Abstract When complex energy systems are analyzed and when a large number of their components is observed, the destruction of exergy related to a single component is dependent on its own properties, but also on the characteristics of other components. The advanced exergy analysis is useful for providing supplementary information on the interaction between the components. It also exposes the real improvement potential related to each component of a system, but also of a system as a whole. In this paper, an existing complex industrial plant with 33 components and 70 streams is analyzed using the first and second level of exergy destruction splitting for the boiler, as a main plant component from the aspect of destroying the useful work. From the total unavoidable exergy destruction 97.28% comes from the internal irreversibility, 2.72% comes from the irreversibilities of other components, while 95.26% of the unavoidable exergy destruction (186.49 kW) comes from the internal irreversibility, and 4.74% from the external irreversibility. The final result of the advanced exergy analysis for the steam generator is the total value of the avoidable exergy destruction as a real potential that can be avoided. It is 16.19% of the total exergy destruction of the component. That is less than the data obtained in the first decomposition level (186.49 kW) merely due to the existence of mexogenous exergy destruction.