The power cut was first reported at 7.04am this morning (Mon).
National Power Grid said at least 500 homes were affected.
The unplanned power cut is in LS10, LS15, LS3, LS6 and LS9.
National Power Grid said on their live map: "We are currently working hard to restore your power however we are unable to provide an accurate restoration time.
"Please call us on 105 if you have any specific questions.
"The power cut affecting your property has been caused by an unexpected problem with the electricity cable that serves your area."
The power is expected to be restored by 8.45am.