Around 1,200 homes are still without power in Swansea, Cardiff and east Wales following stormy weather.
Western Power said more than 50 faults were affecting networks which control power to large numbers of homes, with more affecting smaller communities.
Several roads were blocked by fallen trees as driving rain and strong winds, with speeds of up to 60mph, continue to cause problems across Wales.
Cardiff Council alone was called to more than 57 reports of fallen trees.
Between 40mm and 60mm of rain is forecast for east Wales.
The Met Office issued a "be prepared" warning for the whole of Wales, with a risk of localised flooding and winds exceeding 50-60mph.
A windspeed of 63mph was recorded at Aberdaron in Gwynedd, and 66mph at Mumbles near Swansea.
A Western Power spokesperson said staff are dealing with 10 times the normal volume of faults due to the weather with trees bringing down cables and debris on power lines.
She said all offices are open with staff working to resolve problem as quickly as possible.
Around 5,000 homes were originally without power.
A group of homes in the Cynon Valley were evacuated for a couple of hours while trees were made safe.
Newport University's city centre campus was closed after wind caused damage to the roof.
A university spokesperson said there had been no internal damage and the campus was expected to open as normal on Monday, although a final decision would be made first thing.
Fallen trees are reported to have blocked roads in Powys, Merthyr Tydfil, Newport and the Vale of Glamorgan.
The M48 Severn Bridge was also closed in both directions to high sided vehicles on Sunday morning due to strong winds.
Drivers are also being warned to take care on the M4 because of fallen trees, with one lane blocked eastbound near Bridgend.
A Cardiff Council spokesman said they set up an emergency response centre to coordinate the volume of calls of fallen trees, which came city-wide, from Adamsdown to Radyr.
Rhondda Cynon Taf Council said it had been alerted to a number of fallen trees, including some that have fallen onto cars and also onto a house.
Firefighters in south, mid and west Wales say they have been busy this morning dealing with minor weather-related calls.
They say there are concerns about strong winds blowing down shop signs and causing damage to roofs in Swansea, Port Talbot, Ammanford and parts of south-east Wales.
At Wildmill in Bridgend, roof debris from a block of flats blew down into the street.
Resident Rob Parry said: "The roof is from a block of flats and the fire service have cleared the road, but the roof is just on the side now.
"Some of the debris hit a car, but thankfully it wasn't damaged."
A group of Bron-y-Deri residents in Mountain Ash, in the Cynon Valley, had to evacuate their homes after a tree fell onto a conservatory.
Resident Steven Bull said there were concerns about the stability of other trees in the road.
"Our house is next to a slope where there's six or seven trees, and one of the trees fell on the back of another house, on their conservatory, and smashed the fence," he said.
"There are seven firefighters there at the moment.
"There was a loud crash. I thought some of my fencing had come off."