalent of a reliable power source across a wide geographical area.

The UK have a massive solar and wind project bringing them power from Morocco, some 4000 km away. Sounds great...until there's a problem. If the cities using this power don't have 100% reliable backup there will be trouble.

Frankly, it does not help that articles such as this one provide false information that get repeated and becomes widely distributed:

https://www.energy.gov/eere/articles/how-much-power-1-gigawa...

Here, the energy department claims 3.125 million 320 W panels give you 1 GW.

Not even close. First, 320 W panels NEVER make 320 W.

Why?

That rating is at 25° C and ideal lighting conditions. Panels have a negative temperature coefficient. At real operating temperatures they do not output the rated peak output. At actual operating temperatures you will lose 5% to 7% of that. Add other real-life installation factors and 10% is likely a very safe estimate.

That means a 320 W panel will, at best, under ideal condition, produce somewhere in the range of 290 to 300 W peak for a few seconds at the top of the solar day.

That would bring the 3.125 million panel installation down to 938 MW (assuming 300 W peak per panel) for 15 to 30 seconds per day.

Just to deliver a 1 GW peak for a few seconds we have to multiply the number of panels by a factor of almost 7%. That brings the count up to 3.344 million panels.

However, these panels will not produce the equivalent of 1GW of power for 24 hours. If the intent is to get there with solar, we need more panels and lots of batteries.

How many panels?

Well, on a perfect day the power generation curve is an inverted parabola. The integral of that curve over time gives us the energy generated during that period. Doing the math we see that is 66% of the equivalent 12 hour constant power period.

That means we need to multiply the size of the array by 1.5 to collect the equivalent constant power energy over 12 hours. That brings us to 6.688 million panels.

And, yes, lots of batteries are required for this to work.

Next, we need to at least double this to collect energy to supply at night. That gets the count up to 13.376 million 320 W panels. And millions of batteries.

That number is 4.3 times larger than what the energy department mistakenly quotes in the linked article.

And yet this does not stop there. One could (should?) easily double the size of this array yet again to account for weather, dirt and failures. If I round that out to a 10x multiple, we now need 31.25 million panels to supply a steady 1GW day and night while only using solar power.

What remains to be calculated is the massive land use this represents. One cannot just use the size of the panels. Solar installations have a packing factor. The idea is that you need space around the panels for access, maintenance, installation and other needs.

That number seems to be in the order of 10 acres per MW of peak generation:

https://www.nrel.gov/docs/fy13osti/56290.pdf

In the case of this realistic 1GW plant with 31.25 million panels, the land requirement would be about 100K acres. This is about 156 square miles or a square of over 12 miles per side.

[Schroedingersat]

An incredibly incoherent and long winded way of saying you don't know the term 'capacity factor' and don't understand what dispatchable loads are isn't evidence you weren't lying.

As to the amount of backup needed: https://www.nature.com/articles/s41467-021-26355-z

Then consider all the dispatchable loads that decrease the gap even further.

[robomartin]

You excel at insulting people online. We've been here before. This is what you do instead of having conversations. Not taking your bait.

My claim is that solar requires 100% backup.

OK, let's break it down:

    Solar Output:
    Under ideal conditions, roughly inverted parabolic output

    1.00 ┼                       ╭────╮                   
    0.90 ┤                     ╭─╯    ╰─╮                 
    0.80 ┤                   ╭─╯        ╰─╮               
    0.70 ┤                  ╭╯            ╰╮              
    0.60 ┤                 ╭╯              ╰╮             
    0.50 ┤                 │                │             
    0.40 ┤                ╭╯                ╰╮            
    0.30 ┤               ╭╯                  ╰╮           
    0.20 ┤              ╭╯                    ╰╮          
    0.10 ┤              │                      │          
    0.00 ┼──────────────╯                      ╰───────── 

    Clouds and weather can cause up to 100% drop in output any time
    Rain will drop your peak output practically down to zero all day
    Dirt will drop total output by a variable amount until cleaned

    1.00 ┼                        ╭───╮                   
    0.90 ┤                     ╭─╮│   ╰╮                  
    0.80 ┤                   ╭─╯ ││    │ ╭╮               
    0.70 ┤                  ╭╯   ││    │ │╰╮              
    0.60 ┤                 ╭╯    ││    │ │ ╰╮             
    0.50 ┤                 │     ││    │ │  │             
    0.40 ┤                ╭╯     ││    ╰─╯  ╰╮            
    0.30 ┤               ╭╯      ││          ╰╮           
    0.20 ┤              ╭╯       ││           ╰╮          
    0.10 ┤              │        ││            │          
    0.00 ┼──────────────╯        ╰╯            ╰───────── 

    Daytime:
      You need up to 100% backup to be available at any time.

    Night:   
      To state the obvious, 100% backup is required.

    Conclusion:
      If you need reliable 100% backup at any point
      during 24 hours, this backup capacity has to be 
      available 24/7/365.

The above is absolutely true.

Regarding the link you provided. I am familiar with this article, which, of course, confirms my point.

Figure 5, which is titled "Maps of electricity system reliabilities under the most reliable solar-wind mix without excess generation or energy storage", puts the US at less than 88%.

This means that, ON AVERAGE, 12% of the time you need 100% backup for the most optimal form of solar and wind combined.

I loudly highlighted ON AVERAGE because it is important to understand this is a problem when dealing with statistics. You cannot apply the average of the average of the average to an entire population. This is known as the tyranny of the averages.

Averages are fantastic to wave hands around and talk about generalities. They do not cover my little town of 300K residents going dark for two hours because the solar system powering it had no backup.

The real numbers, once you start to get closer to local realities, are not represented by these average. The real numbers are much worse.

Solar cannot exist without external backup. Solar and wind cannot exist without external backup. That's the real conversation we have to have.

Somehow people read this to mean that I am saying solar and wind are bad and not usable. That is not AT ALL what I am saying. I am simply highlighting that we cannot "go green" just with these technologies. And it gets much, much worse, when we start to throw in hundreds of millions of electric vehicles. My point, in the aggregate, is that we, in the US, desperately need to change our thinking with regards to nuclear. Otherwise we are going to end-up with a bunch of solar and wind backed-up by massive amounts of power being generated by burning stuff.

    Try again.
    No personal attacks this time.
    Where, exactly, did I lie?
    Show your work.