The loss of power caused a flaring incident on Monday night, the filing showed.
Exxon did not immediately respond to a request for comment.
The plant went down due to heavy wind and rain, two industry sources said.
A severe storm passed through Joliet on Sunday, according to the National Weather Service, leaving thousands without power.
"Situations like this take time to recover as they will have to see if the sudden shutdown did damage to any of the units," one of the sources said.
The Joliet refinery mainly processes Canadian crude oil and produces around 9 million gallons a day of gasoline and diesel, according to the company website.
