A method for operating a closed loop regenerative thermodynamic power generation cycle system is presented. The method includes supplying a high-temperature working fluid stream at a first pressure P1 to an expander, and extracting a partially expanded high temperature working fluid stream from the expander at a second pressure P2. Each of the first pressure P1 and the second pressure P2, are higher than a critical pressure of the working fluid; and the second pressure P2 is lower than P1. The method further includes regeneratively supplying the extracted high temperature working fluid stream at the second pressure P2 to a low temperature working fluid stream at the first pressure P1. A closed loop regenerative thermodynamic power generation cycle system is also presented.