Lothian and Borders Police are now appealing for witnesses following the explosion on Wednesday night.
Inspector Ian Moffat said: “We are still trying to establish the full circumstances of this incident. However, it appears an attempt has been made to cut through the electrical cable to remove it.
“Whoever was responsible put their life in serious risk and there is potential that they may have suffered electrical burns or other injuries.
“We are keen to trace those who were at the site last night and anyone who can help identify them is asked to contact police immediately.”
A spokeswoman for Lovell told The Scotsman: “Lovell is in the process of connecting the power supply to the site where the company is currently constructing 116 units.
“Vandals broke into the site in an attempt to steal copper wiring after the site was closed.
“Further security measures have been implemented following the incident and we are committed to working with the police to ensure people are made aware of the dangers of construction sites.”
A ScottishPower spokesman said: “Anyone who tries to steal live electricity cables is showing a staggering disregard for their own safety, the safety of the public, and that of our employees.”
He added: “It beggars belief that anyone would put their life on the line by interfering with live electricity to steal cables with a minimal scrap value.”