Northern Powergrid' s latest estimate for power being restored is midnight tonight.
It has had hundreds of people in parts of Halifax, Sowerby Bridge, Ripponden, Hebden Bridge, Cragg Vale, Mytholmroyd and Todmorden to say they are without electricity.
Most have been without power since the early hours of yesterday (Saturday).
Northern Powergrid warned yesterday on social media: "If you are still without power, it is very likely that you will be off through the night and into tomorrow.
"If you can seek alternative accommodation with family and friends it is recommended to do so - or if you know someone without power, consider if you can offer support."
The network operator said last night it had restored power to 182,000 of around 240,000 customers whose power supplies have been affected by Storm Arwen across the North East, Yorkshire and northern Lincolnshire.
It said engineers were continuing to restore customers by switching electricity supplies, where possible, through alternative routes on its network and was ready to commence with repairs at first light today
The storm has caused varying degrees of damage across the whole of Northern Powergrid’s operating area, with the North East region taking the brunt of the storm. Fallen trees and flying debris have damaged electricity infrastructure in numerous locations and travel conditions remain challenging in some places.
Rod Gardner, Northern Powergrid’s Major Incident Manager, said: “Today has been one of the most challenging we have seen in over a decade with our teams being unable to safely climb for over 24 hours, due to the storm force winds.
"Although this has been frustrating, safety of our people is paramount. We have focused our efforts on work which could be completed to assess the scale of damage and response needed to repair the network.
“Despite the challenges, we have been restoring supplies wherever we can and we will continue to work into the night to restore as many of the remaining customers as possible. However, if your supplies are not restored by midnight, you are likely to remain without power into tomorrow.
“We apologise and understand the impact this has on customers who are still without power, especially at this time of year. We are advising that if you are currently without power, you may wish to consider seeking alternative accommodation with family and friends. Also, if you know someone without power, consider if you can offer any support.”
“Our contact centre, social media and website remain extremely busy. At this point, we ask that you only contact us if you are at risk, so we can help keep our channels clear for those who may need us in an emergency.”
Some residents in Mytholmroyd and Cragg Vale have also been without water after the power outage hit a Yorkshire Water pumping station.
Calderdale Council says it has had reports of wires down at Hays Lane in Mixenden, Clough Road in Greetland, Old Town Mill Lane in Hebden Bridge, Kebs Road in Todmorden and Top of the Hill in Colden, and is urging care when travelling in these areas.
Meantime, The Piece Hall announced yesterday that today's and yesterday's Winter Makers Markets were cancelled after the storm caused severe damage to the tents being used by the traders that could not be repaired in time.
The historic venue itself was shut temporarily yesterday morning but re-opened after lunchtime and will be open as usual today.
And the gates to Shibden Park had to be shut yesterday after a fallen tree blocked the path. The main gate is being reported as open today but with access to the top car park only. The cafe is open as usual.