SP Manweb has said the storm caused some of the worst damage it had seen in more than 15 years.
The company was still working to restore power supplies to customers four days after the storm ripped through Shropshire and mid and north Wales on Friday evening.
It said faults on main lines were taking time to repair.
Many areas across Shropshire were without power throughout the entire weekend with soup kitchens set up in village halls were generators could be taken in.
Across the country, 30,000 homes remained without electricity on Wednesday with some rural areas unlikely to have power restored for several more days or even weeks.
The Business Secretary has promised to do everything possible to restore power to homes affected before Christmas.
A spokesman for SP Manweb said: “We apologise to all of our customers who have been affected by the damage, we understand the stress and inconvenience this has caused many households and we appreciate everyone’s patience whilst we continue to try to resolve the ongoing issues on the power network.
“Over the weekend, Storm Arwen brought winds of over 90mph and, as a result, that has caused some of the worst damage we have experienced in over 15 years and far worse than previous weather events.
“In many areas, the damage has been severe due to fallen trees and other wind-blown debris and engineers are also dealing road closures and access challenges making some of our repairs even harder.
“The time it has taken us to get our customers back on is reflective of the number of faults and severity of the damage to the network; where normally we would deal with one or two faults on a main line and be able to get a larger number of customers back on, we found even with the line repaired, many spurs that feed into it had been impacted by fallen trees requiring secondary repairs. This slowed restoration times as wer were only able to reconnect handfuls of customers at a time."
The company said fit was keeping customers up-to-date and providing welfare services for anyone left without power.
"We are also offering our customers reimbursement for hot food if they continue to be off supply and offering accommodation to vulnerable customers if they are likely to still be off supply.”