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𝑃𝑚𝑖𝑛 = 𝑁𝐻 ∗ 𝑀𝑖𝑛(𝐸𝑜𝐻) (7) 1012 Calculating the Maximum is the challenging step. Let us first define the Electricity Cost per Bitcoin (ECPB): 𝐸𝐶𝑃𝐵 = 𝑇𝐸𝐶𝑃𝐵 ∗ 𝐴𝐵𝐸𝑃 (8) 𝑅𝑃𝐵 with: • TECPB is Total Energy Consumption Per Block (TWh) • ABEP is Average Bitcoin Electricity Price ($/kWh) • RPB is Reward Per Block (in bitcoin (BTC)) There are 2016 blocks in a difficulty recalculation period. Therefore, 𝑇𝐸𝐶𝑃𝐵 = Tot. En. Con. Betw. Dif. Recal. (TWh) (9) 2016 Total Energy Consumption Between Difficulty Recalculation (TECBDR) is calculated as 𝑇𝐸𝐶𝐵𝐷𝑅 = 𝑃 ∗ 𝐻𝐵𝐷𝑅 = 𝑁𝐻 ∗ 𝐸𝑜𝐻 ∗ 𝐻𝐵𝐷𝑅 (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, 𝐻𝐵𝐷𝑅 (h) = 𝑇𝐷𝑅𝐵𝑥+2016 − 𝑇𝐷𝑅𝐵𝑥 (11) Now we can calculate Yearly Energy Consumption Between Difficulty Recalculation (YECBDR) in TWh/year, 𝑌𝐸𝐶𝐵𝐷𝑅 (TWh/year) = 𝑇𝐸𝐶𝐵𝐷𝑅 ∗ 365 ∗ 24 (12) 𝐻𝐵𝐷𝑅 Now, an Average Bitcoin Electricity Price (ABEP) in $/kWh for the whole world is needed. Since it is rather difficult and tedious to find the mining locations every 14 days since 2009, at this step, we made use of the bitcoin mining pool data between 1 June and 4 June 2018, which is shown in Table 1. Firstly, we define Average Bitcoin Production Percent ABPP per locations as follows: Average Bitcoin Production Percent China (𝐴𝐵𝑃𝑃 ) = 0.7 𝐶h𝑖𝑛𝑎 Average Bitcoin Production Percent Europe (𝐴𝐵𝑃𝑃 𝐸𝑢𝑟𝑜𝑝𝑒 ) = 0.1 Average Bitcoin Production Percent America (𝐴𝐵𝑃𝑃 𝐴𝑚𝑒𝑟𝑖𝑐𝑎 ) = 0.1 Average Bitcoin Production Percent Rest of the World (𝐴𝐵𝑃𝑃 ) = 0.1 Now, let us define the Average Bitcoin Electricity Price (ABEP). To do this, we need to use average electricity prices in China, Europe, US, and an average figure for the rest of the world [20]: Average Electricity Price China ($/kWh) (𝐴𝐸𝑃 ) = 0.08 𝐶h𝑖𝑛𝑎 Average Electricity Price Europe ($/kWh) (𝐴𝐸𝑃 𝐸𝑢𝑟𝑜𝑝𝑒 ) = 0.15 Average Electricity Price America ($/kWh) (𝐴𝐸𝑃 𝐴𝑚𝑒𝑟𝑖𝑐𝑎 ) = 0.1 Average Electricity Price Rest of the World ($/kWh) (𝐴𝐸𝑃 Hence, ABEP will be: 𝐴𝐵𝐸𝑃 ($/kWh) = (𝐴𝐸𝑃 𝐶h𝑖𝑛𝑎 ∗ 𝐴𝐵𝑃𝑃 𝐶h𝑖𝑛𝑎 ) 𝑊𝑜𝑟𝑙𝑑 + (𝐴𝐸𝑃 𝐸𝑢𝑟𝑜𝑝𝑒 ∗𝐴𝐵𝑃𝑃 𝐸𝑢𝑟𝑜𝑝𝑒 )+ (𝐴𝐸𝑃 𝑊𝑜𝑟𝑙𝑑 ∗𝐴𝐵𝑃𝑃 ) 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; 𝑅𝑒𝑠𝑡 ) = 0.1 ) + (𝐴𝐸𝑃 𝐴𝑚𝑒𝑟𝑖𝑐𝑎 𝑊𝑜𝑟𝑙𝑑 ∗ 𝐴𝐵𝑃𝑃 𝐴𝑚𝑒𝑟𝑖𝑐𝑎 (13)PDF Image | Energy Consumption of Bitcoin Mining
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