"We haven't had a power outage caused by a tree in a right of way since 2009," she said.
Councilman Courtney Persinger, a Republican from South Hills, is also concerned about the reliability of the system in the city.
The power outages were especially hard on the elderly and businesses in the South Hills ward.
"It's a major problem," Persinger said.
He believes major investment in electrical infrastructure is needed.
"It doesn't take a lot of sense to figure out that when you have trees growing up through lines, that the tree will wipe out those lines when it falls," he said.
Persinger said he understood that the company had a system for maintaining the rights of ways but it wasn't working.
Persinger lives in South Hills and was without power for about two and a half days after the recent storm.
Republican Brent Burton, another South Hills council member, was without power for four days. Burton is hoping for better communication between the company and individuals living in the affected areas.
"I don't know what can be done," Burton said. "I'm not an expert and I don't want to speak to that.
"But what I can do as a city leader is facilitate discussions between the company and my constituents," he added.
Democrat councilman Sam Minardi also represents a South Hills ward.
"I think it's obvious we have problems in South Hills," Minardi said. "But I also understand that these weren't your typical storms."
Minardi would like to speak to company representatives to make sure that the area is prepared going forward, he said.
"We have to do something to ensure that we're not without power for a week every time we have a large storm," he said.
Minardi was without power for two days.
"But my neighbors across the street didn't have power for a week," he said. "That's what's really concerning and I don't understand that at all."
Appalachian Power budgeted about $22.2 million for right-of-way maintenance in West Virginia during the current fiscal year. This is up from $16 million to $18 million in years past, Matheney said.
Company employees and contractors have trimmed 134,454 trees and removed 138,637 in rights of way throughout the state, she said.