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the Pareto principle and solar power

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Alan Georges:
We’re all probably familiar with the Pareto principle: you get about 80% of the results from the first 20% of effort.  Sometimes it’s called the 80/20 rule, and probably a few other things besides.  A while back a friend pointed out that not only does the Pareto principle hold, but that powers of this ratio work as well.  For example, Pareto squared would give 64% of the results from the first 4% of effort.  Since then I’ve been mulling this idea over in regard to solar power.

Taking this even further, I put calculator to paper and made a table.  Starting with a $100 per month electric bill, it shows about what you can expect for each power of 0.8 and 0.2 down to some ridiculous level.  Now, all of these numbers are rough-and-ready, but as the currently fashionable phrase goes, they’re directionally correct.  Anyway, here we go:

Start with a $100 electric bill at $0.13 per KW-H, and in round numbers it's 25 KW-H per day.  Figure on 5 hours per day of sun; that’s the average in a lot of the U.S., though it will vary.  Look up “insolation chart” and you’ll find what you need.  So to make 25 KW-H over 5 hours, it’d take a 5 KW system.  The “P” column is the “Pareto to the power” column.

W-H/day   P   %lifestyle  %pwr  size solar    comment

      25K    0      100       100        5 KW         baseline, normal living
      5K      1      80          20         1 KW         still a pretty big system
      1K      2      64            4       200 W         easy, cabin-sized system
      200    3       51           0.8       40 W        pretty small
      40      4       41           0.16      8 W         dinky, portable

Don’t get hung up if something’s 20% or even 50% off, the idea is to examine the Pareto-to-some-power principle and look at a few directionally correct round numbers.

The first system, 25 KW-H per day, is doable with a professional solar install.  Get your checkbook out.  But you know, for some rich geezer who wants to get off-grid and not worry about hurricane season, it’s not a bad way to go.  I’d admire the system and want to be the guy’s neighbor.

The second line is a pretty big and it too might mean a professional install.  You’re not going to run an electric water heater or heat pump on this one, and even running a stove for very long is not doable.  But you can run a refrigerator, the control electronics and fan on a gas furnace, and pretty much everything else within reason on this system.  No central AC, deal with it, but you might run a window unit a little.  Honestly, this is about the level of power consumption I grew up on.  Like the Pareto principle says, it’s 80% of the base standard of living.

The next line, “Pareto squared,” is where things get interesting.  This is at the DIY system level and lots of us here have something like this.  You might get by with a small 12v refrigerator, a laptop computer, LED lights, 100 watt ham radios for hours, CB, etc. off this with no problem, and with some budgeting you can watch a movie in the evening.  Even running a microwave oven for 5 minutes here and there isn’t out of the question.  Pretty useful, it’s right at about 64% of a “normal” modern lifestyle, and seems nice compared to other extended outage options.  Also, if you have a generator, you can run a few larger items, say refrigerator or room AC, recharge batteries, and be pretty much back at the 5 KW-H/day lifestyle — as long as the gasoline lasts.

The next line, “Pareto cubed,” is where things get tight.  This is about the size of one of those Harbor Freight systems.  You can do a lot with it though: lights, recharge cell phones and AA batteries, talk at 100 watts on ham during half-hour comm windows or use a CB all day long.  Couldn’t really watch a movie, but it’d be no problem to run a battery radio for entertainment and news.  You could run a laptop and a cell phone wi-fi some on this.  Yeah, you’d have to really watch your power usage, but with lights and all it’s an OK life, and right on 51% of the baseline.

The last line, “Pareto to the fourth,” is getting down to a minimum, but compared to zero power it’s still really good.  This is about the size of one of those Goal Zero notebook systems that uses a 4x AA pack for its battery “bank.”  Look at what it can do: a reading light at night, recharge a cell phone, charge batteries for an AM/FM/SW radio.  What’s more, it’s portable.  It’s a lot better than most of the poorer first-worlders had it a century ago.  Right in keeping with Pareto, you could call it 41% of the modern life.

OK, that ran long.  I haven’t put out a good mega-post in a while though, and this Pareto-to-some-power has been rattling around in my brain for a while.  Thoughts?

David in MN:
The Freakonomics guys did a show about solar power where they did a breakdown that solar panels were more closely tied to political ideology than effectiveness. Thhey compared solar panel usage in San Francisco to more conservative inland California. The long and short is that people aren't using them where they would be effective but using them in foggy San Fran where they are not. In other words it's a way of signaling how virtuous one is.

I've also done the calculations you're looking at. Like setting up for a minimalist off-grid system. But I have a problem. My highest draws are all winter where we get cloud cover all the time. Yes, I could offset energy costs by having panels out in June when we get 16 hours of sun but it's 70 degrees, the windows are open, and I'm cooking on a grill.

But let me give the flipside. There are companies up here getting damn good results with vertical turbines and wind is probably our best bet. So I have been looking and I agree that you probably can get by 80% on 20%. At that point it becomes an engineering optimization problem. And I assume you've seen the same as us where the advent of moore efficient appliances and LED bulbs has driven down the energy use in the past decade.

It will be interesting to see if others feel similar.

Alan Georges:
No, of course, solar power isn't generally an economic winner for daily use.  Nor is the intent here to show how to spend $10k on a small solar power system to live like a virtue-signaling miser and save the remaining $20 electric bill per month.  That is not the point here.

The point is that when grid power is out, even a small amount of electricity is enormously useful.  Moreover, the high cost of solar power should not deter people – modern survivalists – from using it as a backup, because a small but practical system can be made for very little money.

Having a quiet, reliable backup source of electricity that does not require gas or rely on wind is a good thing.  This has nothing to do with political ideology.

I think most of us agree that you don't put all your eggs in one basket.

A couple months ago there was a good point made in a TSP episode with Steven Harris, that solar has become cost effective for some new installations.  It is becoming more and more expensive to hook into the grid in some areas so that bends the return curve. In fact, solar + propane/natural gas generator is looking very good for property which is ultra cheap because of distance to utilities.  This 'land discount' should be included in calculations when looking at new installs.

On the return aspect, yes, even a little electricity is a remarkable thing.  And it will only get better as power consumption of devices goes down.  So maybe a 'Pareto meets Moore's Law' situation could occur.

The biggest issue is that air conditioning bumps up against thermal efficiency and that cant budge by any known technology.


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