An energy conversion system comprising: - a Solid Oxide Fuel Cell (SOFC) unit having an anode and a cathode side, configured for receiving a fuel and a stream of oxidant and for converting a fraction of chemical power of the fuel directly into electric power through one or more electrochemical reactions occurring on the anode and the cathode side of the SOFC unit involving said fuel and said oxidant, parts of the fuel and of the stream of oxidant being maintained unconverted following said electrochemical reactions; - a combustor unit arranged to receive the unconverted fuel and the unconverted oxidant from the SOFC unit, configured for the combustion of the unconverted fuel using the unconverted oxidant, thereby converting the unconverted fuel and the unconverted oxidant into product gas; - an expander unit arranged to receive the product gas exiting the combustor and configured for expanding said product gas exiting the combustor into flue gas; - a cooler unit in thermal relationship with a heat sink and configured for cooling said flue gas exiting the expander unit; - a separator for removing condensed species from the cooled gas exiting the cooler unit, thereby obtaining a recycled stream; - a mixer, producing said stream of oxidant by mixing at least a part of the recycled stream with an external oxygen stream; - a first compression unit configured for increasing the pressure of said oxidant (26, 4, 8) to a value suitable for the SOFC unit and the combustor unit, wherein said increased pressure oxidant is used by the SOFC unit; and - a splitter dividing the increased pressure oxidant stream in a first flow used in the SOFC unit and in a second flow used in the combustor. - a Solid Oxide Fuel Cell (SOFC) unit having an anode and a cathode side, configured for receiving a fuel and a stream of oxidant and for converting a fraction of chemical power of the fuel directly into electric power through one or more electrochemical reactions occurring on the anode and the cathode side of the SOFC unit involving said fuel and said oxidant, parts of the fuel and of the stream of oxidant being maintained unconverted following said electrochemical reactions; - a combustor unit arranged to receive the unconverted fuel and the unconverted oxidant from the SOFC unit, configured for the combustion of the unconverted fuel using the unconverted oxidant, thereby converting the unconverted fuel and the unconverted oxidant into product gas; - an expander unit arranged to receive the product gas exiting the combustor and configured for expanding said product gas exiting the combustor into flue gas; - a cooler unit in thermal relationship with a heat sink and configured for cooling said flue gas exiting the expander unit; - a separator for removing condensed species from the cooled gas exiting the cooler unit, thereby obtaining a recycled stream; - a mixer, producing said stream of oxidant by mixing at least a part of the recycled stream with an external oxygen stream; - a first compression unit configured for increasing the pressure of said oxidant (26, 4, 8) to a value suitable for the SOFC unit and the combustor unit, wherein said increased pressure oxidant is used by the SOFC unit; and - a splitter dividing the increased pressure oxidant stream in a first flow used in the SOFC unit and in a second flow used in the combustor.