Electrical appliances including televisions and microwaves were damaged by the surge caused during the theft of the metal from two substations in Sheffield on Saturday.
The electricity supply to 369 homes in the Jordanthorpe and Batemoor areas was cut off when thieves escaped with copper worth thousands of pounds by cutting through power conductors at the substations.
Staff from CE Electric UK, which distributes electricity across Yorkshire, worked throughout the weekend to restore power to the stricken homes and had to visit the affected properties individually to carry out safety checks.
Up to 40 homes were still to be re-connected last night as workers were unable to gain access to the properties. Letters and contact details were left asking the owners to call CE Electric UK when they return home.
CE Electric UK's communications manager, Siobhan Barton, said: "The problem of copper theft is one which we are having to deal with on an almost daily basis, and it is now reaching epidemic proportions.
"Not only does it cost us a great deal of money and time as a company, it is causing huge disruption for our customers and we are doing all we can to prevent the thefts from happening."
The Yorkshire Post revealed last month that copper thefts in the North have cost CE Electric UK 629,000 in the first eight months of this year, with the Yorkshire region accounting for nearly half of the figure.
Other companies including Yorkshire Water, BT and the National Grid have also reported significant increases in copper cable thefts.
The latest thefts, which are thought to be linked, were reported to CE Electric UK between 7.40am and 9.40am on Saturday and South Yorkshire Police stepped up patrols in the affected areas.
Repairs to the two substations were completed on Saturday evening before power was restored to half of the affected properties. Workers from CE Electric UK continued to carry out safety checks at homes up until midnight on Saturday, resuming yesterday morning. Power was restored to most properties by 2pm yesterday.
Global demand for copper, especially from China, has soared. Last month, the metal cost 4,854 a tonne, compared with 2,916 a tonne in 2005.
Thieves often arrive at night in Transit-type vans similar to those used by electricity companies, leading people to believe legitimate work is being carried out.
CE Electric UK spends about 1m to replace stolen metal and up to 2m repairing damage caused by thieves and vandals every year. It is investing 10m on security improvements.
Anyone with information about the thefts from the Whitethorns View and Bowshaw View substations can call South Yorkshire Police on 0114 220 2020.