Bottom-up Lumped-parameters Thermodynamic Modelling of the Italian Residential Building Stock: Assessment of High-resolution Heat Demand Profiles

The methodological approach adopted for the bottom-up representation of the building stock is summarized in Figure 1. Archetypes are differentiated based on a) geometry, b) construction period, and c) climate-dependent construction materials (Figure 1).

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Figure 1. Tree structure of archetype combinations

Four building geometries are defined to represent the variety of the Italian building stock, in accordance with ISTAT data [13], namely: single-family, double-family, multifamily and apartment block. In relationship with the evolution of the national legislation, also four construction periods (influencing materials and heat transfer coefficients) can be identified: before 1975; from 1976 to 1990; from 1991 to 2005; from 2006 to 2020. To these, a fifth construction period is added to characterise nZEBs, considering that, as prescribed by the Italian Law 90/2013, all private buildings to be constructed after December 31^st 2020 will need to fall in such category. Finally, six climate-dependent groups of construction materials are considered, one for each Italian climatic area. This is made to account for the fact that, for instance, buildings of an identical type and period can be more or less insulated depending on the typical climate of their region. The combination of such options provides a total figure of 120 different building archetypes.

Sub-section 2.1 details how each building archetype is characterized by means of an independent thermodynamic lumped-parameters model. The thermophysical parameters required to populate each modelled archetype are derived from ISO standards and existing national or European projects, and they are discussed in sub-section 2.2. Sub-section 2.3 presents the methods adopted to characterise the nZEB archetypes based those constructed for the existing building stock. Sub-section 2.4 details how the large-scale aggregation of heating and cooling loads related to each building archetype is performed. Finally, sub-section 2.5 presents the defined nZEB penetration scenarios.

2.1 Lumped-parameters building modelling approach

Vivian et al. [14] discuss the suitability of various degrees of complexity of lumped-parameters (RC, resistance-capacitance) thermodynamic building models in reproducing the real trends of heating and cooling demand profiles. In particular, they demonstrate that, while both 5R1C and 7R2C models ensure a good degree of accuracy in reproducing peaks and seasonal trends of heat demand, the two-capacitance model ensures a significantly more accurate representation of cooling loads. Comparable benchmarks are suggested also by Georges et al. [15].

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Figure 2. Schematic representation of a generic building archetype

Caldera et al. [16] have already proposed a lumped-parameter model for the representation of the Italian building stock, yet based on a single-capacitance approach. The approach for the calculation of the energy needs for heating and cooling adopted in the present study complies instead with the abovementioned findings and adopts a RC network model based on the ISO 52016:2017, further simplified by decreasing the number of temperature nodes in opaque elements. A whole building is indeed modelled as a single, box-shaped thermal zone (Figure 2) composed of 10 building elements (i.e. roof, floor, and four vertical walls – further differentiated into transparent and opaque surfaces). Each building element is characterized by a conductive resistance coupled with a capacitance applied to the node facing the internal volume (transparent building elements have null capacitance), by assuming that the mass is concentrated in a single node.

Figure 3 reports the equivalent-circuit representation, where it is assumed that there are no mechanical ventilation appliances, as they are not common in Italian existing residential buildings. The unknown variables are $θ_{int,eli,t}$, $θ_{ext,eli,t}$ and, alternatively, $Φ_{HC,t}$ or $θ_{a,t}$. It is worth noting that the scheme in Figure 3 represents, for simplicity, only one building element, coupled with the resistances representing the heat transfer coefficient for ventilation ($H_{ve}$) and thermal bridges ($H_{tb}$); an additional parallel connection between $θ_{e,t}$ and $θ_{a,t}$, with the same components reported in the figure, needs to be added for each additional building element.

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Figure 3. Equivalent-circuit representation of the building thermodynamic model

Equations 1-4 show the corresponding mathematical model formulation, whereas the system is solved with respect to a fixed set-point temperature $θ_{a, t}$ for unknown $Φ_{HC,t}$. It is worth noting that the first two explicit equations resulting from the product (representing the energy balances on, respectively, the first and second node of the equivalent circuit from the left in Figure 3) are repeated for each of the 10 building elements, varying the parameters accordingly. The third equation resulting from the matrix-vector product, instead, represents the overall energy balance on the archetype.

$\mathbf{Ax}=\mathbf{b}$  (1)

$\mathbf{A}=\begin{bmatrix} h_{se,eli}+h_{eli} & -h_{eli} & 0\\ -h_{eli} & h_{eli}+h_{ci,eli}+\frac{k_{eli}}{△t} & -\frac{1-f_{HC}}{A_{tot}}\\ 0 & A_{eli}h{ci,eli} & f_{HC} \end{bmatrix} $ (2)

$\mathbf{x}=\begin{bmatrix} θ_{ext,eli,t} \\ θ_{int,eli,t}\\ Φ_{HC,t} \end{bmatrix}$ (3)

$\mathbf{b}=\begin{bmatrix} h_{se,eli}θ_{e,t}+a_{sol}(I_{dir,eli,t}F_{sh,eli}+I_{diff,eli,t}-φ_{sky} & \forall \in E\\ \frac{1}{A_{tot}}[(1-f_{int})Φ_{int,t}+(1-f_{sol})Φ_{sol,t}]+h_{ci,eli}θ_{a,t}+\frac{k_{eli}}{△t}θ_{int,eli,t-1} & \forall i \in E\\ \sum_i A_{eli}h_{ci,eli}θ_{a,t}+\frac{C_{int}}{△t}(θ_{a,t}-θ_{a,t-1})+(H_{ve}+H_{tb})(θ_{a,t}-θ_{e,t})-f_{int}Φ_{int,t}-f_{sol}Φ_{sol,t} &  \end{bmatrix}$ (4)

2.2 Main thermophysical parameters and coefficients

Each building element is characterised by a number of thermophysical parameters that populate the system reported in Equation 1. The standard UNI/TR 11552:2014 provides the main thermophysical parameters of the opaque components that are most used in the Italian building stock. The standard also reports the most common wall, roof or floor stratigraphy with respect to the climatic zone and the period of construction of the considered building. Table 1 reports the calculated U-values for the example of single-family archetypes.

Table 1. U-values [W.m-2. K-1] for single-family buildings, by construction period, climatic zone and building element

Depending on the layers and materials adopted, a conductive heat transfer coefficient, $h_{eli}$, is evaluated for each element starting from the U value computed according to ISO 6946:2017, which specifies the characteristics related to the dynamic thermal behaviour of a complete building component and provides methods for their calculation. The calculation is reported in Equation 5.

$U=\frac{1}{h_{si,eli}+h_{eli}+h_{se}}$ (5)

where, $h_{si,el}$ and $h_{se,eli}$ are the internal and external surface heat transfer coefficients, comprising both convective and radiative heat transfer) are derived from ISO 13789:2017.

The same standard provides also values for the internal surface convective heat transfer coefficient, $h_{ci,eli}$, depending on the direction (vertical or horizontal) of the thermal flow on the i-th building element.

The overall heat exchange coefficient by (natural) ventilation ($H_{ve}$) is computed by means of Equation 6 as a function of the air flow rate $q_{V,t}$.

$H_{ve}=ρ_aC_aQ_{V,t}$  (6)

The calculation of the overall heat transfer coefficient for thermal bridges ($H_{tb}$) is reported in Equation 7.

$H_{tb}=\sum_kl_{tb,k}ψ_{tb,k}$ (7)

where, $l_{tb,k}$ and $ψ_{tb,k}$, respectively the length and the linear thermal transmittance of a linear thermal bridge, are gathered from 14683:2017. To this regard, an exception is represented by buildings realized after 2005; for this category, $H_{tb}$ is assumed equal to a 15 % increase of the overall heat transfer value due to transmission, as prescribed by “Decreto legislativo 19 agosto 2005, n.192”.

The remaining thermophysical coefficients are obtained from tabulated values contained in ISO 52016:2017, with the exception of the heat capacity of the building element ($k_{eli}$), which is considered applied on the internal node and is calculated according to ISO 13786:2005.

Special mention must be made of the shading reduction factor $F_{sh}$. The latter, representing the ratio between the actual and theoretical direct irradiance on a building element, can range between 0 and 1, i.e. from “null” to “complete” direct irradiance. Its assessment is highly building-specific, as it depends on detailed geometrical data on the building itself and on nearby obstacles, making it virtually impossible to compute a single average value for large-scale aggregates. For this work – based on a representative analysis carried out on a generic building in Turin, under the assumptions of a two-floors building with obstacles on four sides, as for a typical urban context – an average value of 0.75 is assumed. Nonetheless, possible deviations from this value are also identified in the range 0.50-1, and used to carry out a sensitivity analysis (sub-section 3.1).

2.3 nZEB archetype characterisation

The nZEB archetypes are characterised assuming they originate from a refurbishment intervention on existing buildings, as a result of the improvement of the insulation properties. In fact, the Italian “DM 26/06/2015” prescribes a set of minimum requirements that both new and refurbished buildings must satisfy to be considered nZEB. At the current stage of the work, aimed at defining the energy needs, the nZEB archetypes are defined considering the thermophysical performance of the envelope, neglecting the limits related to the energy appliances. The decree prescribes, for each climatic zone, a specific transmittance limit for each building element, without distinction between different building geometries (single-family, etc.). Accordingly, all transmittance values are assumed equal to the limit values prescribed for nZEBs (Table 2).

Table 2. U-values [W.m^-2.K^-1] limits for nZEBs, by climatic zone and building element

Achieving such limit values requires significant enhancements of the insulation properties of existing buildings. Required transmittance reductions for vertical walls range from -82.4 % to -16 %, depending on the building geometry and climatic zone, whilst reductions in the transmittance of transparent surfaces (windows) range from -78.3 % to -23.1 %. The envelope renovation must be carried out through processes of thermal insulation coating; a proper insulating material needs to be added to roof, ground floor and walls, while windows needs to be substituted. For vertical walls, fiberglass is considered the preferable insulating material, and the thickness of the additional insulation is calculated for each case as reported in Table 3.

Furthermore, the Italian “DM 26/06/2015” specifies that all U-value limits for nZEBs are intended as already comprehensive of all thermal bridges. Accordingly, the overall thermal bridges transmittance $H_{tb}$ is null for all nZEB archetypes.

Table 3. Thickness [cm] of fiberglass insulation to reach nZEB status, by climatic area and construction period

2.4 Simulation algorithm and regional aggregation

The system of equations summarised by Equation 1 is implemented in a Python 3.6 environment and solved for each combination of geometry, period of construction and climate-dependent construction materials, with a province-scale resolution in terms of irradiance and external temperature data. The latter data are obtained from the database of the Comitato Termotecnico Italiano (CTI), which provides “typical-year” time series of climatic data for Italy based on the European Standard EN ISO 15927-4:2005.

The algorithm is also constrained to follow a set of rules aimed at reproducing real-life typical dynamics and Italian normative prescriptions. Firstly, a precise period in which heating is allowed is set for each climatic zone, in accordance with the Italian legislation (Table 4).

Table 4. Heating periods by climatic zone

Secondly, each combination of archetype and district-scale temperature series is solved for three different possible thermostat regulation settings. These correspond to the most typical regulation settings of Italian households, as identified by Corrado et al. [17]. Table 5 reports the three possible settings for sunlight hours (07:00-22:00), where the high set point is assumed to be 20°C and the low set point 16°C. Night-hours regulation is instead assumed to be identical in all cases and corresponding to the low set point.

Table 5. Thermostat regulation settings for different user types

The logic by which the R1 setting is solved is here reported as an example: during the heating period, and if the outdoor temperature is lower than 18°C, the algorithm reformulates Equation 1 to compute $θ_{a, t}$ assuming the heating is initially off. Whereas $θ_{a, t}$  would fall below the pre-defined indoor comfort threshold – set at 20°C or 16°C depending on the period of the day – Equation 1 is solved in its standard form to compute the required $Φ_{HC,t}$ to keep comfort conditions.

In any other period, $Φ_{HC,t}$  is conversely set to provide, if outdoor temperature is above 25°C, cooling energy. An upper indoor comfort temperature threshold of 26°C is set for both day and night, and a similar resolution logic to that of the heating period is adopted to compute the cooling needs.

Finally, district-scale results are aggregated at regional (NUTS-2) level, based on the data by ISTAT [13] about the district and regional distributions of buildings associated with the defined archetypes (initially assuming a null penetration of nZEBs) and of households associated with the three defined patterns of thermostat control. In particular, the following shares (among all Italian households) are identified for each setting: 25.3 % for setting R1, 26.3 % for setting R2 and 48.4 % for setting R3.

2.5 Scenarios definition

Three scenarios of progressive building stock refurbishment policies towards nZEBs are considered. These are based on the expected penetration of nZEBs in Italy, in the short-to-medium term, according to three different sources, namely: the national strategies PANZEB and STREPIN (which set targets for 2020), and the European project ZEBRA2020 (which sets more ambitious targets for 2030). The rationale by which refurbishment policies are simulated is that older and more energy-intensive buildings (those constructed before 1975), which also represent the largest share of the current building stock, shall be renovated first. Accordingly, the nZEBs shares estimated by the three sources for the whole building stock are here applied following the abovementioned rationale. The resulting penetration of nZEBs is, in all cases, such that only buildings belonging to the oldest construction period are interested by the intervention. Table 6 summarises the scenarios and the corresponding percentage share of renovated buildings.

Table 6. Percentage share of renovated buildings in each scenario