Although conventional exergy-based analyses uncover a path towards plant improvement, they suffer from some limitations, which are addressed by advanced exergy-based analyses. Advanced exergy-based methods identify interdependencies among plant components, and reveal the potential of improvement both at the component and plant level. Thus, data obtained from these methods pinpoint strengths and weaknesses of energy conversion systems and are of great importance when complex plants with a large number of interconnected components are considered. In this paper an advanced exergoeconomic analysis is applied to an advanced zero emission plant (AZEP). The most important components, in terms of the total avoidable costs, are the components constituting the main gas turbine system, while of particular importance are also the components of the mixed conducting membrane reactor incorporated in the plant. It has been found that for the most influential components of the plant, the largest part of investment cost rates and costs of exergy destruction are unavoidable. Additionally, for both the investment cost and the cost of exergy destruction, the interactions among the components are in most cases of lower importance, since for the majority of the components, the endogenous parts of the costs (related to the operation of the components themselves) are significantly larger than the corresponding exogenous parts (related to the operation of the remaining components). Nevertheless, strong interactions have been found among the components of the mixed conducting membrane reactor.