The £776 million system was partly shut down between Murrayfield Stadium and the centre of the capital after five balloons became entangled in overhead cables.
The operators feared it would cause damage to the pantograph, a piece of equipment which connects the power from the overhead line to trams.
A spokeswoman for Transport for Edinburgh was not able to confirm whether balloon interference was one of several "disaster scenarios" they planned for before the system went live in May.
The balloons drifted into the 750-volt power lines outside McDonald's in St Andrews Square at about 3pm yesterday. Operators switched off the power on the network between St Andrews Square and Murrayfield Stadium for almost two hours, while contractors removed the debris.
The line between Shandwick Place and the airport remained open.
The Transport for Edinburgh spokeswoman said: "There was a group of five balloons which became entangled in overhead wires. It was the string that was causing the problem because there was a concern it could have caused damage to the pentograph, which is an extremely important piece of equipment.
"If it had wrapped itself around that, it could have caused real damage. That's why we took the decision to shut down the line between Murrayfield and the city.
"As a precaution we decided to isolate power and remove it to ensure there was no damage caused to the pantograph.
"These are still the early days of a new service as such we decided to use caution in our approach. We have been accepting tram tickets on our bus network until the full route can be re-instated."
Tram user Andy Connelly-Nimmo tweeted: "Get bus to Haymarket, so I can get tram without getting soaked, as it's the stop nearest a bus stop. Trams only going to next stop! Grr!"