A modified form of hybrid method for advanced exergy analysis is introduced and applied to an anode gas recirculation solid oxide fuel cell system. The results are compared with the corresponding values achieved from applying the well-known engineering method of advanced exergy analysis to the system. The modified hybrid method proved to be accurate and less time consuming and also, in contrast with the hybrid method introduced in literature, doesn't require the violation of the conservation of mass or exergy balance. In addition the modified hybrid method is more appropriate for parametric studies and optimization of energy conversion systems. The results obtained from both the advanced exergy methods are found to agree with one another and differ from those obtained from conventional exergy analysis. The values of endogenous and unavoidable endogenous exergy destruction rates for modified hybrid method are approximately 4% higher than the corresponding values obtained by the engineering method. The unavoidable conditions required for the analyses in both methods are obtained by a micro-structure analysis showing that the energy and exergy efficiencies of the system, under unavoidable conditions can be higher by up to 26%, 24.8%, respectively, compared to the corresponding values under the real conditions. As the highest avoidable endogenous exergy destruction rates occur in the inverter, 6.6 kW, and the stack, 3.7 kW, more attention should be paid to these components when the system performance is to be optimized. A different order, however, is achieved by applying the conventional exergy analysis.