## 3 Configuration of the System and Conditions  
### Recompressed S-Co\({}_{2}\) System Layout  
To study robust data reconciliation for S-CO\({}_{2}\) systems, we set up a schematic recompressed S-CO\({}_{2}\) cycle for measurement simulations. The layout of the recompressed S-CO\({}_{2}\) system is shown in Figure 3, mainly based on the original design proposed by [PERSON] et al. [3]. The system was supposed to have already been constructed, and various types of measurement sensors were deployed all over the system. The cycle included two compressors (C1, C2), two regenerators (R1, R2), one turbine (T), a high-temperature heat source (H), and a condenser (COND). In the recompression cycle, only a part of the CO\({}_{2}\) passed through the condenser to be cooled down to the inlet temperature of C1, while the other part was directly entering C2. The two streams merged at the outlet of the low-temperature regenerator, R1. Then, they entered the heat source H to be heated up to a predetermined temperature, after which they flowed into the turbine T to expand and generate power. Subsequently, they entered the two regenerators sequentially to preheat the incoming CO\({}_{2}\). The cooling water (13, 14) entering and exiting COND was also included in the scope of robust data reconciliation analysis in order to provide more redundancy of measurements. Figure 3: Recompressed S-CO\({}_{2}\) system layout. The shaft power generated by T was supplied to drive C1 and C2 and then transformed into electricity by G.  
To simplify the thermal model and the simulation process, several assumptions were proposed for the schematic S-CO\({}_{2}\) system studied in this work:  
1. For all the heat exchangers in the system (including COND, R1, R2, and H), they were assumed to have a \"perfect\" design, which meant their heat transfer loss and pressure drop were not considered. 2. For C1, C2, and T, it was assumed that there was no leakage of S-CO\({}_{2}\), and their mechanical loss during the energy conversion process was also ignored. 3. As for the mixture point a, the pressure of outflow No. 6 took the minimum of inflows No. 4 and No. 5. For the split point b, the pressure of outflow No. 3 and No. 12 took the value of inflow No. 11. No extra pressure drop and heat loss were considered for them. Despite these assumptions, the robust data reconciliation framework studied in this paper could still be verified and be applied to the actual S-CO\({}_{2}\) systems, with estimations about the various losses over the conversion process. They could be easily added to the analysis process. For the current system, removal of these factors helped to give prominence to the most important parameters. Under the assumptions above, the state parameters of each point under the standard condition are shown in Table 2, slightly different from the original design of [PERSON] et al. [3]. To acquire the enthalpy of each point, the open-source property library CoolProp [34] was applied. Once the state parameters were decided, the performance of the schematic S-CO\({}_{2}\) system and its key devices could be calculated through heat balance calculation, which is listed in Table 3. It should be noted that the total efficiency of the generator was supposed to be 99% when transforming the shaft power output. As the outstanding index of the cycle, the round-trip efficiency (RTE) of the system can be decided, which is defined as:  
\[\text{RTE}=\frac{W}{Q}=\frac{W_{\text{T}}-W_{\text{C1}}-W_{\text{C2}}}{Q} \tag{10}\]  
where \(W\) is the shaft power output of the system and can be computed through the subtraction of the shaft power generated by the turbine, T, and the power consumed by  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Substance** & **State Point** & \begin{tabular}{c} **Mass Flow** \\ **(kg/s)** \\ \end{tabular}  & \begin{tabular}{c} **Pressure** \\ **(MPa)** \\ \end{tabular}  & \ \begin{tabular}{c} **Temperature** \\ **(\({}^{\circ}\)C)** \\ \end{tabular}  & \begin{tabular}{c} **Enthalpy** \\ **(kJ/kg)** \\ \end{tabular}