An analysis was carried out for different thermodynamic cycles of power plants with air turbines. Variants with regeneration and different cogeneration systems were considered. In the paper, we propose a new modification of a gas turbine cycle with the combustion chamber at the turbine outlet. A special air by-pass system of the combustor was applied and, in this way, the efficiency of the turbine cycle was increased by a few points. The proposed cycle equipped with a regenerator can provide higher efficiency than a classical gas turbine cycle with a regenerator. The best arrangements of combined air–steam cycles achieved very high values for overall cycle efficiency—that is, higher than 60%. An increase in efficiency to such degree would decrease fuel consumption, contribute to the mitigation of carbon dioxide emissions, and strengthen the sustainability of the region served by the power plant. This increase in efficiency might also contribute to the economic resilience of the area.