Disruption started earlier in the evening after problems with overhead wires caused delays. The decision was then taken to close the station around 10pm.
A message was posted on the ScotRail website, saying: “A failure of the electricity supply at Glasgow Central is causing disruption to trains forcing bosses to close the station.”
Some people were able to secure a seat on a replacement bus, though queues were tremendously lengthy and many were forced into ordering taxis to make the journey home.
Most trains due to leave on Sunday morning have been cancelled with replacement bus services on instead.
National Rail posted on their Twitter feed on Sunday morning that disruption is expected to continue at the station until at least 5pm.