Energy Renovation of Residential Buildings in Cold Mediterranean Zones Using Optimized Thermal Envelope Insulation Thicknesses: The Case of Spain

The residential sector of the European Union consumes 27% of the final energy of the European Union, and approximately two-thirds of the existing dwellings in the European Union were built before 1980. For this reason, the European Union aims to transform the existing residential building stock into nearly zero-energy buildings by 2050 through energy renovation. The most effective method to achieve this goal is to increase the thermal insulation of opaque elements of the thermal envelope. This study aims to assess the energy, environmental and economic impacts of the energy renovation of the thermal envelopes that are typical of the existing multi-family buildings of the 26 provincial capitals in the cold climate zones of Spain. To achieve this goal, the insulation thickness to be added to the walls, roof and first floor framework is optimized by a life cycle cost analysis, and the existing building openings are replaced, thus minimizing both the total heating costs and the total heating and cooling costs. The study uses four thermal insulation materials for four different heating and cooling systems in 10 different models. The results obtained will be used to propose energy renovation solutions to achieve nearly zero-energy buildings both in Spain and in similar Mediterranean climate zones.


Introduction
The final energy consumption in the European Union reached 288 Mtoe in the residential sector and 154 Mtoe in the service sector in 2017, with 42% of the final energy consumption coming from the building sector [1]. Energy consumption from space heating accounted for 67% of the residential energy consumption [2]. In addition to the elevated energy consumption of the residential sector (27% of the total), the residential building stock is aged, with 68% of existing dwellings built before 1980 [3]. In light of this problem, the European Union, through the Energy Performance of Buildings Directive (EPBD) 2018 [4], intends to achieve a decarbonised and highly energy-efficient housing stock by 2050 and to ensure a long-term renovation that transforms the existing buildings into nearly zero-energy buildings. For that purpose, Member States are required to establish a strategy of renovating residential, non-residential, public and private buildings with short-term (2030), medium-term (2040) and long-term (2050) goals. EPBD 2018 [4] amends both EPBD 2010 [5] and the Energy Efficiency Directive 2012 [6].
EPBD 2010 [5] was added to the building regulations on the energy savings of the different Member States. The energy and environmental impact of the implementation of EPBD 2010 [5] on the residential sector of European countries with Mediterranean climates was analysed in Spain [7], Italy [8], Greece [9], Cyprus [10] and Portugal [11]. These regulations have restricted both heating and cooling energy demands and have established maximum thermal transmittances for the elements that make up the thermal envelope of a building, depending on the climate zone in which the building is located. The most effective method for the energy refurbishment of the residential building stock is to increase the thermal insulation of the opaque elements of the thermal envelope; this increased insulation achieved average energy savings of 45% in Italy [12] and 40% in Spain [13]. In addition, Varela Luján et al. [14] found that, in Spain, renovating façades using external thermal insulation composites reduced energy losses by 57% and energy gains by 39% compared to those with the façade in its original state. However, it is neither practical nor economical to increase the insulation thickness until both the heat losses for heating and heat gains for cooling are eliminated through the thermal envelope. It is, therefore, necessary to find a balance between the cost of the insulation used and the potential heating and cooling savings in the building [15]. The optimum insulation thickness of the thermal envelope of a building can be determined by a life cycle cost analysis to achieve maximum net savings in terms of heating and cooling costs, taking into account the heating and cooling degree-days; the costs and properties of both the insulation materials and fuels used; the main characteristics of the heating and cooling systems; the electricity costs; and the economic parameters, such as the interest rate, inflation rate and lifetime [16].
The optimum insulation thickness for different elements of the thermal envelope of buildings has been evaluated in several studies conducted in Turkey. Sisman et al. [17] determined the optimum insulation thickness for external walls and roof for different degree-day regions. Bektas Ekici et al. [18] studied the optimum insulation thickness for various types of external walls with respect to different materials, fuels and climate zones. Kurekci [16] determined the optimum insulation thickness for building walls by using the heating and cooling degree-day values of all provincial centres. Ozel studied the effect of the exterior surface solar absorptivity on the thermal characteristics and optimum insulation thickness [19]; conducted a cost analysis for the optimum thicknesses and assessed the environmental impact of different insulation materials [20]; carried out a thermal, economic and environmental analysis of insulated building walls in cold climates [21]; and studied the effect of the glazing area on the optimum insulation thickness for different wall orientations [22]. Sagbansua and Balo [23] studied the potential use of eco-efficient materials in buildings instead of conventional materials using the optimum insulation thickness method, considering both the ecological impact and the financial feasibility. In addition, in the Mediterranean environment, Annibaldi et al. [24] studied the environmental and economic benefits of the optimum insulation thickness using a life cycle cost analysis of historic buildings in Italy, and Derradji et al. [25] determined the energy savings due to glazing effects on the optimum insulation thickness in a classic home in Algeria. Outside the Mediterranean environment, Yuan et al. [26] calculated the optimum insulation thickness for different insulation materials and fuels for six different climate zones in Japan, and Nematchoua et al. [27] studied the most economical and optimum thermal insulation thickness for buildings in wet and hot tropical climates in Cameroon.
This study aims to assess the energy, environmental and economic impacts of the energy renovation of the thermal envelope of existing residential buildings in the cold climate zones of Spain and to assess the optimum insulation thickness to be added to the walls, roof and first floor framework by a life cycle cost analysis and the replacement of the existing building openings. The optimization of the insulation thickness is performed to minimize both the total heating costs and the total heating and cooling costs using thermal insulation materials including expanded polystyrene (EPS), wool mineral (MW), polyurethane (PUR) and extruded polystyrene (XPS) for different heating and cooling systems with heating oil boilers, natural gas boilers, biomass boilers and electric heat pumps. The residential building studied is the multi-family housing block that was used in [7,28,29] to assess the energy and environmental impacts of the EPBD in Spain. The existing thermal envelope of the building has the main features of the thermal envelopes of the existing residential stock in the studied areas [30]. The methodology developed includes the evaluation of the main energy and environmental parameters of the renovated buildings to be able to compare the obtained solutions with other different energy renovation solutions. In addition, it is expected that the results of this study will help propose energy renovation solutions for existing residential buildings in order to achieve nearly zero-energy buildings according to the current regulation, namely, the Basic Document on Energy Saving of the Technical Building Code (CTE-DB-HE) [31].

Methodology
The methodology developed in this study is as follows: (i) identification of the main cities located in cold climate zones and the main characteristics of these climate zones; (ii) definition of the studied building with a thermal envelope that represents the main characteristics of the existing residential building stock; (iii) evaluation of the optimal thickness of the thermal insulation for the walls, roof and first floor framework to minimize the total heating costs and the total heating and cooling costs with different thermal insulation materials and heating and cooling systems; and (iv) evaluation of the main energy and environmental parameters of the renovated building and verifying whether it is a nearly zero-energy building in accordance with the current CTE-DB-HE [31].

Climate Zones
The studied buildings will be located in all the Spanish provincial capitals in climate zones D1, D2, D3 and E1, which are the Spanish cold climate zones [28,31]. This study uses heating degree-days with a base temperature of 20 • C and cooling degree-days with a base temperature of 20 • C, which correspond to the reference weather for these climate zones as provided by the Ministry of Industry, Energy and Tourism and the Institute for Diversification and Saving of Energy (IDAE) [32]. The heating degree-days and cooling degree-days are used in the energy simulations of buildings using HULC [33], which is the official software tool used to verify compliance with the energy consumption and energy demand restrictions of CTE-DB-HE [31] and to certify the energy performance of buildings. To proceed with the energy renovation of the buildings, it is important to understand the climate zones in which the design of the thermal envelopes of the buildings was based. According to the Basic Document Norm on Thermal Conditions in Buildings [34], the selected Spanish provincial capitals are in January climate zones W, X, Y and Z, with minimum mean temperatures during January of 5 • C, 3 • C, 0 • C and −2 • C, respectively. Figure 1 shows both the climate zones and January climate zones of the selected provincial capitals of Spain. Table 1 shows the climate zones and their corresponding heating degree-days and cooling degree-days, as well as the January climate zones, of the provincial capitals studied. Table 1. Climate zones (CZs) and their corresponding heating degree-days (HDD) and cooling degree-days (CDD), and January climate zones (JCZs) of the cities studied.

Main Characteristics of the Studied Building
The studied building [7,28,29] has a ground floor and 5 levels. The base is square with an area of 484.00 m 2 , and the height of each floor is 3.00 m. The main façade has a northerly orientation. Figure  2 shows the floor plan and a 3D view of the studied building. On the ground floor are the main entrance and a car parking space. Each of the 5 floors has 4 types of dwellings, with a total living area of 2216.57 m 2 . The window-to-wall ratio is 0.1612. Table 2 shows the spaces that compose each type of dwelling. The roof is hipped and has a height of 2.00 m.

Main Characteristics of the Studied Building
The studied building [7,28,29] has a ground floor and 5 levels. The base is square with an area of 484.00 m 2 , and the height of each floor is 3.00 m. The main façade has a northerly orientation. Figure 2 shows the floor plan and a 3D view of the studied building. On the ground floor are the main entrance and a car parking space. Each of the 5 floors has 4 types of dwellings, with a total living area of 2216.57 m 2 . The window-to-wall ratio is 0.1612. Table 2 shows the spaces that compose each type of dwelling. The roof is hipped and has a height of 2.00 m. Sustainability 2020, 12, x 5 of 32  The thermal envelope for the existing building of each January climate zone is equal to the maximum thermal transmittances allowed by the Basic Document Norm on Thermal Conditions in Buildings [34] (in effect from 1981 to 2007). Moreover, these maximum thermal transmittances are  The thermal envelope for the existing building of each January climate zone is equal to the maximum thermal transmittances allowed by the Basic Document Norm on Thermal Conditions in Buildings [34] (in effect from 1981 to 2007). Moreover, these maximum thermal transmittances are used by default for residential buildings built before 2008 by CE3X [35], which is the most frequently used official tool for the energy performance certification of existing buildings [36]. Table 3 shows the thermal transmittance according to the January climate zone for each element of the thermal envelope of the building and the corresponding exchange surfaces. The compositions of the different elements that make up the building enclosures and their main characteristics, as well as the compositions of the building openings, were reported in [30], where Cádiz and Valencia correspond to January climate zone W, Cáceres corresponds to January climate zone X, Madrid corresponds to January climate zone Y and León corresponds to January climate zone Z.

Case Studies
This study calculates the optimum insulation thickness to be added to the walls, roof and first floor framework of the thermal envelope of the studied building in order to minimize the total heating costs and total heating and cooling costs of the energy renovation. In addition, this study assesses the energy, environmental and economic impacts of this energy renovation using the thermal insulation materials EPS, MW, PUR and XPS with the following systems to meet the thermal requirements of the buildings:

•
System 1: Heating oil boilers with thermal performances of 0.85 to meet the heating and domestic hot water (DHW) requirements and electric cooling systems with thermal efficiencies of 2.00. • System 2: Natural gas boilers with thermal performances of 0.92 to meet the heating and DHW requirements and electric cooling systems with thermal efficiencies of 2.00. • System 3: Biomass boilers with thermal performances of 0.85 to meet the heating and DHW requirements and electric cooling systems with thermal efficiencies of 2.00.
• System 4: Electric heat pumps with seasonal coefficients of performance of 2.50 and seasonal energy efficiency ratios of 3.00 to meet the heating, cooling and DHW requirements.
The existing building openings are replaced by openings with a thermal transmittance of 1.92 W/m 2 ·K (double-chamber PVC frame and low-emissivity double-pane glass, with 30% of the space occupied by the framework) and a price of 282.63 €/m 2 in 2018; these data are from the construction database of the Valencia Institute of Building [37]. The thermal conductivity and price of the insulation materials used, corresponding to 2018, were also extracted from the database [37] (Table 4). Moreover, Table 5 shows the prices of the different energy carriers (fuels and electricity) used in 2018. The price of electricity depends on its annual consumption: the price of electricity 2 is used with system 4, and the price of electricity 1 is used with the remaining systems. Table 4. Thermal conductivity, in W/m·K, and price, in €/m 3 , of the insulation materials used [37].

Energy Carrier Price (€/kWh) Source
Heating oil 0.0713 [38,39] Natural gas (annual consumption between 20 and 200 GJ) 0.0770 [40] Biomass (A1 certified pellets in bulk) 0.0462 [41] Electricity 1 (annual consumption between 2500 and 5000 kWh) 0.2430 [42] Electricity 2 (annual consumption between 5000 and 15,000 kWh) 0.2042 [42] 2.4. Thermal Transmittance and Overall Thermal Transmittance The thermal transmittance of element e of the thermal envelope of the building, U e , in W/m 2 ·K, is calculated with the following equation: where e corresponds to the walls, roof and first floor framework; R e . corresponds to the thermal resistance of element e of the building envelope, in m 2 ·K/W, and is calculated using the following equation: where R si,e and R se,e are the surface thermal resistance of element e of the thermal envelope of the building for indoor air and outdoor air, respectively, in m 2 ·K/W, and R n,e is the thermal resistance, in m 2 ·K/W, of layer n of element e of the thermal envelope of the building, calculated with the following equation: where x n,e is the thickness of layer n of element e of the thermal envelope of the building, in m, and λ n,e is the thermal conductivity of the material that makes up layer n of element e of the thermal envelope of the building, in W/m·K. Equations (1)-(3) and the values used for R si,e and R se,e were obtained from [43].
Thus, the result of the overall thermal transmittance of the thermal envelope of the building, U, in W/m 2 ·K, is: where e is the walls, roof, first floor framework and openings that make up the thermal envelope of the building and A exch,e is the exchange surface of element e of the thermal envelope of the building, in m 2 , reported in Table 3.

Energy and Environmental Impacts of the Existing Building
The heating and cooling energy demands for element e of the existing building per unit of the exchange surface and year, ED exis heat,e and ED exis cool,e , respectively, in kWh/m 2 ·year, are calculated with the following equations: ED exis heat,e = 0.024·HDD·U exis e , ED exis cool,e = 0.024·CDD·U exis e , where HDD is the heating degree-days with a base temperature of 20 • C (Table 1); CDD is the cooling degree-days with a base temperature of 20 • C (Table 1); and U exis e is the thermal transmittance of element e of the existing building, in W/m 2 ·K ( Table 3).
The annual heating and cooling energy costs per unit of exchange surface of element e of the existing building, EC exis heat,e and EC exis cool,e , respectively, in €/m 2 ·year, are calculated with the following equations: EC exis cool,e = 0.024·CDD·C elec ·U exis e ε , where C f uel is the price of the fuel used, in €/kWh, reported in Table 5; C elec is the price of electricity, in €/kWh, reported in Table 5; η is the thermal performance or seasonal coefficient of performance of the heating system, expressed per-unit; and ε is the thermal efficiency or seasonal energy efficiency ratio of the cooling system, expressed per-unit. For heat pumps, C f uel = C elec . The heating and cooling energy demands of the existing building per unit of living area and year, ED exis heat and ED exis cool , respectively, in kWh/m 2 ·year, are calculated using the following equations: where A liv is the living area of the building, which is 2216.57 m 2 . The final energy consumption for heating, cooling and DHW of the existing building per unit of living area and year, FEC exis heat , FEC exis cool and FEC exis DHW , respectively, in kWh/m 2 ·year, are calculated using the following equations: where ED exis 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), in kWh/m 2 ·year, obtained from the corresponding energy demands in [44].
The resulting final energy consumption of the existing building per unit of living area and year, FEC exis total , in kWh/m 2 ·year, is: The total primary energy consumption and non-renewable primary energy consumption of the existing building per unit of living area and year, TPEC exis total and NRPEC exis total , respectively, in kWh/m 2 ·year, are calculated using the following equations: where f f uel TPE is the conversion factor from the final energy to the total primary energy for the fuel used, in kWh TPE /kWh FE ; f elec TPE is the conversion factor from the final energy to the total primary energy for electricity, in kWh TPE /kWh FE ; f f uel NRPE is the conversion factor from the final energy to the non-renewable primary energy for the fuel used, in kWh NRPE /kWh FE ; and f elec NRPE is the conversion factor from the final energy to the non-renewable primary energy for electricity, in kWh NRPE /kWh FE . The factors of conversion from the final energy to the total primary energy and the factors of conversion from the final energy to the non-renewable primary energy were obtained from IDAE [45] (Table 6). The CO 2 emissions of the existing building per unit of living area and year, EM exis total , in kg CO 2 /m 2 ·year, are calculated with the following equation: where f f uel EM is the conversion factor from the final energy to CO 2 emissions for the fuel used, in kg CO 2 /kWh FE , and f elec EM is the conversion factor from the final energy to CO 2 emissions for electricity in kg CO 2 /kWh FE . The conversion factors from the final energy to CO 2 emissions were obtained from IDAE [45] (Table 6).
The IDAE conversion factors [45] (Table 6) are the same as those used by CE3X [35] and HULC [33]. Finally, the assignment of labels for the non-renewable primary energy consumption and CO 2 emissions was made using the boundaries between classes used by CE3X [35] and HULC [33] (Table 7).

Energy, Environmental and Economic Impacts of the Renovated Building
The heating and cooling energy demands of element e of the renovated building per unit of exchange surface and year, ED reno heat,e and ED reno cool,e , respectively, in kWh/m 2 ·year, are calculated using the following equations: where U reno e is the thermal transmittance of element e of the renovated building, in W/m 2 ·K, and U reno e for openings is 1.92 W/m 2 ·K. Equation (1) and Equation (2) are used to calculate U reno e for the walls, roof and first floor framework, and thus, the thermal resistance of element e of the renovated building, R reno e , in m 2 ·K/W, is: where R exis e is the thermal resistance of element e of the existing building, in m 2 ·K/W, obtained using Equation (1) with U exis e , and R insu e is the thermal resistance of the insulation added to element e of the building, in m 2 ·K/W, obtained from Equation (3) using both the optimum insulation thickness required, in m, and the thermal conductivity of the selected insulation, in W/m·K ( Table 4).
The annual heating and cooling energy cost per unit of exchange surface of element e of the renovated building, EC reno heat,e and EC reno cool,e , respectively, in €/m 2 ·year, are calculated with the following equations: A life cycle cost analysis is used to determine the optimum insulation thickness [47], considering a 5.00 % interest rate, i, and 2.50 % inflation rate, g. Since i is higher than g, the present worth factor, PWF, is calculated with the following equation: where N is the lifetime, in years, and r is the actual interest rate, calculated with the following equation: The value of r obtained using Equation (24) is 2.44%. In addition, considering an N of 30 years and applying Equation (23), the PWF obtained is 21.10.
The optimum insulation thickness is calculated to minimize both the total heating cost and the total heating and cooling costs, since in cold climate zones, the calculation to minimize the total cooling cost is meaningless, as suggested in [48].
Accordingly, the optimum insulation thickness that minimizes the total heating cost of element e of the building, x heat opt,e , in m, is calculated with the following equation: where λ is the thermal conductivity of the insulation used, in W/m·K, reported in Table 4. The cost of the insulation that minimizes the total heating cost for element e of the building per unit of exchange surface, C heat insu,e , in €/m 2 , is calculated using the following equation: where C insu is the insulation cost, in €/m 3 , reported in Table 4. The cost of the energy renovation of element e of the building with an optimized insulation thickness that minimizes the total heating cost per unit of exchange surface, C reno heat,e , in €/m 2 , is obtained from Equation (26) for the walls, roof and first floor framework, and its value is 282.63 €/m 2 for the openings, since the current openings are replaced with new openings.
The total heating cost per unit of exchange surface of element e of the building, TC reno heat,e , in €/m 2 , is calculated using the following equation: The total net savings for element e of the renovated building with an optimized insulation thickness that minimizes the total heating cost per unit of exchange surface, ECS reno heat,e , in €/m 2 ·year, is calculated using the following equation: ECS reno heat,e = EC exis heat,e − EC reno heat,e .
The payback period for element e of the renovated building with an optimized insulation thickness that minimizes the total heating cost, PP reno heat,e , in years, is calculated using the following equation: The cost of the energy renovation of the building with an optimized insulation thickness that minimizes the total heating cost per unit of exchange surface, C reno heat , in €/m 2 , is calculated with the following equation: The total net savings for the renovated building with an optimized insulation thickness that minimizes the total heating cost per unit of exchange surface, ECS reno heat , in €/m 2 ·year, is calculated using the following equation: The payback period for the renovated building with an optimized insulation thickness that minimizes the total heating cost, PP reno heat , in years, is calculated using the following equation: Furthermore, the optimum insulation thickness that minimizes the total heating and cooling costs for element e of the building, x heat+cool opt,e , in m, is calculated with the following equation: The cost of the insulation that minimizes the total heating and cooling costs per unit of exchange surface for element e of the building, C heat+cool insu,e , in €/m 2 , is calculated using the following equation: The cost of the energy renovation of element e of the building with an optimized insulation thickness that minimizes the total heating and cooling costs per unit of exchange surface, C reno heat+cool,e , in €/m 2 , is obtained from Equation (34) for the walls, roof and first floor framework, and its value is 282.63 €/m 2 for the openings, since the current openings are replaced with new openings.
The total heating and cooling costs per unit of exchange surface for element e of the building, TC reno heat+cool,e , in €/m 2 , is calculated using the following equation: The total net savings for element e of the renovated building with an optimized insulation thickness that minimizes the total heating and cooling costs per unit of exchange surface, ECS reno heat+cool,e , in €/m 2 ·year, is calculated using the following equation:

ECS reno
heat+cool,e = EC exis heat,e + EC exis cool,e − EC reno heat,e + EC reno cool,e .
The payback period for element e of the renovated building with an optimized insulation thickness that minimizes the total heating and cooling costs, PP reno heat+cool,e , in years, is calculated using the following equation: The cost of the energy renovation of the building with an optimized insulation thickness that minimizes the total heating and cooling costs per unit of living area, C reno heat+cool , in €/m 2 , is calculated with the following equation: The total net savings for the renovated building with an optimized insulation thickness that minimizes the total heating and cooling costs per unit of living area, ECS reno heat+cool , in €/m 2 ·year, is calculated using the following equation: The payback period for the renovated building with an optimized insulation thickness that minimizes the total heating and cooling costs, PP reno heat+cool , in years, is calculated using the following equation: The heating and cooling energy demands of the renovated building per unit of living area and year, ED reno heat and ED reno cool , respectively, in kWh/m 2 ·year, are calculated using the following equations: The final energy consumption for the heating, cooling and DHW of the renovated building per unit of living area and year, FEC reno heat , FEC reno cool and FEC reno DHW , respectively, in kWh/m 2 ·year, are calculated using the following: where ED reno DHW is the average energy demand of DHW per unit of living area and year for the studied building in the cities selected with the same climate zone and January climate zone, according to the current CTE-DB-HE [31], in kWh/m 2 ·year, calculated in [28], and f is the average of the minimum solar contributions required for the studied building in cities selected with the same climate zone and January climate zone according to the current CTE-DB-HE [7,31], expressed per unit.
Thus, the final energy consumption of the renovated building per unit of living area and year, FEC reno total , in kWh/m 2 ·year, is: The total primary energy consumption and non-renewable primary energy consumption of the renovated building per unit of living area and year, TPEC reno total and NRPEC reno total , respectively, in kWh/m 2 ·year, are calculated using the following equations: The CO 2 emissions of the renovated building per unit of living area and year, EM reno total , in kg CO 2 /m 2 ·year, are calculated with the following equation: Equations (18)- (29) and Equations (33)-(37) were obtained and adapted from [16,17], and Equations (43)-(49) were used in [28,29].
The IDAE conversion factors [45] (Table 6) are the same as those used by CE3X [35] and HULC [33]. Finally, the labels for the non-renewable primary energy consumption and CO 2 emissions are assigned using the boundaries between classes used by CE3X [35] and HULC [33] (Table 7).
In addition, whether the renovated building is a nearly zero-energy building according to the current CTE-DB-HE [31] is verified. To accomplish this task, it must be demonstrated that in climate zones D1, D2 and D3, the energy demand for heating is less than or equal to 27.90 kWh/m 2 ·year, the energy demand for cooling is less than or equal to 15.00 kWh/m 2 ·year, and the non-renewable primary energy consumption is less than or equal to 61.35 kWh/m 2 ·year and that in climate zone E1, the energy demand for heating is less than or equal to 41.35 kWh/m 2 ·year, the energy demand for cooling is less than or equal to 15.00 kWh/m 2 ·year, and the non-renewable primary energy consumption is less than or equal to 71.80 kWh/m 2 ·year [28]. Tables 8-11 show the optimized insulation thicknesses to be added to the walls, roof and first floor framework in order to minimize the total heating costs and total heating and cooling costs, as well as the corresponding energy renovation costs, total net savings and payback period, for each of the climate zones by the January climate zone, the system used and the insulation material. The overall thermal transmittance, the heating and cooling energy demands, the final energy consumption, the total primary energy consumption, the non-renewable primary energy consumption, the CO 2 emissions, the non-renewable primary energy consumption rating and the CO 2 emissions rating for each climate zone by the January climate zone, the system used and the insulation material are shown in Table 12 for the existing buildings (no additional insulation material required) and in Tables 13-16 for the renovated buildings. In addition, the total net savings from the reduction in non-renewable primary energy consumption are presented for each of the systems used by the climate zone, January climate zone and insulation material and with an optimization of the insulation thickness to minimize the total heating costs ( Figure 3) and the total heating and cooling costs ( Figure 4). The total net savings due to the CO 2 emissions reduction for each system used by the climate zone, January climate zone and insulation material with the optimization of the insulation thickness to minimize the total heating costs ( Figure 5) and the total heating and cooling costs ( Figure 6) are also presented. Table 8. Optimized insulation thicknesses to be added to the walls, roof and first floor framework (FFF), in m; energy renovation cost per unit of living area (C), in €/m 2 ; total net savings per unit of living area (ECS), in €/m 2 ·year; and payback period (PP), in years, for climate zone D1 by January climate zone, system used, insulation material and optimization criterion.   Table 9. Optimized insulation thicknesses to be added to the walls, roof and first floor framework (FFF), in m; energy renovation cost per unit of living area (C), in €/m 2 ; total net savings per unit of living area (ECS), in €/m 2 ·year; and payback period (PP), in years, for climate zone D2 by January climate zone, system used, insulation material and optimization criterion.         Table 14. Overall thermal transmittance (U), in W/m 2 ·K; heating energy demand (HED), in kWh/m 2 ·year; cooling energy demand (CED), in kWh/m 2 ·year; final energy consumption (FEC), in kWh/m 2 ·year; total primary energy consumption (TPEC), in kWh/m 2 ·year; non-renewable primary energy consumption (NRPEC), in kWh/m 2 ·year; CO 2 emissions (EM), in kg CO 2 /m 2 ·year; non-renewable primary energy consumption rating (R NRPEC ); and CO 2 emissions rating (R EM ) for climate zone D2 by January climate zone, system used, insulation type and optimization criterion for renovated buildings.  Table 15. Overall thermal transmittance (U), in W/m 2 ·K; heating energy demand (HED), in kWh/m 2 ·year; cooling energy demand (CED), in kWh/m 2 ·year; final energy consumption (FEC), in kWh/m 2 ·year; total primary energy consumption (TPEC), in kWh/m 2 ·year; non-renewable primary energy consumption (NRPEC), in kWh/m 2 ·year; CO 2 emissions (EM), in kg CO 2 /m 2 ·year; non-renewable primary energy consumption rating (R NRPEC ); and CO 2 emissions rating (R EM ) for climate zone D3 by January climate zone, system used, insulation type and optimization criterion for renovated buildings.   Figure 3. Total net savings, in €/m 2 ·year, versus non-renewable primary energy consumption reduction, in kWh/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating costs. . Total net savings, in €/m 2 ·year, versus non-renewable primary energy consumption reduction, in kWh/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating and cooling costs.    . Total net savings, in €/m 2 ·year, versus non-renewable primary energy consumption reduction, in kWh/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating and cooling costs. Figure 5. Total net savings, in €/m 2 ·year, versus CO2 emissions reduction, in kg CO2/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating costs. Figure 6. Total net savings, in €/m 2 ·year, versus CO2 emissions reduction, in kg CO2/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating and cooling costs.

Results and Discussion
The average reductions in the overall thermal transmittances of the renovated buildings compared to those of the existing buildings are 80.67% in January climate zone W, 77.47% in January climate zone X, 71.26% in January climate zone Y and 70.67% in January climate zone Z (Tables 12-16). These reductions are achieved by replacing the current openings with new openings in addition to adding, on average, 104 mm of insulation to the walls, roofs and first floor frameworks of the renovated buildings in January climate zone W, 99 mm to those in January climate zone X and 94 mm to those in January climate zones Y and Z (Tables 8-11).
In each of the climate zones and January climate zones, for each system and insulation material, the cost of the energy renovation for the cases in which the insulation thickness is optimized to Figure 5. Total net savings, in €/m 2 ·year, versus CO 2 emissions reduction, in kg CO 2 /m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating costs.
Sustainability 2020, 12, x 26 of 32 Figure 5. Total net savings, in €/m 2 ·year, versus CO2 emissions reduction, in kg CO2/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating costs. Figure 6. Total net savings, in €/m 2 ·year, versus CO2 emissions reduction, in kg CO2/m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating and cooling costs.
The average reductions in the overall thermal transmittances of the renovated buildings compared to those of the existing buildings are 80.67% in January climate zone W, 77.47% in January climate zone X, 71.26% in January climate zone Y and 70.67% in January climate zone Z (Tables 12-16). These reductions are achieved by replacing the current openings with new openings in addition to adding, on average, 104 mm of insulation to the walls, roofs and first floor frameworks of the renovated buildings in January climate zone W, 99 mm to those in January climate zone X and 94 mm to those in January climate zones Y and Z (Tables 8-11).
In each of the climate zones and January climate zones, for each system and insulation material, the cost of the energy renovation for the cases in which the insulation thickness is optimized to Figure 6. Total net savings, in €/m 2 ·year, versus CO 2 emissions reduction, in kg CO 2 /m 2 ·year, for each system used by insulation material and building climate zone (climate zone and January climate zone), with the insulation thickness optimized to minimize the total heating and cooling costs.
The average reductions in the overall thermal transmittances of the renovated buildings compared to those of the existing buildings are 80.67% in January climate zone W, 77.47% in January climate zone X, 71.26% in January climate zone Y and 70.67% in January climate zone Z (Tables 12-16). These reductions are achieved by replacing the current openings with new openings in addition to adding, on average, 104 mm of insulation to the walls, roofs and first floor frameworks of the renovated buildings in January climate zone W, 99 mm to those in January climate zone X and 94 mm to those in January climate zones Y and Z (Tables 8-11).
In each of the climate zones and January climate zones, for each system and insulation material, the cost of the energy renovation for the cases in which the insulation thickness is optimized to minimize the total heating costs is less than that of the corresponding cases in which the insulation thickness is optimized to minimize the total heating and cooling costs. The order of the insulation materials from the lowest to the highest cost of energy renovation for each system used is MW, PUR, EPS and XPS; the order of the systems from the lowest to the highest cost of energy renovation for each insulation material used is system 3, system 4, system 2 and system 1. Of all the systems, the system with the lowest cost of energy renovation corresponds to the case in which MW is used as the insulation and the insulation thickness is optimized to minimize the total heating costs. Furthermore, within the same climate zone, the order of the January climate zones from the lowest to the highest cost of energy renovation is Z, Y, X and W; however, within the same January climate zone, the order of the climate zones from the lowest to the highest cost of energy renovation is D3, D2, D1 and E1 with the optimization of the insulation thickness to minimize the total heating costs, and D1, D2, D3 and E1 with the optimization of the insulation thickness to minimize the total heating and cooling costs (Tables 8-11).
In each of the climate zones and January climate zones, for each system and insulation material, the total net savings for the cases in which the insulation thickness is optimized to minimize the total heating and cooling costs is greater than that of the corresponding cases in which the insulation thickness is optimized to the minimize the total heating costs. The order of the insulation materials from the highest to the lowest total net savings for each system used is MW, PUR, EPS and XPS; the order of the systems from the highest to the lowest total net savings for each of the insulation materials used is system 1, system 2, system 4 and system 3. Of all the systems, the system with the highest total net savings corresponds to the case in which MW is used as the insulation and the insulation thickness is optimized to minimize the total heating and cooling costs. Furthermore, within the same climate zone, the order of the January climate zones from the highest to the lowest total net savings is W, X, Y and Z. However, within the same January climate zone, the order of the climate zones from the highest to the lowest total net savings is E1, D1, D2 and D3 when the insulation thickness is optimized to minimize the total heating costs and is E1, D3, D2 and D1 when the insulation thickness is optimized to minimize the total heating and cooling costs (Tables 8-11).
In each of the climate zones and January climate zones, for each system and insulation material, the payback period for the cases in which the insulation thickness is optimized to minimize the total heating and cooling costs is shorter than that of the corresponding cases in which the insulation thickness is optimized to minimize the total heating costs. The order of the insulation materials from the shortest to the longest payback period for each system used is MW, PUR, EPS and XPS; the order of the systems from the shortest to the longest payback period for each insulation material used is system 1, system 2, system 4 and system 3. Of all the systems, the system with the shortest payback period corresponds to the case with MW as the insulation and the insulation thickness optimized to minimize the total heating and cooling costs. Furthermore, within the same climate zone, the order of the January climate zones from the shortest to the longest payback period is W, X, Y and Z; however, within the same January climate zone, the order of the climate zones from the shortest to the longest payback period is E1, D1, D2 and D3 with the optimization of the insulation thickness to minimize the total heating costs and E1, D3, D2 and D1 with the optimization of the insulation thickness to minimize the total heating and cooling costs (Tables 8-11).
The highest total net savings is accompanied by both the greatest reduction in non-renewable primary energy consumption and the greatest reduction in CO 2 emissions in the renovated buildings that use systems 1 and 2 in climate zone D1 and January climate zone W. The greatest total net savings occurs in the renovated buildings that use system 3 in climate zone D1 and January climate zone W, while both the greatest reduction in the non-renewable primary energy consumption and the greatest reduction in the CO 2 emissions occur in those located in climate zone D3 and January climate zone X. Finally, in the renovated buildings that use system 4, the highest total net savings occurs in those located in climate zone D1 and January climate zone X, the greatest reduction in the non-renewable primary energy consumption occurs in those located in climate zone D1 and January climate zone X, and the greatest reduction in CO 2 emissions occurs in those located in climate zone D1 and January climate zone W (Tables 12-16 and Figures 3-6).
Notably, considering the energy demand for heating, the energy demand for cooling and the non-renewable primary energy consumption (Tables 13-16), the renovated buildings that become nearly zero-energy buildings according to the current CTE-DB-HE [31] are as follows: • Those located in climate zone D1 that use system 1 or 2 and MW insulation and in which the insulation thickness is optimized to minimize the total heating and cooling costs.

•
Those located in climate zone D2 that use system 1, 2 or 4 and MW insulation.

•
Those located in climate zone D3 that use MW insulation and in which the insulation thickness is optimized to minimize the total heating and cooling costs; those that use system 1, 2 or 4 and PUR insulation and in which the insulation thickness is optimized to minimize the total heating and cooling costs, or that use MW insulation and in which the insulation thickness is optimized to minimize the total heating costs; those that use system 1 or 2 and EPS insulation and in which the insulation thickness is optimized to minimize the total heating and cooling costs, or that use XPS insulation and in which the insulation thickness is optimized to minimize the total heating and cooling costs; and those that use system 1 and PUR insulation and in which the insulation thickness is optimized to minimize the total heating costs.

•
Those located in climate zone E1.
In future studies, the methodology developed will be used to evaluate the optimum thermal envelope insulation thicknesses in other cold Mediterranean climate zones and will be improved to (i) customize the optimal energy renovation solution for each city selected; (ii) evaluate the optimized thermal envelope insulation thicknesses to obtain the maximum possible energy performance rating; and (iii) adapt the thermal envelope insulation thickness to hot and temperate Mediterranean climate zones where air conditioning is of great importance.

Conclusions
This study assessed the energy, environmental and economic impacts of the energy renovation of the thermal envelope of the existing residential buildings in the 26 provincial capitals in the cold climate zones of Spain. The insulation thickness to be added to the walls, roof and first floor framework was optimized by a life cycle cost analysis, and the replacement of the building openings was assessed. The optimization of the insulation thickness was carried out to minimize both the total heating costs and the total heating and cooling costs using four insulation materials for four different heating and cooling systems.
On average, the overall thermal transmittance in the renovated buildings was reduced by between 70.67% and 80.67% compared to that of the existing buildings. These reductions were achieved by adding, on average, between 94 mm and 104 mm of insulation to the walls, roofs and first floor frameworks of the renovated buildings, in addition to replacing the building openings with new openings.
In each of the climate zones and January climate zones, although the case with the lowest energy renovation cost was that in which system 3 and MW insulation were used and the insulation thickness was optimized to minimize the total heating costs, the case with the highest total net savings and the shortest payback period was that in which system 1 and MW insulation were used and the insulation thickness was optimized to minimize the total heating and cooling costs.
The greatest reductions in non-renewable primary energy consumption occurred in the renovated buildings that used system 1 or 2 in climate zone D1 and January climate zone W, in those that used system 3 in climate zone D3 and January climate zone X, and in those that used system 4 in climate zone D1 and January climate zone X. Additionally, the greatest reductions in CO 2 emissions occurred in the renovated buildings that used system 1, 2 or 4 in climate zone D1 and January climate zone W and in those that used system 3 in climate zone D3 and January climate zone X.
The results obtained in this study will serve as a starting point for proposals of energy renovation solutions for existing residential buildings in order to achieve nearly zero-energy buildings in the cold climate zones of Spain; however, in the future, it would be interesting to evaluate the possibilities for customizing the method developed for each selected city, as well as the optimized thermal envelope insulation thicknesses to obtain the highest energy performance rating possible. Finally, the methodology developed in this study, in addition to being used in other cold Mediterranean climate zones, could be adapted to hot and temperate Mediterranean climate zones where air conditioning is of great importance.