# NZEB Renovation Definition in a Heating Dominated Climate: Case Study of Poland
## 4 Cost-Optimal Heat Transfer Coefficients of Renovated Building Envelope  
Table 11 shows the calculation results of the discounted cumulative cost for different variants of external wall renovation. The U-value of un-insulated walls was 0.82 W/(m\({}^{2}\) K) for the two-storey building with a flat roof. Depending on the heating energy cost per 1 GJ the cost-optimum U-value (the renovation variant characterised with lowest discounted, cumulative cost), is from 0.20-0.12 W/(m\({}^{2}\) K) (Table 11, highlighted), depending on the heating energy cost in EUR/GJ: 4.8, 7.1, 9.5, 11.9, and 14.3. In the case of the lowest energy price the cumulative cost is the lowest for the existing uninsulated wall. This means that renovation is not economically viable in this case. In other terms, there is no economic motivation to renovate a house in the case of having a cheap energy carrier. Figure 2 shows the change of discounted cumulative cost depending on the energy cost and U-values for a renovated external wall. The cost optimum U-value is characterized with the lowest discounted, cumulative cost. Increasing trends at the ends of the chart show that either renovation cost or energy loss cost is starting to dominate in the cumulative cost. The results confirm that the cost optimum U-value depends strongly on the energy cost. In the case of cheap energy carriers, like fire wood or low quality coal, wall renovation is not cost-effective. The situation will change with the change of energy price or carrier, resulting from heat source replacement. For example cost of energy from wooden pellets is twice as high as that from fire wood. \begin{table}
\begin{tabular}{c c c} \hline \hline \multirow{2}{*}{**Element**} & \multirow{2}{*}{**Quantity**} & \multirow{2}{*}{**Unit**} & \multicolumn{2}{c}{**U**} \\ \cline{3-3}  & & & **W/m\({}^{2}\) K** \\ \hline External wall & 162.5 & m\({}^{2}\) & 1.03 \\ Suspended floor & 84.0 & m\({}^{2}\) & 0.73 \\ Pitched roof & 96.7 & m\({}^{2}\) & 0.72 \\ Windows & 31.2 & m\({}^{2}\) & 2.60 \\ External door & 1 & pcs. & 2.60 \\ \hline \hline \end{tabular}
\end{table} 
Table 10: The heat transfer coefficients and surfaces of external elements of the one-storey building with an attic. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline \multicolumn{1}{c}{\multirow{2}{*}{**U-Value, Insulation Cost and Energy Loss Per M\({}^{2}\) for**}} & \multicolumn{6}{c}{**Heating Energy Cost in EUR Per 1 GJ**} \\ \cline{3-10}  & \multicolumn{2}{c}{**External Wall Depending on Insulation Thickness**} & \multicolumn{2}{c}{**4.7**} & \multicolumn{2}{c}{**7.1**} & \multicolumn{2}{c}{**9.5**} & \multicolumn{2}{c}{**11.9**} & \multicolumn{2}{c}{**14.3**} \\ \hline
**d** & **U-Value** & **K** & **K\({}_{\text{VAT}}\)** & **Energy Loss** & \multicolumn{2}{c}{**Discounted, Cumulative Cost in EUR per m\({}^{2}\)**} \\ \hline
**cm** & **W/(m\({}^{2}\) K)** & **EUR/m\({}^{2}\)** & **EUR/m\({}^{2}\)** & **GJ/(m\({}^{2}\)year)** & **K\({}_{\text{Rad},  
The cost-optimal U-value for the all renovated building elements is shown in Table 12. It shows the results of calculation made for other elements of the two building models. For each building element the thickness of the additional insulation d and the cost of renovation are given. The optimal thermal transmittance strongly depends on the energy price. The Table 12 shows the values for the lowest and the highest energy price per GJ. The minimum and maximum U-values were used for defining the renovation variants used in the second stage of the analysis:  
* First variant (W1)--the building envelope was renovated according to the cost-optimum thermal transmittance specified for energy price of 4.7 EUR per GJ; and
* Second variant (W2)--the building envelope was renovated according to the cost-optimum thermal transmittance specified for energy price of 14.3 EUR per GJ. The energy price has a strong influence on the cost-optimal U-values of renovated elements.