Never heard of a power station in Princes Street.
There is a railway station at the east end of Princes Street, known as Edinburgh Waverley. Part of the station car park has recently been sold for redevelopment, during which a former gasworks dating from 1819 has been excavated. This station was originally the North British Railway's station.
The Caledonian Railway also reached Edinburgh and their station was at the west end of Princes Street, just at the start of Lothian Road, and was known as Edinburgh Princes Street station. Following the merger of the railways, a new junction was put in further west, so that Caledonian trains could then run to the North British station and Princes Street station was closed in 1964. The old station building is now the Caledonian Hilton Hotel.