No, Sydney does not have a nuclear power station. Australia does not have any operational nuclear power plants.
Lucas Heights
The main station before Sydney Central was the original Sydney Station, opened on the 26th of September 1855 and replaced in 1874.
North Sydney railway station was created in 1932.
Sydney Parade railway station was created in 1835.
Central Station.
Hartlepool Nuclear Power Station was created in 1983.
Cooper Nuclear Station was created in 1974.
There is only one nuclear power station in Sydney, which is used for research purposes. Other than this they play no role in providing power in Australia. Australia does however have the resources of uranium for it but export the majority of it to China.
Sanmen Nuclear Power Station was created in 2013.
Wylfa Nuclear Power Station was created in 1971.
Chapelcross nuclear power station was created in 1959.