I am not aware of any reason you need to be a business to write off your electricity expense in the US. Quite a few sole-proprietorship "businesses" are run without formal structures.
For example, you are allowed to deduct expenses from a hobby (a hobby is also a business that looses money for 3 or more years ) up to the income of the hobby. This is why I recommended earlier to try to have a few dollars profit after expenses in case the IRS does call you a hobby instead of a business.
If you are a hobby and not a business, and the IRS accepts that, then you will not owe self employment tax on the BTC mined. The determination of hobby can be made by percentage of income vs your normal paycheck...but you won't know what those subjective percentages are until after you are audited.
If you can prove on paper that you have a profit motive and you loose money, the write-off could extend to cover your personal income (unlike the hobby) or the losses could be carried forward.
If the IRS determines you are a business, you may be subject to self employment tax on the earned BTC if you get an auditor in a good mood. It you have a big enough mine it may be worth forming an S-Corp and paying an attorney to figure out how to limit those taxes. Probably not worth it. I'm considering my small after work "hobby" passive income since it involves far less time than dealing with tenants.