Scottish and Southern Electricity Networks (SSEN) reported the fault at one of its local substations in the DD4 area, in the east of the city, at 10.30am.
A total of 51 homes were affected, with all save for 17 now reconnected.
Engineers have been working to resolve the problem since about 10.40am.
A marker on SSE website pinpointing where the fault has taken place.
All homes should have their power restored by 3pm.
An SSEN spokeswoman said statement on their website said: “We’d like to apologise to our customers for the inconvenience and thank them for their patience as our engineers work to restore their power as quickly and as safely as possible.”
