How do you account for variable expenses that depend on source documents if the source documents will not be received until the following month or accounting period?

E.g. Record electricity use for the month of December. Dilemma: The bill will be sent in January of the following year.

I will assume you are using an accrual based accounting system. When the account is received you will make a balance day adjustment recording the expense in December with an accrued liability carried forward. You could alternatively make a reasonable estimate based on past consumption