Massachusetts Attorney General Martha Coakley announced Thursday that she was seeking more than $16 million in fines against National Grid for what she said was the company’s subpar performance in restoring power after Tropical Storm Irene last August and the rare early snowstorm in October.

“We believe that Massachusetts customers deserve better,” Coakley said at a news conference Thursday. “I am hopeful that this will send a message that they can, and should, be doing better.”