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(50/2e) [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(50/2e) + 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(50/2e) + 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.
I turned this into a spreadsheet so I could plug in the variables and play about with it a bit.
It seems to me that the key assumption is "r = the average percentage of income miners spend on energy [unit less ratio]" and setting this to 0.8.
In short the model says power consumption is directly linked to the price - as the price goes up miners earn more and they spend more on electricity.
It drops with each halving of course as the block reward drops, but if as anticipated fees replace some or all of that lost income the effect will be smaller.
Couple of worked examples, using more or less the numbers above, the only difference was to use average fee income over the last few days to get 4.56 BTC/hour for the current era, increased to 9 BTC/hour for the next:
Current era (3), fee income 4.56/hour:Price: $50,000 Energy consumed: 56 GW
Price: $100,000 Energy consumed: 112 GW
Price: $200,000 Energy consumed: 224 GW
Next era (4), fee income 9/hour:Price: $50,000 Energy consumed: 37 GW
Price: $100,000 Energy consumed: 74 GW
Price: $200,000 Energy consumed: 148 GW
As you can see according to the model the energy consumed is a straight line with the price. And at current rates bitcoin at $200k suggests about 1.5% of total world energy production will go to Bitcoin mining - anyone who doesn't think that is insane, really needs their head examining ...
How did you come to the 0.8 value for r? And do you think it will change over time?
I presume it is really a competition thing, if a miner can manage on a smaller margin, they can spend more on power (i.e. r will be greater) and thus bring in more income. There is actually no incentive to drive r down.