# Energy Renovation of Residential Buildings in Hot and
## 2 Methodology
### Estimation of the Best Energy Renovation Solutions
#### 2.6.1 Estimation of the Energy Parameters to Achieve NZEB  
The heating and cooling energy demands for element \(y\) of the building per unit of exchange surface per year, \(ED_{heat,y}\) and \(ED_{cool,y}\), respectively, in kWh/m\({}^{2}\)-year, are calculated using the following equations:  
\[ED_{heat,y}=0.024\cdot HDD\cdot U_{y} \tag{19}\]  
\[ED_{cool,y}=0.024\cdot CDD\cdot U_{y} \tag{20}\]  
where \(y\) denotes the walls, roof, FFF, and openings that make up the thermal envelope of the building; and \(U_{y}\) is the thermal transmittance of element \(y\) of the thermal envelope of the building, in W/m\({}^{2}\)-K.  
Equations (19) and (20) were adapted from [17].  
The heating and cooling energy demands of the building per unit of living area per year, \(ED_{heat}\) and \(ED_{cool}\), respectively, in kWh/m\({}^{2}\)-year, are calculated using the following equations:  
\[ED_{heat}=\sum_{y}ED_{heat,y}\cdot\frac{A_{exch,y}}{A_{liv}} \tag{21}\]  
\[ED_{cool}=\sum_{y}ED_{cool,y}\cdot\frac{A_{exch,y}}{A_{liv}} \tag{22}\]  
where \(A_{exch,y}\) is the exchange surface of element \(y\) of the thermal envelope of the building, in m\({}^{2}\), and \(A_{liv}\), which is the living area of the building.  
Equations (21) and (22) were adapted from [12].  
The final energy consumptions for heating, cooling, and DHW of the building per unit of living area per year, \(FEC_{heat}\), \(FEC_{cool}\) and \(FEC_{DHW}\), respectively, in kWh/m\({}^{2}\)-year, are calculated using the following equations:  
\[FEC_{heat}=\frac{ED_{heat}}{\eta} \tag{23}\]\[FEC_{cool}=\frac{ED_{cool}}{\varepsilon} \tag{24}\]  
\[FEC_{DHW}=\frac{ED_{DHW}\cdot(1-f)}{\eta} \tag{25}\]  
where \(ED_{DHW}\) is the DHW energy demand of the building per unit of living area per year, in kWh/m\({}^{2}\cdot\)year, and \(f\) is the annual solar contribution to meet the DHW requirement, per unit. For the existing building, \(ED_{DHW}\) is the average DHW energy demand per year for existing multi-family buildings built before 2008 (in the selected cities with the same climate zone and January climate zone) obtained from IDAE [52], and \(f\) is zero. For the corresponding renovated building, \(ED_{DHW}\) is the average energy demand of DHW per unit of living area per year according to the CTE-DB-HE [33], as calculated in [35], and \(f\) is the solar contribution for DHW considered for the studied building to meet the CTE-DB-HE [33], as reported in Table 5.  
The resulting final energy consumption of the building per unit of living area per year, \(FEC_{total}\), in kWh/m\({}^{2}\cdot\)year, is  
\[FEC_{total}=FEC_{heat}+FEC_{cool}+FEC_{DHW} \tag{26}\]  
The non-renewable primary energy consumption of the building per unit of living area per year, \(NRPEC_{total}\), in kWh/m\({}^{2}\cdot\)year, is calculated using the following equation:  
\[NRPEC_{total}=FEC_{heat}f^{fuel}_{NRPE}+FEC_{cool}f^{flec}_{NRPE}+FEC_{DHW}f^{ fuel}_{NRPE} \tag{27}\]  
where \(f^{fuel}_{NRPE}\) is the conversion factor from the final energy to the non-renewable primary energy for the fuel used, in kWhNRPE/kWhFE; and \(f^{flec}_{NRPE}\) is the conversion factor from the final energy to the non-renewable primary energy for electricity, in kWhNRPE/kWhFE. The aforementioned conversion factors were obtained from IDAE [53] (Table 8) and are the same as those used by HULC [42].  
Equations (23)-(27) were used in [35].