A closed cycle plant for converting thermal power to mechanical or electrical power including: a closed circuit inside which a working fluid circulates according to a predetermined circulation direction, a volumetric expander configured to receive at the inlet the working fluid in a gaseous state. The volumetric expander includes: a jacket having an inlet and an outlet for enabling the introduction and discharge the working fluid; an active element housed in said jacket and suitable for defining, in cooperation with said jacket, a variable volume expansion chamber; a main shaft; a valve active that opens and closes the inlet and outlet, and a generator connected to the main shaft. The valve includes a regulation device configured to vary the duration of the introduction condition, or the maximum through cross-section of the inlet.