## 2 Analysis Methods
### Advanced Exergy Analysis  
Advanced exergy analysis [29; 30; 31; 32] is introduced into the novel CCHP system based on TC-CCES to make the quality of the conclusions from conventional method better. Exergy destruction is separated into detailed parts, e.g., unavoidable/avoidable parts and endogenous/exogenous parts. Moreover, more valuable details can be received by combining the above two splitting measures for improving the system performance. It is noteworthy that exergy destruction is due to irreversibilities within the system, and exergy loss is the exergy transfer to the environment. Here, exergy loss is associated with the overall system but not with a component because each exergy stream exiting a component is considered either at the fuel or at the product side. Therefore, it is mainly concerned the exergy destruction in this section. The component exergy destruction is not only dependent on the irreversibility occurring within the component itself, but also related to the interconnections among different components, which can therefore be written as:  
\[\dot{E}_{\text{D},k}=\dot{E}_{\text{D},k}^{\text{EN}}+\dot{E}_{\text{D},k}^{ \text{EX}} \tag{20}\]  
where \(\dot{E}_{\text{D},k}^{\text{EN}}\) and \(\dot{E}_{\text{D},k}^{\text{EX}}\) stands for the parts that determined by the component itself and the other components, respectively. The component exergy destruction is able to be alternatively separated to the unavoidable part \(\dot{E}_{\text{D},k}^{\text{UN}}\) and avoidable part \(\dot{E}_{\text{D},k}^{\text{AV}}\):  
\[\dot{E}_{\text{D},k}=\dot{E}_{\text{D},k}^{\text{UN}}+\dot{E}_{\text{D},k}^{ \text{AV}} \tag{21}\]  
where \(\dot{E}_{\text{D},k}^{\text{UN}}\) will always exists owning to the technological limitations, while \(\dot{E}_{\text{D},k}^{\text{AV}}\) could be lessened by improvement measure. The splitting approach proposes the real potential to improve a specific component. By coupling the above two concepts, four more detailed parts can be erected as follows:  
\[\dot{E}_{\text{D},k}=\dot{E}_{\text{D},k}^{\text{EN,AV}}+\dot{E}_{\text{D},k}^ {\text{EN,UN}}+\dot{E}_{\text{D},k}^{\text{EX,AV}}+\dot{E}_{\text{D},k}^{ \text{EX,UN}} \tag{22}\]  
where \(\dot{E}_{\text{D},k}^{\text{EN,AV}}\) and \(\dot{E}_{\text{D},k}^{\text{EN,UN}}\) stand for the parts that can be and cannot be lessened, respectively, when the component works in the best running mode; \(\dot{E}_{\text{D},k}^{\text{EX,AV}}\) and \(\dot{E}_{\text{D},k}^{\text{EX,UN}}\) are the parts that can be and cannot be decreased, respectively, through promoting the characteristics of the other components and the system integration. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Component** & \(\dot{E}_{\text{F},k}\) & \(\dot{E}_{\text{P},k}\) \\ \hline C1 & \(\dot{W}_{\text{C1}}+\dot{m}_{3}e_{3}^{\star}\) & \(\dot{m}_{3}\big{(}e_{4}^{\star}+c_{4}^{\text{M}}-c_{3}^{\text{M}}\big{)}\) \\ C2 & \(\dot{W}_{\text{C2}}\) & \(\dot{m}_{5}(e_{6}-e_{5})\) \\ HE1 & \(\dot{m}_{4}(e_{4}-e_{5})\) & \(\dot{m}_{16}(e_{17}-e_{16})\) \\ HE2 & \(\dot{m}_{6}(e_{6}-e_{7})\) & \(\dot{m}_{18}(e_{19}-e_{18})\) \\ HE3 & \(\dot{m}_{20}(e_{20}-e_{21})\) & \(\dot{m}_{9}(e_{10}-e_{9})\) \\ HE4 & \(\dot{m}_{12}(e_{12}-e_{13})\) & \(\dot{m}_{22}(e_{23}-e_{22})\) \\ T1 & \(\dot{m}_{10}(e_{10}-e_{11})\) & \(\dot{W}_{\text{T1}}\) \\ T2 & \(\dot{m}_{11}\big{(}e_{1}^{\star}+c_{11}^{\text{M}}-e_{12}^{\text{M}}\big{)}\) & \(\dot{W}_{\text{T2}}+\dot{m}_{11}e_{12}^{\star}\) \\ TV1 & \(\dot{m}_{1}\big{(}c_{1}^{\text{M}}-c_{2}^{\text{M}}\big{)}\) & \(\dot{m}_{1}\big{(}e_{1}^{\star}-e_{1}^{\star}\big{)}\) \\ TV2 & \(\dot{m}_{\text{Reg}}\) & \(\dot{m}_{10}\) \\ CS & \(\dot{m}_{2}(e_{2}-e_{3})\) & \(\dot{m}_{13}(e_{14}-e_{13})\) \\  & \(\dot{E}_{\text{P},tot}=\) & \\ Overall system & \(\dot{E}_{\text{P},tot}=\) & \\  & \(\dot{E}_{\text{D},tot}=\) & \(\dot{E}_{\text{D},k}\) & \(\dot{E}_{\text{L},tot}=\dot{m}_{21}(e_{21}-e_{15})\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: The exergy definitions in the CCHP system based on TC-CCES.