Estimating the energy/power consumption of the Bitcoin Network

[BurtW]

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:

Short Version : The electrical power consumed by the Bitcoin network - in megawatts - is equal to the price of one bitcoin - in dollars.
(“Law” valid up to the next reward halving under the hypothesis described below)

Long Version :

I wanted to know how much electricity is consumed by the Bitcoin network. Unfortunately most of the available resources make assumptions on the efficiency of the miners and the mining difficulty.

I state that the difficulty does not matter, nor the efficiency of the miners, and that the only factors that have an influence on the electrical power of the network are :
- the price of electricity paid by miners
- the content of the block reward

The fun conclusion is that with the current block reward of 25 BTC per block and a mean price of electricity of $0.15 per kWh, the electric consumption of the network in MW (megawatts) is exactly the price of one bitcoin in dollars.

Hypothesis :
1. Miners are rational actors. Therefore once they have bought a mining rig, they will not stop it unless the cost of running it is higher than the price of the mined bitcoins. However if the price drops or if the difficulty grows too high they should stop mining.
2. Miners pay their electricity bill. There is no such thing as free electricity. Some miners may not pay the real price and I will discuss the effect of that later. I will take a price of $0.15 per kWh.
3. The network is in a stable state : 25 BTC per block = 3600 BTC per day (I know this is not the case nowadays). The fees are negligible.

So a rational miner :
- has already a mining rig, which consumes electric power if running.
- Every day he has to make a simple choice : either he runs its rig or not.
- The price at which he bought the rig is irrelevant to this decision. It’s a “sunk cost”.

If the marginal cost of running the rig can turn the electricity into a profit (price of electricity >= price of the bitcoins mined) then the rational miner should run it. If not he should turn if off.

Now let’s suppose that the bitcoin network in only made of rational miners : the equilibrium is reached when the price of all newly mined bitcoin is strictly equal to the price paid as electricity by the miners.

A few calculations :

Miners mine 3600 bitcoins a day.
Miners collectively spend the same amount of dollars in electricity (equilibrium point of the equation that follow rational miners).

3600 BTC = amount spent daily in electricity

P = power of the network in MW (megawatts)
X = price of one bitcoin
Price of electricity = 0.15 USD/kWh = 150 USD/MWh

So we have 3600*X = P*24*150 or P=X.

Therefore : given the current reward, in a stable bitcoin network run by only rational miners, the electric power consumed by the network in megawatts equals the price of one bitcoin in US dollars.

At the current price ($600 per BTC) it means that the network consumes something like 600MW. That is one third of the electric capacity of the plant of Fessenheim that made the news today (in France).

I just wanted to share that with you…

(originally posted in “Economics” but feel free to move it elsewhere if needed)

[BurtW]

Yes, efficiency does not matter when calculating the power consumption of the entire Bitcoin network.

Power consumption only depends on five things:  the exchange rate of BTC, the era, the average amount of fees per hour, the cost of energy, and the average gross profit margin of the miners.

Watch this:

x = exchange rate [USD/BTC]
e = era [0..32] (we are currently in era 1)
f = average fees per hour [BTC/hour]
c = cost of energy [USD/kWh]
g = average gross profit margin [unitless ratio]

From the era we can caclulate the average hourly BTC subsidy rate:

s = 6(50/2^e) [BTC/hour]

And the amount of BTC all the miners in the world would 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 would make:

u = b(x) [USD/hour]

Given the worldwide average gross profit margin the amount spent worldwide on energy would be:

u(1 - g) [USD/hour]

And finally, the worldwide power consumption would be:

P = u(1 - g)/c [kW]

  = b(x)(1 - g)/c [kW]
  = (s + f)(x)(1 - g)/c [kW]
  = (6(50/2^e) + f)(x)(1 - g)/c [kW]

Notice that 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 hashrate.

[BurtW]

That is an interesting point with respect to the dream of having 1 BTC = $100,000 (or pick your favorite high number).

Using my previously derived formula for the power consumption:

P = (6(50/2^e) + f)(x)(1 - g)/c [kW]

where:

x = exchange rate [USD/BTC]
e = era [0..32] (we are currently in era 1)
f = average fees per hour [BTC/hour]
c = cost of energy [USD/kWh]
g = average gross profit margin [unitless ratio]

we can look at the power consumption in each era assuming a price of $100,000 per BTC.

In order to make it simple I will make the following assumptions:

x = $100,000 per BTC
f = fees per hour will keep the coinbase above 6 BTC/hour (1 BTC/block) in all eras
c = $0.10 per kWh
g = 0.1 miner gross profit margin

Code:

    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

[titulng]

it need a energy of a nuclear power station or more

[BurtW]

it need a energy of a nuclear power station or more

That depends on the parameters you enter into the equation.

[cbeast]

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!

[BurtW]

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.

[BitcoinLlama]

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.

[blunthammer]

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?

[mmsmears]

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?"

[blunthammer]

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

There is one important difference between a professional data center and a "mining" data center, that can make the second one an order of magnitude cheaper : reliability.

A professional data center has contracts with clients who want an uptime for their servers that stays as close as possible to 100%.
This means :
- double entry of electricity plus local backups (batteries + fuel generators),
- Internet access with very high availability and bandwidth,
- 24/7 surveillance by qualified teams,
- active cooling,
- good fire security.
In those datacenters, a downtime of one minute is a financial trouble, a downtime of one hour is a disaster.

On the contrary, a mining data center can run :
- on a single electricity line, with no backup,
- over a single ADSL router,
- with passive cooling,
- and basic fire security (just to be sure that in case of fire nobody is killed)
A mining center can be shutdown in seconds in case of problem, for a few hours or a few days if needed, and the only cost will be a "loss of opportunity".

The photos of the "chinese mine" that were posted last months shows something that has nothing in common with the first world datacenters that I have know of.

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.

 

[Adrian-x]

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

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

[Adrian-x]

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!

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.

[marcus_of_augustus]

Bitcoin = Digital Energy

[Adrian-x]

Bitcoin = Digital Energy

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

[Bitmore]

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!

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!

[cbeast]

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!

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.

[Oscilson]

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

[marcus_of_augustus]

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

Or Antarctica, in the polar vortex zone.

[Ayers]

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