B777 FLT CREW ON NORTH ATLANTIC HAS IDG FAILURE AND ACFT IS RECONFIGURED BY STARTING APU. A SECOND REDISPATCH POINT BECOMES NECESSARY DUE TO APU FUEL USAGE AND IS OVERLOOKED BY FLT CREW.

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WHILE AT CRUISE FL340 MACH .84 I NOTICED WE HAD AN EICAS MESSAGE 'ELECTRICAL GENERATOR DRIVE L.' WE FOLLOWED THE CHKLIST AND DISCONNECTED THE L GENERATOR AND STARTED THE APU. THE ELECTRICAL SYNOPTIC SHOWED THE SYS WORKED AS IT SHOULD WITH THE APU NOW CARRYING THE LOAD OF THE L MAIN BUS. WE SPOKE WITH DISPATCH AND MAINT. WE CALLED UP THE CAPT FROM HER BREAK AND BRIEFED HER THOROUGHLY. THE ELECTRICAL ISSUE WAS WELL UNDER CTL BUT FUEL WAS NOW A FACTOR SINCE THE APU CARRIED PENALTIES. DISPATCH AGREED WITH OUR DECISION TO PROCEED TO ZZZ. WE WERE ALSO STUCK AT FL340 DUE TO OPPOSITE DIRECTION FLOW OF AIRPLANES. WE ASKED FOR FL360 BUT WERE DENIED. LATER; WITHIN 2 HRS OF 'HO' THE FIRST RE-DISPATCH MESSAGE RECEIVED WAS UNACCEPTABLE DUE TO NOT ENOUGH FUEL AT POINT 'HO.' A SECOND RE-DISPATCH MESSAGE WAS ACCEPTABLE. WE CONSTANTLY CHKED ZZZ AND ZZZ1 WX SINCE ZZZ VISIBILITY WAS AT THE TIME 1 3/4 MI. ZZZ1 WAS ABOVE 5 MI VISIBILITY. AS WE PASSED THE 50W POINT; WE GOT CLRED DIRECT WELL BEYOND 'HO' AND AT FL360 THEN FL380. THE FUEL WAS NOW LESS OF A CONCERN SINCE WE NOW SHOWED LNDG WITH APPROX 20K LBS. A LATER ATIS SHOWED VISIBILITY DOWN TO 1/2 MI BUT THE DIRECT ROUTING MADE THINGS BETTER. SINCE THE SECOND EARLIER RE-DISPATCH WAS ACCEPTED AND NO NOTICEABLE CHANGES TOOK PLACE; THE DIRECT ROUTING AND CLRNC TO CLB TO FL360 AND SHORTLY THEREAFTER FL380 MADE THE SITUATION SEEM EVEN BETTER EVEN THOUGH THE ZZZ ATIS VISIBILITY WAS DOWN TO 1/2 MI. HAVING ALREADY ACCEPTED THE SECOND RE-DISPATCH AND MORE DIRECT ROUTING (NOT OVER 'HO' -- THE RE-DISPATCH POINT) MADE US LESS CONCERNED WITH 'HO' AND MORE FOCUSED ON THE REQUIRED LNDG FUEL. AT THE TIME WE GOT DIRECT ROUTING BEYOND 'HO;' WE HAD RECEIVED AND ACCEPTED THE RE-DISPATCH AND WAS ON SCHEDULE TO HAVE THE NEW (SECOND RE-DISPATCH) FUEL OVER 'HO.' THE DIRECT ROUTING AND CLRNC TO HIGH ALTS IMPROVED OUR SITUATION. WE EVENTUALLY LANDED AT ZZZ WITH PLENTY OF FUEL (OVER 20K LBS). WE WERE CONSTANTLY GETTING WX UPDATES FOR ZZZ; ZZZ1; AND ZZZ2. WE ALSO KEEP A CLOSE WATCH ON ZZZ ESTIMATED LNDG FUEL. WE NEVER DECLARED AN EMER OR 'MINIMUM FUEL.'