## 2 Materials and Methods
#### Methodology Limitations  
There are some limitations derived from the calculations that have been carried out to obtain the POS:  
1. The exact pre-evaluated POS has been obtained for 4 reference buildings and 4 reference climates.
2. The reference buildings have been considered in two orientations for the POS calculations: main facades oriented N-S, and E-W.  
In order to evaluate the accuracy of the 32 POS when they are applied in different buildings (in terms of their typology or thermal characteristics), the authors have calculated how well the POS perform for a combination of 42 buildings and 13 climates. The results of this are reported in Figure 1, where the best POS is reported for each combination of building typology and climate. In Figure 2, the primary energy saving obtained implementing the  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**SFH17** & **SFH13** & **MFH4** & **MFH1** \\ \hline Average \(\hat{\text{U}}\)-value \({}^{*}\) & 2.12 & 2.23 & 1.89 & 2.54 \\ (W/m\({}^{2}\)K) & 1.57 & 1.33 & 3.46 & 2.96 \\ Uw (W/m\({}^{2}\)K) & 2.7 & 3.6 & 5.65 & 5.7 \\ Windows per Wall & N: 30 & NW: 8 & N: 16 & N: 6 \\ Orientation (\%) & W: 22.7 & SE: 8 & S: 16 & S: 12 \\ \hline \hline \end{tabular} \({}^{*}\) Average U-value is the sum weighted by area of the U-values of walls, windows, roof, and slab-on-grade.  
\end{table}
Table 1: Reference buildings characteristics.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Climatic Zone** & **SFH17** & **SFH13** & **MFH4** & **MFH1** \\ \hline W1S2 & POS1 & POS5 & POS9 & POS13 \\ W2S2 & POS2 & POS6 & POS10 & POS14 \\ W2S3 & POS3 & POS7 & POS11 & POS15 \\ W3S2 & POS4 & POS8 & POS12 & POS16 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Type of POS according to the climatic zone and type of reference building.  
best POS is showed. Analyzing these figures, it can be concluded that the energy savings for other combinations are as high as required for an optimal solution and, as a consequence, the POS make up a heuristic solution that can be applied to achieve the goals reflected in Figure 2.  
The advantage of this methodology consists in the fact that providing a building typology and a climate, an optimal solution in terms of LCC is suggested. The accuracy of the solution has been evaluated in terms of its performance in terms of the energy savings and the results have been satisfactory. The main limitation is that it could be very difficult to find a building similar to the one that is going to be refurbished. The possibility of the previous has been reduced by defining properly the 42 buildings using previous reference buildings derived from other studies such as the Episcope-Tabula project [21] and gathering data from the HAPPEN project partners.  
The application in this study is totally correct, because the typology of the buildings SFH1, 2, 3 and MFH1, 2, 3 exactly corresponds to the one of the reference buildings that can be found in the Valencian Community due to the participation of IVE and EVha in the HAPPEN project. For further details of the thermal and geometrical characteristics of these buildings, Appendix B can be consulted.  
Figure 1: Full set of Packages of Optimal Solutions.