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ππππ = ππ» β πππ(πΈππ») (7) 1012 Calculating the Maximum is the challenging step. Let us first define the Electricity Cost per Bitcoin (ECPB): πΈπΆππ΅ = ππΈπΆππ΅ β π΄π΅πΈπ (8) π ππ΅ with: β’ TECPB is Total Energy Consumption Per Block (TWh) β’ ABEP is Average Bitcoin Electricity Price ($/kWh) β’ RPB is Reward Per Block (in bitcoin (BTC)) There are 2016 blocks in a difficulty recalculation period. Therefore, ππΈπΆππ΅ = Tot. En. Con. Betw. Dif. Recal. (TWh) (9) 2016 Total Energy Consumption Between Difficulty Recalculation (TECBDR) is calculated as ππΈπΆπ΅π·π = π β π»π΅π·π = ππ» β πΈππ» β π»π΅π·π (10) 106 1018 where HBDR is Hours Between Difficulty Recalculation (h). Let us define the Difficulty Recalculation Block (DRBx) and Next Difficulty Recalculation Block (DRBx+2016), Timestamp of Difficulty Recalculation Block (TDRBx), and Timestamp of Next Difficulty Recalculation Block (TDRBx+2016), then, π»π΅π·π (h) = ππ·π π΅π₯+2016 β ππ·π π΅π₯ (11) Now we can calculate Yearly Energy Consumption Between Difficulty Recalculation (YECBDR) in TWh/year, ππΈπΆπ΅π·π (TWh/year) = ππΈπΆπ΅π·π β 365 β 24 (12) π»π΅π·π Now, an Average Bitcoin Electricity Price (ABEP) in $/kWh for the whole world is needed. Since it is rather difficult and tedious to find the mining locations every 14 days since 2009, at this step, we made use of the bitcoin mining pool data between 1 June and 4 June 2018, which is shown in Table 1. Firstly, we define Average Bitcoin Production Percent ABPP per locations as follows: Average Bitcoin Production Percent China (π΄π΅ππ ) = 0.7 πΆhπππ Average Bitcoin Production Percent Europe (π΄π΅ππ πΈπ’ππππ ) = 0.1 Average Bitcoin Production Percent America (π΄π΅ππ π΄ππππππ ) = 0.1 Average Bitcoin Production Percent Rest of the World (π΄π΅ππ ) = 0.1 Now, let us define the Average Bitcoin Electricity Price (ABEP). To do this, we need to use average electricity prices in China, Europe, US, and an average figure for the rest of the world [20]: Average Electricity Price China ($/kWh) (π΄πΈπ ) = 0.08 πΆhπππ Average Electricity Price Europe ($/kWh) (π΄πΈπ πΈπ’ππππ ) = 0.15 Average Electricity Price America ($/kWh) (π΄πΈπ π΄ππππππ ) = 0.1 Average Electricity Price Rest of the World ($/kWh) (π΄πΈπ Hence, ABEP will be: π΄π΅πΈπ ($/kWh) = (π΄πΈπ πΆhπππ β π΄π΅ππ πΆhπππ ) πππππ + (π΄πΈπ πΈπ’ππππ βπ΄π΅ππ πΈπ’ππππ )+ (π΄πΈπ πππππ βπ΄π΅ππ ) The final step to calculate Electricity Cost per Bitcoin (ECPB) is to calculate Reward Per Block (RPB). The reward is given in bitcoin (BTC). It starts with 50 BTC and halves every 210,000 blocks. It follows as in; π ππ π‘ ) = 0.1 ) + (π΄πΈπ π΄ππππππ πππππ β π΄π΅ππ π΄ππππππ (13)PDF Image | Energy Consumption of Bitcoin Mining
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