Total spokeswoman Tricia Fuller declined to comment.
The refinery's 150,000-bpd crude distillation unit (CDU), the larger of two at the plant, was among the units restoring production on Wednesday, the sources said.
The power loss occurred around 1 a.m. CST (0700 GMT) on Wednesday.
Last week, Total cut production in half on the refinery's 60,000-bpd coker for a planned overhaul. Cokers process residual crude oil from the distillation units.
CDUs do the primary refining of crude oil and provide hydrocarbon feedstock to all other units.