Northern Powergrid has so far restored electricity to 18,680 customers who were affected by powers cuts caused when Storm Ophelia hit the region.
It said the gale-force storm had caused power cuts for customers predominantly in Northumberland, County Durham and North Yorkshire.
Around 1,400 properties in the DL8, TS12, TS14, YO21 and YO22 postcodes are among those without power at present.
A further 620 in the WF12, WF4 and WF5 postcode area of West Yorkshire are also affected.
Meanwhile, smaller clusters of homes in the Ripon, Bradford, Leeds, Halifax and Huddersfield areas also affected.
Rod Gardner, Northern Powergrid’s head of network operations, said: “We’ve been closely monitoring Storm Ophelia over the past few days. The storm, which is expected to continue to affect our region until early afternoon, has caused some disruption on parts of our network but our staff were ready to respond.
“We have worked throughout the night to safely restore power for our customers as quickly as possible. Overnight and this morning we’ve restored electricity supplies to some 18,650 customers and we’d like to reassure those still affected that we will continue to work until all customers have their power restored.
“We invest around Â£1 million every day on maintaining and upgrading our network but weather like Storm Ophelia can cause damage to our power network as result of fallen trees and windborne debris coming into contact with our network.
"The storm is expected to pass through our region by early afternoon and we’ll continue to monitor it closely and be ready to support our customers should it cause any further damage to our network.”
Northern Powergrid will be deploying its helicopter later today, once the storm passes, to carry out inspections and provide intelligence of any other damage which may have been caused by Storm Ophelia to its overhead network.
It has been diverting electricity through alternative routes on its network, wherever possible, and will carry out further repair work once it is safe for linesmen to climb.
In the meantime, it is urging anyone who spots any damaged cables or other equipment not to approach the area, but to report it immediately by calling the free 105 national number.
Click here for a map of the latest power cut locations in Yorkshire.