# NZEB Renovation Definition in a Heating Dominated Climate: Case Study of Poland
## 2 Calculation Methodology
### Stage I--Cost-Optimal U-Values for Renovated Elements of the Building Envelope
\begin{table}
\begin{tabular}{c c} \hline \hline
**City** & **HDD, Kd** \\ \hline OPOLE & 3488 \\ GORZOW WIEL & 3548 \\ GDANSK & 3597 \\ POZNAN & 3672 \\ WARSZAWA & 3686 \\ LODZ & 3696 \\ TORUN & 3697 \\ WROCLAW & 3716 \\ ZIELONA GORA & 3724 \\ KATOWICE & 3743 \\ KRAKOW & 3748 \\ LUBLIN & 3825 \\ KIELCE & 3835 \\ SZCZECIN & 3879 \\ RZESZOW & 3936 \\ BYDGOSZCZ & 3941 \\ BIAKYSTOK & 4095 \\ OLSZTYN & 4117 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of heating degree days (HDD) for main Polish cities. The difference between the prices was very high, for example energy from fire wood is seven times cheaper than from electricity. In reality, direct electrical energy is very seldom used for heating purposes. That is why the further analysis was carried out for the following energy prices: 4.7, 7.1, 9.5, 11.9, 14.3 EUR per 1 GJ in the case of optimization of heat transfer coefficients. They do not correspond to specified energy carriers and differ by a fixed value 2.4 EUR per GJ. Such solution was chosen to make the study more useful. In many cases in Poland people use different energy source combinations at once, e.g., coal + fire wood, gas + coal, gas + fire wood. In such cases the price of energy can be different from the one given in the Table 4. Additionally, the renovation process can also include changes depending on the heat source, e.g., from coal to gas with different energy prices. Due to the fact that people in Poland very often use two or more energy carriers and prefer to buy cheap, low-quality coal. As a result, the low energy price not always means biomass. Because the aim of this paper is to propose a general NZEB renovation definition, fixed energy prices were chosen and not the energy carriers. For the second stage of optimization (cost-optimal renovation standard) only three prices 4.7, 9.5, and 14.3 EUR per 1 GJ were used. The lowest energy price does not represent biomass. In many cases people in Poland buy cheap, low-quality coal, or even burn garbage. As a result the price of energy can be very low and emission of pollutants very high. In order to show how used energy prices correlate with certain new energy sources additional Table 5 was prepared. The discount factor was calculated with the use of the following equation:  
\[R_{d}(i)=\sum_{i=1}^{n}\frac{\left(1+s\right)^{i}\cdot\left(1+e\right)^{i}}{ \left(1+d\right)^{i}} \tag{4}\]  
where:  
* \(R_{d}\)_(i)_ -- sum of discount factors for the year i,
* \(d\)--discount rate;
* \(s\)--annual inflation rate;
* \(e\)--energy price increase rate over the inflation rate in the analysed period; and
* \(n\)--number of years (lifetime of 30 years is considered). \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \multirow{2}{*}{**Energy Carrier**} & \multicolumn{2}{c}{**Price with Tax**} & \multicolumn{4}{c}{**Calorific Value**} & \multicolumn{2}{c}{**Price with Tax**} \\ \cline{2-7}  & **Value** & **Unit** & **in MJ** & **Unit** & **in kWh** & **Unit** & **EUR per GJ** & **EUR per KWh** \\ \hline Electrical energy & \multirow{2}{*}{0.13} & EUR/kWh & - & - & - & - & 36.38 & 0.130 \\ (tariff G-11) & & & & & & & \\ Firewood & 35.71 & EUR/m3 & 7200 & MJ/mp & 2000 & kWh/m3 & 4.96 & 0.019 \\ Wooden pellet & 0.20 & EUR/kg & 19.0 & MJ/kg & 5.28 & kWh/kg & 10.78 & 0.038 \\ Hard coal & 0.18 & EUR/kg & 29.0 & MJ/kg & 8.06 & kWh/kg & 6.32 & 0.024 \\ Eco-pea coal & 0.21 & EUR/kg & 27.5 & MJ/kg & 7.64 & kWh/kg & 7.79 & 0.029 \\ Heating oil & 0.58 & EUR/L & 39.0 & MJ/L & 10.83 & kWh/L & 14.77 & 0.052 \\ Natural gas & \multirow{2}{*}{0.38} & EUR/m3 & 39.5 & MJ/m3 & 10.97 & kWh/m3 & 9.65 & 0.036 \\ LPG (liquid gas) & 0.38 & EUR/L & 24.0 & MJ/L & 6.67 & kWh/L & 18.39 & 0.057 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The energy price with the tax (23%) pre GJ and kWh for chosen energy carriers [40; 41; 42; 43].