ScotRail announced that none of their trains are able to pass through Haymarket at all as a result of the issues.
Network Rail have also had to temporarily restrict access to Edinburgh Waverley due to the volume of people currently in the station.
However, the station is now fully open again.
Due to the overhead line issues in Edinburgh, the Caledonian Sleeper is also expected to be delayed via the Edinburgh to London Euston service on Friday evening.
Engineers are continuing to investigate the cause of the power failure to get trains back on the move.
Network Rail Scotland are dealing with the overhead line fault between Haymarket and Edinburgh Waverley.
A Network Rail spokesperson said: “We've had to isolate the power supply in the area, including to Edinburgh Waverley.
"Please check with your train operator for updates.”