A total of 66 homes are without power in the Carlisle and Cockermouth areas.
There are currently 54 properties without power in the Embleton area, with power off since shortly before 11am today.
A spokeswoman for Electricity North West said: "Engineers are at the site, they have been there for about half an hour.
"There is a fault with the overhead lines."
The spokeswoman added that it does appear that the problem was caused by extreme weather.
Postcodes affected are:
CA13 0RR, CA13 0RU, CA13 0RS, CA13 0SU, CA13 9UX
An exact time for restoration is yet to be established, but the worst case scenario would see power lost until 8pm.
Customers in Carlisle are also without power, as 12 homes have been without electricity since shortly after 10am today.
This is in the area of Reeth Road.
"This is due to an underground fault, with power going off at 10:11 this morning.
"Engineers have been at the site for an hour."
The Carlisle problem is not weather related.
An estimated time of restoration has been set as 4.21pm for this fault.
Postcodes affected are:
CA2 6SP, CA2 6SX
Comments: Our rules
We want our comments to be a lively and valuable part of our community - a place where readers can debate and engage with the most important local issues. The ability to comment on our stories is a privilege, not a right, however, and that privilege may be withdrawn if it is abused or misused.
Please report any comments that break our rules.
Read the rules here