What is the average amount of electrical power required to complete one Bitcoin transaction? Once a bitcoin has been mined, if I want to use it to pay for something, what is the average amount of electrical power required to process that payment or bitcoin transfer? Does this vary with the value of the transaction, and if so in what manner?

Please note that I am not asking about the electricity cost, as that would clearly depend on the location as well as what deal you've been able to strike with the power company. Hopefully the number of kWh, J, or whichever other unit happens to be convenient, will be easier to answer reasonably objectively.

Answers for any point in time during which Bitcoin has existed are acceptable, but more recent data is better. It is acceptable to exclude costs that are not actually related to the data being transferred being about bitcoins per se (for example, I see no real need to calculate how large a percentage of Internet core router traffic is for bitcoin transfers and account for that).

(I did find e.g. Energy to confirm one block? and Can it really be true that the Bitcoin system consumes almost $1.000.000 in electricity per day? as well as (on Skeptics) Does one transaction on Bitcoin require 215kWh? but all of these appear to conflate the total power usage of the Bitcoin network with the power required for a transaction using already mined Bitcoin by lumping the two together.)
Once a bitcoin has been mined, if I want to use it to pay for
  something, what is the average amount of electrical power required to
  process that payment or bitcoin transfer?


That a transaction is processed could mean it has gone all the way from its generation up to its addition on the blockchain within a mined block confirmed by all nodes.

The only significant consumption in the process is the guessing of the correct hash of the block that includes this transaction along with cca 2000 (meaning around 500 byte transaction size on average) other transactions included in it. This guessing (lottery) difficulty varies with time thus the energy consumption varies. Current guessing difficulty is 1,452,839,779,146 (https://bitcoinwisdom.com/bitcoin/difficulty), and the average number of guesses to make is 2^32 * difficulty (2^32 * 1,452,839,779,146 = awfully high).

Now you can find the energy consumption for example by examining some high end mining device like AntMiner S9 and checking its hashing rate (for this example 14,000,000  Mhash/s, https://en.bitcoin.it/wiki/Mining_hardware_comparison) and its power consumption (1,375 W).

Average_number_of_guesses / hashing_rate = Guessing_time
Guessing_time * power_consumption = Energy_spent_for_mining_a_block
Energy_spent_for_mining_a_block / number_of_transactions_in_block = Energy_spent_per_transaction


If I've done calculation correctly this should be around 85 kWh per average transaction. (Note that not every mining device on the network is AntMiner S9 so this figure should be used with reserve).


  Does this vary with the value of the transaction, and if so in what
  manner?


It does not vary with transaction value but the size of transaction in bytes and this varies by the number of inputs and outputs of transaction. If has more inputs and outputs it will be bigger in size thus allowing less transactions in a block and the last equation will change accordingly. For example if transaction is 1000 bytes big instead of average 500 used in last equation it will use around 170 kWh