Systems and methods relating to variable pressure turbines are disclosed. A power generation system may include a closed cycle system configured to generate power, a combustor, and a control system. The closed cycle system may include a working fluid circulating in a closed cycle path. The combustor may provide thermal energy to the working fluid. Further, the control system may be configured to determine to increase an amount of power generated by the closed cycle system, and in response to the determination to increase the amount of power generated by the closed cycle system, cause an increase in pressure of the working fluid in the closed cycle path.