Workers at the Liddell plant were allegedly exposed to the deadly fibre while working on the door, prompting partial shutdown of the plant.
The Australian Manufacturing Workers Union said Macquarie Generation, a NSW government-owned corporation, had admitted the door should have been included on an asbestos register in accordance with WorkCover guidelines.
The dispute comes at a bad time for the NSW Government, which has been talking up the health of the state's energy network after a series of blackouts in inner-Sydney last month.
Together, the two power stations provide about half of NSW's power supply, forcing energy minister Frank Sartor to reassure the public that electricity supplies would not be compromised.
"The capacity in NSW is fine," he said.
"This is a short-term dispute about contractors and what is happening in respect of processes and procedures being followed where they have located asbestos."
The power stations are expected to remain partially closed for about a month.
