An electrical turbo-machine includes a stator (101), a rotor (102), and a turbine section (110) driven with a working flow containing vaporizable material, for example water, in vaporized form. The rotor includes cooling channels (106-109) for conducting, through the rotor, a cooling flow containing the vaporizable material in liquid form. The rotor is arranged to conduct the cooling flow through an area where an impeller or impellers (111-114) of the turbine section are directly connected to the rotor and conduct the cooling flow to a same room to which the working flow comes out from the turbine section. The above-presented cooling system facilitates constructing the electrical turbo-machine as a hermetic structure in a power plant where bearings of the electrical turbo-machine are lubricated by the vaporizable material, a supply pump is directly connected to the rotor, and the vaporizable material in gaseous form fills the gas spaces of the stator.