Bitcoin Forum

The old thread got cluttered so this thread is specifically about estimating the power consumption of the Bitcoin network.  The OP from the previous thread was:

    Original target      Subsidy    Est Fees   Power
Era   starting year    BTC/block    BTC/hour      GW
--- ---------------  -----------  ----------  ------
  0            2009  50.00000000  0.00000000  270.00
  1            2013  25.00000000  0.00000000  135.00
  2            2017  12.50000000  0.00000000   67.50
  3            2021   6.25000000  0.00000000   33.75
  4            2025   3.12500000  0.00000000   16.88
  5            2029   1.56250000  0.00000000    8.44
  6            2033   0.78125000  1.31250000    5.40
  7            2037   0.39062500  3.65625000    5.40
  8            2041   0.19531250  4.82812500    5.40
  9            2045   0.09765625  5.41406250    5.40

it need a energy of a nuclear power station or more

That depends on the parameters you enter into the equation.

Bitcoin will incentivize clean, renewable energy development. Bitcoin will incentivize higher efficiency electronic development. It will create jobs, clean the environment, and save all the babies, puppies, and rainbows!

You forgot unicorns.

How will bitcoin incentivize higher efficiency electronic development and unicorns? I think generally speaking many think bitcoin mining is quite dirty.

I have been in the data center business for 20 years and there is another way to look at this as a business...

The power costs what the power costs where you are
The real estate costs what the real estate costs where you locate
Labor costs what the labor costs where you locate
Taxes cost what taxes cost where you locate
The infrastructure costs what the infrastructure costs where you locate - rigs, racks, cables, switches, routers

The question is how can you make money where you are? Can you?

There is consumption and there is cost of consumption. The way the data center world computes power is cost of power (.05)*hours per month (730)* Kw used (1000)= $36,500 per month in power to run a 1MW footprint of rigs or 416 rigs at 2.4Kw of draw each.

There are collateral costs for the cooling required to cool the density of the rigs - remember computers turn electricity into heat - and that adds a factor of .3 to .5 depending on the facility. This means that for every Kw of power used to run a rig, you'll need to consume .3 or .5 of a Kw to power the cooling infrastructure required to keep the wires and boards from burning or melting and to keep the rigs at an operating temperature range.

So the all in cost per MW of power will be $37,595 per month at a .3 cooling uplift. You still have the cost of rigs, racks, cables, switches, etc. to cover and rent for the physical space which on the low end would be $90/kw so figure another $90,000 plus taxes.

So the question is at what scale do you mine bitcoin to clear at least $150K/month?

That's a great answer! 

When seriously considering the future of the Bitcoin network, what you need to ask is "Does my utility bill get cheaper every year?", "Will operating costs consistently match the value of mined bitcoin?",  "How long will it take for BTC value to recover when the block chain discovery gets halved again?" & "Can the network really handle millions of Transactions Per Second after all of the commercial miners are gone?"

If the ultimate goal is the adoption and proliferation of BTC as a currency, then it needs to be treated like one in some regards. Ghetto colo or circus colo while OK when no one cared or was watching is one thing. To bridge the chasm between BTC as a Ponzi scheme, fad, or other such connotation it will take appearing like that which people think of. Do you want your fiat currency in a secured place like a bank or garage in a ghetto?

As it relates to power, there are a number of Utilities that have been around for over 100 years who are investing in real infrastructure using real money (BTC or fiat) that needs to be paid for over time. If a utility has to spend $25M to deliver 100MW and a miner only wants a 5 month contract, good luck. The banks and financiers that underwrite these deals buy risk. Short term contracts that back a $25M spend means there is less time for the bank or lending entity to make money back. So for a $25M nut, the bank will expect a 10% return so the tab is $27.5M that needs to be paid back in 5 months or at least the replacement value needs to be recouped in the 5 months.  Few utilities will take on that much risk for a 20 year contract with unknown entities that set up facilities that are lawsuits and fires waiting to happen. They see it as never getting paid pack.

 

So I just had a thought given the impending cost of production, network growth and price junction and I was wondering if all this data could be used to make a more accurate price prediction models.

Is there a graph of Bitcoin mining energy efficiency (CPU to GPU's to ASIC's and there relative incremental improvements) over time?

From the above you can plot the energy consumption of the Bitcoin network over time by referencing the hash history.

I'd really be interested to see those graphs could be model relative to price say relative to Stephen Reed's Million Dollar Logistic Model (https://bitcointalk.org/index.php?topic=366214.0)

In conjunction with the Bitcoin inflation rate. (Price eras - halving)

This is my conclusion, people call PoW wasteful, but it will force us to value energy through a different economic lens and in turn make us truly environmentally efficient, and then with each halving Bitcoin will give back lots of energy if it is inefficiency used.

Bitcoin = Digital Energy

How so? (sounds good not sure I quite get it.)

The cheapest energy is what?  Coal? 

Heck, I want to invest in relocating a large bc mining operation to the Alaska north slope to facilitate cooling, right next to a large coal fired power plant! 

Heck, I will even supply a free coffee barista 24/7 for all employees!

All energy sources have their benefits and drawbacks, just like everything else in nature. Your solution is interesting. I would prefer geothermal in Siberia or Iceland.

Wind farm in Alaska and BTC mining could be a good combination.

Or Antarctica, in the polar vortex zone.

they should start to use more clean energy for bitcoin mining, what about that that mega solar farm in arizona? they could rent it if possible

Does solar only work in the day?

Usually surplus power is stored up in batteries... but yes... they only work in the day.

Bitcoin heliosynchronous solar powered satellites would be expensive and inefficient, but v.kewl.

Solar powered Bitcoin miners on the moon!  Then all those "too the moon" comments would become true.

I don't really see the point in using theoretical energy consumption as an indicator.

The value created with every block is going to give you a good indicator of the total monetary input into the bitcoin mining industry.
We are already in the ASIC era where first generation units are close to becoming worthless. In contrast to cpus or gpus these units have very few alternative uses.
Their production cost and the value created for the hardware seller as well as the energy expended needs to be contrasted to the total amount of coins created by it, not just the energy cost the miner had.

Sure you can assume a stable system and no hardware costs. But what exactly is that telling you?

Obsolete technology is the byproduct of innovation. We are seeing progress.

Yet, in the last 12 days, more hardware was added than the total of all the hardware running in July, 2014, just 5 months ago. 

Too early to say it is stabilizing.

This

Unprofitable miners quitting have little impact on difficulty. asic's are a 1000 x more powerful than gpu's.

As long as the cost of production is lower than market price miners have a profit incentive.

Hardware costs are not a factor in revenue as they are fixed assets are a sunk costs.
The investment in new hardware is stimulated by large gaps between production cost and market price.

As the profit shrinks, risk in investing in more efficient hardware increase.

This will help humanity create a market price for energy that will drive global economic efficiency, and at the next halving a quarter of the planets energy will be surplus.

Nice to dream but we're not there yet.

The problem is that you obviously do not understand BurtW's calculations.

I will give you a real world analogy to think about:
Mining Gold is profitable but generally requires heavy machinery that runs mostly on fossil fuel.
The equivalent calculation would be to take the value of the global output of newly mined gold and say "Mining gold will consume that value divided by fuel prices of fuel because it is profitable"

You are ignoring the cost of mining equipment, the cost of labor, local conditions, changes in technological requirements that require research etc.

Do you see the issue? You have just reduced a complex problem into one dimension, in the above case fuel and in BurtW's case electricity.

Essentially his observation is not really how much energy the bitcoin network will "try to consume" (even that statement makes no sense. A miner has a limited amount of hashrate so for the network to consume more energy would mean you HAVE to increase the number of miners or their efficiency, both of which require an input of new money through both purchases and research and development)

The observation is: For x amount of money I can buy y amount of electricity.

Even with the current situation we see that calculations purely based on required energy make little sense.
If I buy a 1st generation block erupter it is pretty much useless unless I have very low energy costs. Its price, the cost of its development and ultimately, the fact that it will and is being replaced by new hardware that also requires new investments show that assuming 100% of rewards created by mining flow into energy makes little sense

I will even go as far as speculating that energy costs will become a smaller factor than today if prices ever do climb up significantly.
The limited capacity of producing efficient asic chips for everyone means that you will run into a global scarcity of hardware, driving the prices up for new machines. Furthermore if mining is indeed a billion dollar industry you will have RnD by manufacturers to try and get a competitive edge on both hashrate and energy efficiency. These costs need to be paid for somehow and that is where a portion of the block rewards of miners will go into.

People on these forums have made calculations on the energy cost of producing a bitcoin and arrive at quite low values.
Many blindly assume that that is the only cost for producing a bitcoin and consider them overvalued. What you are missing is
that a miner needs to be bought and that initial investment needs to be paid for. Because difficulty is increasing your miner is producing less and less money until it ultimately is no longer profitable and has become obsolete.

Hence again I will ask, what is the point in assuming a stable network where everyone already has hardware for no cost and technology does not change when that is clearly not the case?

You are completely ignoring the argument I am making against your calculations.
I know it may seem like an elegant approach to correlate or otherwise analyze bitcoin prices solely on energy consumption but it is nevertheless a fundamentally flawed one.



As to your first example, what are you trying to prove to me here?
If a second generation miner produces more hashes per joule of energy than a predecessor its production cost can be higher for a rational miner to still consider purchasing one. The capital for new investments is coming from block rewards (lets ignore irrational mining for now)
Price discovery for bitcoin is linked with mining costs to some degree but clearly you cannot suggest that mining dictates price.
The fact that the protocol has an adaptive difficulty means that a lower price can and will ultimately cause a shrinking in the mining sector, attempting to converge on a moving stable point of cost vs. reward of mining.
Ultimately the valuation of bitcoin dictates the amount of new resources that will be poured into bitcoin mining (or are withdrawn). Once the value of block rewards is lower than the true production cost rational miners will cease and a new stable point with lowered energy and resource requirements is reached.

Now on to your second example and why it illustrates a flaw in the logic. Unless you assume zero technological innovation and zero environmental factors a stable state is never continuously reached. The discovery of a new lithographical process that makes chip design more efficient immediately would create a situation where a new unit can be built that is more efficient and hence has an economic advantage. That advantage dictates if and when new miners are actually commissioned as you expect a rational entity to only engage in upgrades if they will eventually amortize (or at least are expected to!) themselves. There is an almost infinite set of events that can lead to such a change.
You are essentially performing calculations with a static model that can't hold up beyond the hypothetical.


I have the feeling you are entertaining the concept of mining = energy cost because it fits into the current social and political context of our times. It is a grossly reduced model that, in my eyes, fails to adequately capture reality.

Of course you are free to use such a model for future predictions. I hope you are willing to revise it when reality does not conform, as am I willing to accept it if it Ultimately shows to be true.

raid_n:

Your entire argument is:  BurtW, your estimate for g of 0.1 is too low, I think the value of g is higher than that.

So, just change the value of g to what you estimate it should be.

What do you think it should be?  0.5?  0.6?

You don't have to write walls of text to tell us the value I picked out of the air in my example is wrong.  If you could calculate and justify an actual value for g - that would be interesting.

Not at all, changing g statically changes the margin for everyone and every mining unit.
I am not trying to justify any other value for g. I am trying to point out that g in itself is not a constant over time for any one mining unit and mining all together.

Can you model the scenario of someone spending, say 250 million usd on the development of a new mining unit that has a g of 0.2 over the 0.1 of available units in your model? the mining rewards are an incentive to spend that much resources on mining all together, not necessarily just energy. Can you also model how the adaption of such new units reduces the g of other units? Eventually a single unit will be at g <0 and might have to be replaced by a more efficient one. The value generated by bitcoin mining is an incentive to spend almost as much in mining. It will be divided between energy and hardware.
You may want to try to add this advance in technology and hardware cost vs electricity for mining into the model

By the way my mentioned scenario, albeit with different values, must have happened at one stage for the transition from gpu's to dedicated asic machines to even take place.

Just a quick extension.

if we assume a churn on hardware to counter the decay of individual units your model can be reduced to two bounds

[edit] removed asymptotically, does not have to be that way

a) mining converges to 100% expenditure on hardware
b) mining  converges to 100% expenditure on energy.

The reality will be in between. I doubt there will be a fixed factor between both bounds (eg 0.5 spent on new miners, 0.5 on power)

I agree.  The model can be made more accurate if we get a better estimate or calculation for the system wide average value of g.

Then it could be made even more accurate if we could calculate or estimate g(t) or g(e).

can't all hardware expenditure be estimated as energy?

I like.  So then, in addition to an estimate of how much the miners spend on energy versus equipment we would also need to estimate the amount of energy that goes into the NRE, manufacture and delivery of the finished equipment to the miners.

Then again it might be easier to "average this all out" into a single g factor of say 0.1 ;)

Never thought of it like this good answer

In principle you could express it as a total energy bill or reduction in entropy caused.
The point is saying "at value x per unit bitcoin mining will try consume y of the electricity produced" is a statement designed to fuel controversy and suggest to the uninformed reader that this is a fact and not the conclusion of a highly abstract system model.

Maybe we can agree on "resources" as the unit rather than electricity?
It is a better description of the multiple components that make up mining costs and less prone to be misused in the wrong context.


I think you yourself are arguing a case for my critique in the second part. Any external factor (lowered supply of new miners) breaks your assumption and the model of a static equilibrium point. Technological progress is more or less fluid. Any miner that is not state of the art will eventually be replaced by one that is. Your hypothetical equilibrium lies exactly at 0.0. No profit is made, no loss either. The system does not change. Clearly any change, any modification that makes a bit more profit is going to be adapted. But not just by one miner. It will force the entire system to try and find a new equilibrium. This happens constantly as external factors change. Hence there cannot be a static stable state.

My complaint is that that churn of technology needs to be included in the resource cost, not just electricity. It is going to be much higher than anticipated.

Power consumption?
why should we care power consumption?
people always did worst thing to nature. even a btc, couldnt it be a POS ? i would like to.
when speakings about economics widely i could say we didnt evaluate  solar energy, we didnt evaluate wind mills technology, but we were good at oil and nuclear power. were we good at nuclear power????? of course NOT :D We didnt evaluate Thorium.

What the fuck is Thorium????

Thorium's advantages start from the moment it is mined and purified, in that all but a trace of naturally occurring thorium is Th232, the isotope useful in nuclear reactors. That's a heck of a lot better than the 3 to 5% of uranium that comes in the form we need.

Then there's the safety side of thorium reactions. Unlike U235, thorium is not fissile. That means no matter how many thorium nuclei you pack together, they will not on their own start splitting apart and exploding. If you want to make thorium nuclei split apart, though, it's easy: you simply start throwing neutrons at them. Then, when you need the reaction to stop, simply turn off the source of neutrons and the whole process shuts down, simple as pie.

Here's how it works. When Th232 absorbs a neutron it becomes Th233, which is unstable and decays into protactinium-233 and then into U233. That's the same uranium isotope we use in reactors now as a nuclear fuel, the one that is fissile all on its own. Thankfully, it is also relatively long lived, which means at this point in the cycle the irradiated fuel can be unloaded from the reactor and the U233 separated from the remaining thorium. The uranium is then fed into another reactor all on its own, to generate energy.

The U233 does its thing, splitting apart and releasing high-energy neutrons. But there isn't a pile of U238 sitting by. Remember, with uranium reactors it's the U238, turned into U239 by absorbing some of those high-flying neutrons, that produces all the highly radioactive waste products. With thorium, the U233 is isolated and the result is far fewer highly radioactive, long-lived byproducts. Thorium nuclear waste only stays radioactive for 500 years, instead of 10,000, and there is 1,000 to 10,000 times less of it to start with.





We will have plenty of energy/power soon.

imagine a car - refuel, 100 years drive...  100 years.
Start engine, neutrons flow. drive forever !

If i were developer, i would create a Thorium Coin
TRC
energy for P2P power !

If i remember good, 9grams Thorium can run all USA for a year.
and it is everywhere, all around us. in the beaches and so on. we will never lack of energy again..
Thorium is as powerful as bitcoin

I too like the idea of Thorium reactors.  A bit off topic though since the title of this thread is "Estimating the energy/power consumption of the Bitcoin Network"

Are you trying to say that Bitcoin mining will not grow until the cost of electricity becomes the limiting factor?

Lol.

Not in the long term.

In fact, when the price of Bitcoin is going down, it becomes a game of who turns off their miner first.  The price of hardware becomes irrelevant.

And when the price is going up, it is only the matter of time, but hardware will always catch up to the point where electricity becomes the limiting factor.

Since the total electricity costs of the network are paid from the rewards, that amount of money must pass trough the exchanges, and this will put a constant pressure on the Bitcoin price in the downward direction.  This will cause the price to always slowly slide down, so the "price going down" mode of Bitcoin will be much more probable, than "price going up". 

We can already see confirmations of this in the price charts.  Look at the price after the first bubble.

Thorium 229 is fissile.
A nuclear power plant runs on a sustained fission reaction so even a thorium reactor will have to do this.
It is misleading to call thorium non-fissile if you have to breed it to be fissile U233 for a thorium reactor to work.

Unless we master transmutation I do not believe in nuclear energy as a sensible approach to solving the global energy requirements.


No, the rewards pay for the entire mining industry. Miners, research, electricity, network connections, human resources, etc.
That was and is my complaint about the initial model of rewards = energy consumed.
For that statement to be true you need to have a stable state for technology and all other external factors.

To give you an example, you said " when the price of Bitcoin is going down, it becomes a game of who turns off their miner first. "
That is true to some extent. It also implies that if there is a miner that still makes a profit because it is more advanced you will switch to that miner (because eventually it will ROI and make profit, or at leas you assume so).
Exactly this has happened with the transition from GPU to ASIC. The previous generation hardware eventually becomes obsolete due to changes in technology. Look at old personal computers. I am sure many people have an old machine standing around somewhere.
The value of the machine has decayed over time as its usefulness shrank. These resources "used up" if you will.
Some of the mining rewards will flow into hardware that eventually will be used up just like your old pc.
Hence if you say rewards = energy you leave out that entire aspect of mining.

Assuming a stable state for technology is nice for the model because it simplifies it. But it just does not capture reality.

Have you been involved in mining?
Difficulty increase is an indirect indicator for hardware investments. It can help us gauge how much new equipment is being bought.
What is a difficulty increase of 10-20% for each 2016 blocks telling us? Massive investments in new hardware, some of which will make older models obsolete.The interesting part is that even with dropping prices difficulty was/is increasing. I'd say that a lower block reward in the financial sense puts more pressure on miners to switch to more efficient and advanced hardware to stay profitable.

This is a vicious cycle as each improved generation puts all other miners under pressure to also switch. When the value of bitcoin is increasing
this pressure is not felt as much.
I am trying to say that block rewards = energy consumed is a too simplified model.
Block rewards = money spent on the mining industry (all resources combined) is better.

We could then model different assumptions on how these resources are distributed.
If bitcoin's value doubles the first thing that will happen is older inefficient miners will start coming online so you will see a spike in
energy consumption that is bounded by available hardware. A massive buy of new mining hardware will follow increasing the difficulty
to the point where again the most inefficient miners will stop being profitable. The energy consumption may actually temproarily go down during that phase.

The process itself is forming a complex feedback loop.

Now if you want to be a purist we can model the rewards in terms of energy as an abstract unit.
But then you would have to compare it to the global world productivity in terms of energy rather than just the electricity generated.

An interesting outcome of this, and i suspect this is similar to other coins, is that the price will tend towards the amount spent to create it.

IIRC that is what the Satoshi White Paper claimed.

Except when they don't.  For example, for the miners that never manage to get their initial investment back. 





I disagree. 

Since you obviously have to build the miner first, and at that point you indeed need your more complex model of "initial investment + running costs", and also some guessing about the future of BTC price and difficulty.  But, once the hardware is there, the price of said miner becomes irrelevant.

Also, if there is a single location on earth where you can mine Bitcoins profitably, say for example use 0.8 BTC of electricity to generate 1 BTC, it is only enough for one single (perpaps not very smart) miner to calculate that he will make some money in the future, that that said individual can increase the total energy usage of the whole network.  That single individual thus worsens the game for everybody else, and nobody can't do anything to stop him.

Also, actual silicon itself is cheap to mass produce, once you have initial research and development done.  And the cost of silicon can be close to one month of how much that silicon uses in electricity in one month, you can find those calculations somewhere on the forums.  This means, that even a 0.8 "saturation factor" in mining, can be sad to get paid back in just 5 months.


And, also, when the price is going down, nobody is ever adding new hardware, and then why would you even look at the manufacturing price of mining hardware?  Running costs became a pure indicator of when you turn it off or not.

Sometimes a simpler model is even a better one.

Surely you meant to say:  the amount spent to create it, will tend to what the price is.

I'm sure you are aware that Moore's law is slowing down lately.  For example, top Intel processor from 2014 is just 100% faster than top processor from 2008 on a single thread performance basis.  Expect even slower gains in the future.

Once Bitcoin chips reach the state of the art, progress will be slow.  No more need to replace hardware after 6 months.

I tried to invert BurtW's model to get a maximum supportable price without having miners consume more than a given percentage of world energy consumption.
For energy consumption data, I used wikipedia [1] (http://en.wikipedia.org/wiki/World_energy_consumption) and assumed a growth rate of 2.90% [2] (http://physics.ucsd.edu/do-the-math/2012/04/economist-meets-physicist/). I also tried to include the fact, that the halving occurs faster
than in stable state, so an era would only last 3.5 years instead of 4.

These are my results:



[1] http://en.wikipedia.org/wiki/World_energy_consumption
[2] http://physics.ucsd.edu/do-the-math/2012/04/economist-meets-physicist/

Based on the same premise of a 100,000 USD bitcoin for this era (1):
I am assuming an energy consumption of 0.5 W/GH/s and 1.5 GH/s/USD for new miners and a current hashrate of 2,65×10¹⁷ Hashes per second.


Does that make sense? Did I miss something?

I'll look like an idiot if I've made a gross miscalculation but according to this you would need roughly 44 billion USD in current mining equipment to actually reach
that energy consumption level.

[edit]

First mistake already! ;-) (I used a more specific hashrate beforehand I have no idea where that number came from! Calculator memory? who knows. Apparently it wasn't insanely far off)
Numbers before edit: 6,643811699×10¹⁹  outstanding hashrate in usd ->  44292077993,333333333 USD

Just been thinking about this thread some more and it is possible that policies to increase the cost of electricity would come into effect if bitcoin started to use too much of the world's energy resources. These could be targeted at miners specifically. That would have a dampening effect on the above numbers.

That might happen but it would have to be a purely politically motivated punitive decision, not an economic one.

I say this because normally the more energy you use the less you pay for electricity.  Today, industrial consumers of electricity pay less than residential consumers for the same amount of energy and huge industrial users often negotiate an even smaller price due to their massive consumption.

Now what power generation systems really hate is someone who uses huge amount of power on an intermittent basis - like an electric furnace to produce steel.  This is because their peak demands affect the amount of base power generation needed and cause them to have to produce a lot of power that never gets used.  Power generation can not be simply "switched on and off".  Coal and especially nuclear plants have to be left running even when there is low demand and they are overproducing power.  Natural gas generation has a relatively quick "warm up" cycle time so they can be switched on for higher demand seasons like summer air conditioning and turned off during lower demand.  (Note that this pushes a demand cycle back into the natural gas production and delivery system that has to be taken into account there.)

What power generation companies love is a consumer that uses a ton of energy at a very steady rate, someone who can say I need X MW 24/7/365 - like Bitcoin mining for example.  This increases base demand 24/7 so it is a very efficient consumer.  Therefore, economically speaking, very large Bitcoin mining operations should in theory be able to negotiate and receive the very best rates for their power - better than just about any other consumer.

Bitcoin Network Power Consumption Estimate

First, note that Bitcoin mining efficiency does not matter when estimating the trend of the power consumption of the entire Bitcoin network.

The power consumption of the entire network depends on five things:
 
x = the exchange rate [USD/BTC]
e = the era [0..32]
f = the average fees per hour [BTC/hour]
c = the average cost of energy [USD/kWh]
r = the average percentage of income miners spend on energy [unit less ratio]

From the era we can calculate the average hourly BTC subsidy rate:
s = 6(50/2^e) [BTC/hour]

And the average amount of BTC all the miners in the world make per hour:
b = s + f [BTC/hour]

From this we can calculate the amount of USD per hour all the miners in the world make:
u = bx [USD/hour]

Given the worldwide average percentage of income miners spend on energy the amount spent worldwide on energy is:
ur [USD/hour]

And finally, the worldwide power consumption is given by:
P = ur/c [kW]
   = bxr/c [kW]
   = (s + f)xr/c [kW]
   = (6(50/2^e) + f)xr/c [kW]

Notice that mining efficiency does not enter into this equation and does not matter.

You do not need to know or estimate the average overall efficiency of the mining network unless you want to calculate the difficulty and/or hash rate.

Let’s put in some numbers:

x = $50,000; the exchange rate [USD/BTC]
e = 3; the era [0..32]
f = 5; the average fees per hour [BTC/hour]
c = $0.03; the average cost of energy [USD/kWh]
r = 0.8; the average percentage of income miners spend on energy [unit less ratio]

P = (6(50/2^e) + f)xr/c [kW]
   = (6(50/2³) + 5) 50000 ( 0.8 ) / 0.03 = 56,666,666 [kW] = 57 Gigawatts

World power production/consumption is about 15,000 Gigawatts.

Bitcoin mining will trend toward 57/15,000 = 0.38 % of world power production given these values.

This scales by BTC price so:

BTC at $500,000 means power consumption would trend to 3.8% of worldwide power.

BTC at $5,000,000 means power consumption would trend to 38% of worldwide power.

... these numbers are only valid for era=3 though right?

What might be interesting is to hold the ~0.37% of global energy constant (assuming a total energy cost market is willing to pay for 'bitcoin security') and use to estimate different prices for future eras.

Correct.  What we want is steady growth in price through the various eras such that the total energy consumption is kept to a reasonable level where "reasonable" is TBD.

What you are asking for would also require us to estimate:

• Exactly what will be considered "reasonable" 0.5%? 1%? 1.5%?
• The growth of power production over the eras.
• The growth in fees as the subsidy is removed.
• The growth or reduction (fusion may come on line in our lifetime) in the price of energy over time.

Seems pretty daunting to me.  Maybe someone will take a stab at it.

lets see if there is more simply math to work out electric consumption

155exa hash in february(average)

outdated oldschool tech
asics:S9  hashrate: 14th  wattage:1.3kwh
=11071429 asics
=14,392,857kw/h

current tech
asics:s19 hashrate 95th  wattage:3.25kwh
=1,631,579 asics
=5,302,631kw/h

next gen tech
asics:S19pro  hashrate: 110th  wattage:1.3kwh
=1409091 asics
=4,579,545.kw/h

seems easier math then what BurtW keeps promoting

...
soo lets dollarise it -with burtW $0.03 electric cost
s9: kwh*0.03 =$575,714.28
/6block/6.25coin=$15,352.38 per btc

s19: kwh*0.03=$159,078.93
/6block/6.25=$4,242.10 per btc

s19pro: kwh*0.03=$137386.35
/6block/6.25=$3,663.63 per btc

now wasnt that easy

..
these numbers are about the energy power consumption amount. .. but do not include the hardware ROI costs