A fuel cell device comprising: a cell stack comprising a plurality of solid oxide fuel cells electrically coupled to generate power with a fuel gas and an oxygen-containing gas, a fuel gas supply unit to supply the fuel gas to the solid oxide fuel cells; a power conditioning unit that controls the amount of electric current that is generated by the solid oxide fuel cells and that is supplied to an external load; and a controller that controls each of the fuel gas supply unit and the power conditioning unit; characterized by a burning means for burning excess fuel that was not used for generating electricity; wherein the excess fuel that was not used for generating electricity is burned by the burning means at one end of the solid oxide fuel cells; and wherein the controller controls the fuel gas supply unit and the power conditioning unit such that the relationship between a rate of the fuel utilization of the cell stack and the amount of electric current generated by the cell stack is - linear until a minimum flow of the fuel gas supplied to the cell stack is reached necessary to maintain the temperature of the fuel cells above a predetermined temperature during a partial load operation of the fuel cell device - non-linear when the fuel gas supplied to the cell stack is the minimum flow or more necessary for generating power during the partial load operation of the fuel cell device; - reaches a maximum rate of the fuel utilization of the cell stack during partial load operation which maximum rate is the same as the rate of fuel utilization during a rated operation of the fuel cell device, and the relationship during the rated operation is a constant fuel utilization rate over the electric current generated by the cell stack. a cell stack comprising a plurality of solid oxide fuel cells electrically coupled to generate power with a fuel gas and an oxygen-containing gas, a fuel gas supply unit to supply the fuel gas to the solid oxide fuel cells; a power conditioning unit that controls the amount of electric current that is generated by the solid oxide fuel cells and that is supplied to an external load; and a controller that controls each of the fuel gas supply unit and the power conditioning unit; characterized by a burning means for burning excess fuel that was not used for generating electricity; wherein the excess fuel that was not used for generating electricity is burned by the burning means at one end of the solid oxide fuel cells; and wherein the controller controls the fuel gas supply unit and the power conditioning unit such that the relationship between a rate of the fuel utilization of the cell stack and the amount of electric current generated by the cell stack is - linear until a minimum flow of the fuel gas supplied to the cell stack is reached necessary to maintain the temperature of the fuel cells above a predetermined temperature during a partial load operation of the fuel cell device - non-linear when the fuel gas supplied to the cell stack is the minimum flow or more necessary for generating power during the partial load operation of the fuel cell device; - reaches a maximum rate of the fuel utilization of the cell stack during partial load operation which maximum rate is the same as the rate of fuel utilization during a rated operation of the fuel cell device, and the relationship during the rated operation is a constant fuel utilization rate over the electric current generated by the cell stack. - linear until a minimum flow of the fuel gas supplied to the cell stack is reached necessary to maintain the temperature of the fuel cells above a predetermined temperature during a partial load operation of the fuel cell device - non-linear when the fuel gas supplied to the cell stack is the minimum flow or more necessary for generating power during the partial load operation of the fuel cell device; - reaches a maximum rate of the fuel utilization of the cell stack during partial load operation which maximum rate is the same as the rate of fuel utilization during a rated operation of the fuel cell device, and the relationship during the rated operation is a constant fuel utilization rate over the electric current generated by the cell stack.