A method of and a power plant for generating power by combusting carbonaceous fuel with substantially pure oxygen, and a method of modifying a process of generating power by combusting carbonaceous fuel from combusting the fuel with air to combusting the fuel with substantially pure oxygen. The methods include feeding substantially pure oxygen into a furnace for combusting fuel with the oxygen to produce exhaust gas including mainly carbon dioxide and water, recovering low-grade heat from the exhaust gas by using multiple exhaust gas coolers arranged in a downstream portion of the exhaust gas channel, wherein a first portion of the recovered low-grade heat is used for preheating feedwater; pressurizing a first portion of the exhaust gas in multiple exhaust gas compressors so as to produce liquid carbon dioxide, recycling a second portion of the exhaust gas to the furnace via an exhaust gas recycling channel, using a first portion of steam extracted from a steam turbine system to preheat feedwater, wherein the first portion of the recovered low-grade heat is more than 50% of the total amount of recovered low-grade heat, or larger than the first portion of the recovered low-grade heat in the air-fired process, allowing minimizing of the first portion of the extracted steam, and the expanding of a second portion of the extracted steam in at least one auxiliary steam turbine for driving at least one compressor or at least one pump of the power plant.