The fault occurred around 8pm on Monday evening on the overhead line network.
Hundreds of homes in the EH6, EH7, EH15, EH16 and EH22 postcode areas have been affected by the outage.
One Edinburgh resident said that the power cut was also affecting traffic lights.
Scottish Power said they would attempt to reset the network and restore the supply.
They added that they hoped to have the fault repaired by 10:15 tonight.
One member of the Porty People group on Facebook quipped: “This power cut is awful. I might have to speak to my husband soon.”
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