Conventional exergy-based analyses provide useful information that can be used to improve the thermodynamic, economic, and environmental performance of energy conversion systems. However, when the complexity of a system is high, component interactions increase, and improvement strategies become more difficult to detect. Advanced exergy-based analyses have been developed to address such issues, to aid further assessment and to reveal options for improving the overall thermodynamic, economic, and environmental-impact-related effectiveness of energy conversion systems. Specifically, with an advanced exergetic analysis, exergy destruction is separated into (a) avoidable/unavoidable parts that deal with the potential for improving a component and/or a system and (b) endogenous/exogenous parts that show the way and magnitude of component interactions. The purpose of this paper is two-fold: first, to demonstrate the applicability of the method to a complex system by applying it to a new power plant concept and, second, to evaluate the design and operation of the plant and the improvement potential of the implemented CO2 capture technology. The results from this analysis can be used in improving the design of the power plant. The considered power plant is an advanced zero-emission plant that incorporates oxy-fuel technology and has been selected because of its relatively high efficiency in comparison with other alternatives. Overall, the improvement potential of the plant is rather limited due to the relatively low values of the avoidable exergy destruction. Additionally, the analysis shows that component interactions are of relatively low importance because of low exogenous values. However, when the exogenous exergy destructions within the components are further split, additional improvement possibilities are revealed.