The company hopes to restore energy supplies within the next three days as they describe the Storm Arwen damage as a "once in generation event".
Aberdeenshire remains the worst affected area after Storm Arwen which hailed a rare red weather warning led to a cut in electricity as the dangerous winds damaged the supply network.
Scottish and Southern Electricity Networks (SSEN) is encouraging customers still without power to take up support with accommodation and meals.
Graeme Keddie, SSEN's director of corporate affairs, told BBC Good Morning Scotland said: "We've got all of the villages connected and it's now looking at the rural areas.
"We are confident we have a handle on what we can restore in the next couple of days.
"We are looking at making really good progress today and tomorrow and we expect it will be the last final few homes on Friday."
On Tuesday evening, the network said a total of 118,000 customers in total were reconnected to the energy supply, however 9,500 customers are currently off supply.
The areas affected are Aberdeen and Aberdeenshire (with 5,721 without power), Moray (1,526), Angus (1,423), Perthshire (578) and Stirlingshire (252).
Rest Centres and welfare facilities have been established across the affected areas and will remain in place until customers in those locations have been restored.
Additional resources from all over the UK have been working to repair the lines in the Borders and Dumfrieshire with dozens of generators believed to be en-route to power sub stations as opposed to individual homes so they can bypass some of the faults.
An SSEN spokesperson added: “Subject to no new damage being identified or unforeseen challenges with repairs and restorations.”If any customer is without power and is unable to make alternative arrangements to stay with family or a friend, SSEN says they will “reimburse all reasonable costs for alternative accommodation.”
An SSEN spokesperson said: "Anyone who may need support in arranging alternative accommodation should call SSEN’s contact centre on 105.
"Customers are asked to help keep lines clear by calling us only in an emergency and when in genuine need of assistance so that we are able to prioritise our support towards our customers who most need our help.”
Customers can access SSEN’s welfare facilities for free hot food and drinks, as well as claim the cost of takeaways or meals from local establishments.
Chris Burchell, SSEN’s Managing Director, said: “I would like to thank our customers who have shown great resilience, patience and understanding since the impact of Storm Arwen and we fully recognise that urgency of the situation for those who continue to remain off supply. I would like to personally apologise to all customers who have been impacted and would like to reassure everyone still off supply that our teams are working extremely hard to reconnect them as soon as possible.