Northern Powergrid, the company responsible for the electricity distribution network across the region, has restored power to more than 55,000 customers affected by the storm.
Storm Malik, which brought wind speeds of over 80 mph, was “a lot stronger” than originally forecast.
Northern Powergrid says damage is not as severe as destruction caused by Storm Arwen.
It it expected that most of the remaining customers left without power will be restored on Sunday, January 30, by 6pm.
Northern Powergrid director Paul Glendinning said: “We have successfully restored supplies to more than 55,000 customers but given the amount of work that there is to do and the fact that we are expecting more high winds on Sunday evening, it is possible that a relatively small proportion of our customers will remain without power beyond the weekend.
"It will become clearer during tomorrow morning what proportion of these customers may still be without power beyond Sunday.
“We need to complete the necessary assessment of the work required and match it to the resources needed so we can provide a more accurate indication of how long it will take to restore power.
"Until we are able to do that, the estimated times on our website for those customers who we do not expect to reconnect before tomorrow will indicate 18:00 on Sunday 31 January.
"At this stage, we are unable to be any more precise. In many cases we will be able to provide an update during Sunday of an earlier restoration time as the work progresses.
"We will provide updated estimates of restoration times for each incident as soon as more information is available on our website and social media channels.
“We will be working through the night to prioritise the work for tomorrow to get those customers who remain without power as clear an estimate as we can provide of when they will be reconnected. In the meantime, we are advising those customers for whom being without power tonight is a significant problem to err on the side of caution and consider seeking alternative accommodation.”