Climb onto the formerly white metal box to the left of the generator. Jump to grab the whitish louvered vent on the wall between the yellow pipes.
Climb to the right and then jump to grab the edge of the catwalk; pull up. Follow the catwalk, jumping the gap, and continue around behind the generator.
Or, for a shortcut, jump onto the narrow metal railing on the right side of the generator. Jump from there to grab the catwalk behind it on the right and pull up. (Thanks to MMAN for this. Also, apologies for the murky screenshot. It's really dark in there.)
Jump to grab the dangling rope. Lara's weight pulls down a pipe, refueling the generator.
Go around to the front of the generator and use the magnetic grapple to pull out the valve. The generator starts, lighting up the map on the wall and unlocking the door in the corner.
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