A pressurized oxy-combustion circulating fluidized bed power plant having a circulating fluidized bed boiler is provided. A combustion chamber of the boiler is in fluid communication with a separator and configured so that solids produced during combustion enter the separator. The power plant further includes an air separation unit that is in fluid communication with the combustion chamber. The air separation unit is configured to supply substantially pure oxygen to the combustion chamber at a pressure greater than 1 bar. An external heat exchanger is in fluid communication with the separator and in fluid communication with the combustion chamber. The external heat exchanger is configured so that a portion of the solids received in the separator pass through the external heat exchanger and transfer heat to a working fluid, after which the solids are returned to the combustion chamber to moderate or control the temperature in the combustion chamber.