This work applies the Dynamic Advanced Exergy Analysis (DAEA) to a heating and domestic hot water (DHW) facility supplied by a Stirling engine and a condensing boiler. For the first time, an advanced exergy analysis using dynamic conditions is applied to a building energy system. DAEA provides insights on the components’ exergy destruction (ED) by distinguishing the inefficiencies that can be prevented by improving the quality (avoidable ED) and the ones constrained because of technical limitations (unavoidable ED). ED is related to the inherent inefficiencies of the considered element (endogenous ED) and those coming from the interconnections (exogenous ED). That information cannot be obtained by any other approach. A dynamic calculation within the experimental facility has been performed after a component characterization driven by a new grey-box modelling technique, through TRNSYS and MATLAB. Novel solutions and terms of ED are assessed for the rational implementation of the DAEA in building energy installations. The influence of each component and their interconnections are valuated in terms of exergy destruction for further diagnosis and optimization purposes.