Multi-Criteria Analysis of Different Renovation Scenarios Applying Energy, Economic, and Thermal Comfort Criteria

Abstract

Sustainable renovation is a critical aspect for designing energy-efficient buildings with reasonable cost and high indoor living standards. The objective of this paper is to investigate various renovation scenarios for an old, uninsulated building with a floor area of 100 m² located in Athens, aiming to determine the global optimal solution through a multi-criteria analysis. The multi-criteria analysis considers energy, economic, and thermal comfort criteria to perform a multi-lateral approach. Specifically, the criteria are: (i) maximization of the energy savings, (ii) minimization of the life cycle cost (LCC), and (iii) minimization of the mean annual predicted percentage of dissatisfied (PPD). These criteria are combined within a multi-criteria evaluation procedure that employs a global objective function for determining a global optimum solution. The examined retrofitting actions are the addition of external insulation, the replacement of the existing windows with triple-glazed windows, the addition of shading in the openings in the summer, the application of cool roof dyes, the use of a mechanical ventilation system with a heat recovery unit, and the installation of a highly efficient heat pump system. The interventions were examined separately, and the combined renovation scenarios were studied by including them in the external insulation because of their high importance. The present study encompassed the investigation of a baseline scenario and 26 different renovation scenarios, conducted through dynamic simulation on an annual basis. The results of the present analysis indicated that the global optimal renovation scenario, including the addition of external insulation, the installation of highly efficient heat pumps, and the use of shading in the openings in the summer, saved energy by 74% compared to the baseline scenario. The LCC was approximately EUR 33,000, the simple payback period of the renovation process was around 6 years, the annual CO₂ emissions avoidance reached 4.6 tn_CO2, and the PPD was at 9.7%. An additional sensitivity analysis for determining the optimal choice under varying weights assigned to the criteria revealed that this renovation design is the most favorable option in most cases. These results prove that the suggested renovation scenario is a feasible and viable solution that leads to a sustainable design from multiple perspectives.

1. Introduction

The building sector is one of the most energy-intensive sectors, being responsible for approximately 40% of energy consumption and 37% of CO₂ emissions in the European Union (EU), making the built environment a critical target for decarbonization efforts [1]. Furthermore, a significant portion of the building stock in both the EU and Greece is aging and energy-inefficient, with 85% of EU buildings constructed before 2000, and 75% of them are energy-inefficient [2]. As a result, enhancing the energy performance of the existing building stock through renovation is a key strategy for achieving climate neutrality targets by 2050 [3]. Specifically, significant attention has been directed toward holistic renovation solutions that aim to design substantially improved and sustainable buildings [4]. A critical challenge regarding the renovation is the increase in the renovation rate of the existing building stock, which is currently estimated to be 1% per year, an insufficient level [5].

Another critical issue, except for energy savings, is the existence of healthy and comfortable living conditions. Specifically, maintaining indoor operative temperatures within the range of 20–23 °C in winter and 23–26 °C in summer is essential for ensuring acceptable thermal comfort for the majority of the occupants [6]. Of course, the desired temperature levels vary among different groups of people [7]. Therefore, the building sector needs important renovation actions that satisfy different aspects like high energy performance, thermal comfort, economic sustainability, and building decarbonization.

Various studies in literature examine different renovation actions in buildings that aim to reduce mainly the thermal loads, while also emphasizing enhancing indoor thermal comfort. Typical renovation actions include the addition of external insulation in the structural elements, the replacement of windows with efficient double or triple glazing, the installation of fixed or movable shading mechanisms, the installation of central heat pump units and the installation of photovoltaics on the building in combination with batteries for electrical storage. However, there are extra innovative techniques like the use of thermochromic dyes, cool roof materials, thermochromic and thermoelectric glazing, mechanical ventilation systems with heat recovery efficiency, and the application of advanced control systems (e.g., based on artificial intelligence) that exploit energy monitoring of the building. In a detailed work concerning the holistic renovation of an aging Greek building located in Athens [8], it was concluded that the heating loads were reduced by 73%, the cooling loads by 78%, and the total primary energy demand by 88% compared to the baseline scenario. These results prove that high energy savings can be achieved through the renovation of older buildings. These conclusions are further supported by the study of Synnefa et al. [9]. Specifically, they found that the renovation of an old building in Athens, Greece, resulted in an 81% energy reduction and a payback period of around 3 years. Moreover, Kyritsi et al. [10] found that the renovation of two historical buildings in Greece led to a reduction of 35–54% in the heating loads, which is promising considering the interventions’ restrictions associated with such structures.

The next part of the literature study investigates alternative retrofitting actions. For example, Kitsopoulou et al. [11] performed a comparative work of various alternative retrofitting actions, including the use of phase change materials, a cool roof, and mechanical ventilation during the summer, in combination with external insulation. This work was performed for the different climatic zones of Greece. It was concluded that energy savings ranged from 11% in Kastoria to 28% in Heraklion, with Athens and Thessaloniki achieving 21% and 17%, respectively. Furthermore, another recent study by Mihalakakou et al. [12] concluded that the application of green roofs can decrease the cooling demand by up to 70%, a promising conclusion regarding this intervention action. Another interesting idea is the application of a proper control system based on weather data for calibrating the operation of the energy systems. In this direction, a recent work of Łokczewska et al. [13] proved that a 10% reduction in energy demand can be achieved with this strategy regarding the heating load.

Several studies in the literature focus on the environmental assessment of the renovation processes. Apostolopoulos et al. [14] used the VERIFY tool to perform a life cycle assessment of renovations in old Greek buildings. They resulted in a significant reduction in primary energy demand and in CO₂ emissions, of over 90%, indicating the environmental benefits of retrofitting the existing building stock. In another study, Dragonetti et al. [15] highlighted the environmental and economic advantages of building retrofits, while also noting that the seismic reinforcement is also a critical aspect that has to be taken into consideration. Another study by Dascalaki et al. [16] examined the embodied energy recovery of the renovation, and it was estimated within approximately 2 to 10 years. Furthermore, reusing and recycling materials during renovation has been identified as a very promising strategy from an environmental point of view [17].

There are numerous studies regarding the renovation of buildings, particularly older ones with high energy consumption. Many of these studies focus on the energy, economic, and environmental evaluation of renovation actions. However, relatively few studies perform multi-criteria evaluation of the renovation scenarios and consider the thermal comfort conditions in the building among the examined cases. Therefore, this work aims to cover this critical scientific gap by performing a systematic evaluation of various retrofitting scenarios and conducting a multi-criteria assessment of them, considering energy, economic and thermal comfort criteria. This process aims to determine the global optimal solution and to provide a ranking of the most appropriate combination of retrofitting techniques. Moreover, extra evaluation criteria are studied, like the simple payback period, the PMV (Predicted Mean Vote) and the yearly CO₂ emissions reduction. This work is performed with a newly developed and validated simulation tool called “T-DEOS” (Thermal—Dynamic Energy Oriented Simulation), a MATLAB-based program that enables the accurate prediction of the building’s thermal behavior and the performance of its energy systems. The tool also supports the development of grey-box models and energy digital twins of real buildings. Using this tool, the present study conducts a multi-criteria evaluation of different renovation techniques for a typical old, uninsulated building located in Athens, Greece. This work is the first published paper that describes its methodology in detail.

Specifically, the examined retrofitting actions are: (i) the addition of external insulation, (ii) the windows replacement with triple-glazed windows, (iii) the addition of shading in the openings in the summer, (iv) the application of cool roof dyes, (v) the use of a mechanical ventilation system with a heat recovery unit, and (vi) the installation of highly efficient heat pump system. A total of 26 different retrofitting scenarios (separate and combined) were studied, giving emphasis on including the insulation addition in the retrofit building. A multi-criteria evaluation of these scenarios was performed by applying three criteria: (a) maximization of the energy reduction compared to the baseline scenario, (b) minimization of the life cycle cost (LCC), and (c) minimization of the mean yearly PPD. The final overall optimal design was determined by using a global objective function that considered all the indices. Finally, a sensitivity analysis with various weights for the studied criteria of the objective function was applied.

2. Materials and Methods

This section includes the input data regarding the examined building, the retrofitting actions, the model description/validation, and the following methodology.

2.1. The Studied Building

In this work, a typical uninsulated building with a net floor area of 100 m², located in Athens, Greece (37.90° N, 23.73° E), is examined as a representative case study. This building is theoretical and represents typical old buildings that were constructed before 1980 in Athens, when there was no thermal insulation regulation. The height of the building is 3 m, the length of all the wall sides is 10 m, and the four external walls are oriented along the cardinal directions. All the external structural elements are in contact with the ambient air. There is a south window of 5 m² and two windows of 2 m² located in the east and west walls, respectively.

Table 1. Summary of the data regarding the building.

Parameters	Values
Building floor area	100 m2
Building dimensions	10 m × 10 m × 3 m
Location	Athens, Greece (37.90° N, 23.73° E)
South–east–west window areas	5 m2—2 m2—2 m2
U-value of the structural elements	3 W/m2 (uninsulated)
Absorbance	60%
U-value of the windows	6 W/(m2·K) (single windows)
g-value of the windows	60%
Infiltration/ventilation rate	0.3 ACH/0.5 ACH
Occupancy	Two occupants, 80 W/occupant, 75% occupancy
Appliances load	2 W/m2—75% mean operation
Lighting load	5 W/m2—30% mean operation
COP nominal value	3.0 (Heating and Cooling)
Heating/Cooling set points	20 °C/26 °C
DHW demand	50 L/(day·person) at 45%, electrical heater

summarizes the basic data of the examined building. In this work, an equivalent structural element was considered [18] with a thickness of 30 cm, a specific heat capacity of the structural material of 1000 J/(kg·K), a density of 900 kg/m³, and a thermal conductivity of around 1.78 W/(m·K).

The U-value of the structural elements and the absorbance were selected to be 3 W/(m²·K) (uninsulated) and 60%, respectively, while the windows were single with a metallic frame (U-value = 6 W/(m²·K) and g-value = 60%) [19]. The infiltration rate was chosen to be 0.3 ACH, and the ventilation rate was 0.5 ACH. There were two occupants in the building with an average daily occupancy of 75% and a thermal load of 80 W/occupant. The specific thermal load by the equipment (appliances) was 2 W/m² with an average operating fraction of 75%, while for lighting, it was 5 W/m² with a mean operating fraction of 30% [19]. The heating/cooling loads were served by an air-source heat pump with a nominal coefficient of performance (COP) of three for both heating and cooling. The temperature was set to 20 °C for heating and 26 °C for cooling. The domestic hot water (DHW) demand was covered by the electrical heater with 100% efficiency [20], assuming a daily hot water consumption of 50 L per person at 45 °C. According to the Greek Technical Chamber data [19], the average grid water temperature in Athens is 17.8 °C, and it varies from approximately 10.4 °C up to 25.2 °C throughout the year.

2.2. Mathematical Formulation

2.2.1. Building Envelope Thermal Modeling

Thermal Transfer Through Opaque Building Elements

The 1-D heat transfer through the opaque building elements is described with the following differential equation:

$${\displaystyle \frac{\partial }{\partial \mathrm{x}}}\left(\mathrm{k}\cdot {\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{x}}}\right)=\mathsf{\rho }\cdot \mathrm{c}\cdot {\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}$$

(1)

The thermal conductivity is assumed to be independent of the temperature, and therefore, this equation can be written as below:

$$\mathrm{k}\cdot {\displaystyle \frac{{\partial }^2\mathrm{T}}{\partial {\mathrm{x}}^2}}=\mathsf{\rho }\cdot \mathrm{c}\cdot {\displaystyle \frac{\partial \mathrm{T}}{\partial \mathrm{t}}}$$

(2)

In this work, every structural element is constructed with a uniform equivalent material with the same equivalent thermal properties as the real structural element. This assumption is performed in accordance with the ISO 52016-1:2017 [18].

Figure 1 depicts the discretization of the structural element (se) into elementary volumes (or nodes). Specifically, in this figure, various parameters are presented. The heat input (q), measured in [W/m²], the number of nodes (N) nodes, the superscript (^o) represents the previous timestep, the time step is (Δt) in [s], the distance between the nodes (Δx) is in [m], the thermal conductivity (k), in [W/(m·K)], the density (ρ) in [kg/m³], the specific heat capacity (c) in [J/(kg·K)], the outdoor heat convection coefficient (h_out) in [W/(m²·K)], and the indoor heat convection coefficient (h_in) in [W/(m²·K)]. Typical values for the heat convection coefficients are h_in = 8 W/(m²·K) and h_out = 25 W/(m²·K) [8]. The outdoor temperature (T_out) and the incident solar irradiation (G_T) are the input data that were derived from Typical Meteorological Year (TMY) data. These data were retrieved from the PVGIS database [21], and base calculations were performed aiming to calculate the (G_T) from the diffuse horizontal irradiation and the direct beam irradiation.

The energy balance in the first node is described by the following equation, also considering the external incident solar irradiation:

$$\mathrm{a}\cdot {\mathrm{G}}_{\mathrm{T}}+{\displaystyle \frac{{\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}-{\mathrm{T}}_1}{\frac{1}{{\mathrm{h}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}+\frac{\mathsf{\Delta }{\mathrm{x}}_1}{2\cdot {\mathrm{k}}_1}}}-{\displaystyle \frac{{\mathrm{T}}_1-{\mathrm{T}}_2}{\frac{\mathsf{\Delta }{\mathrm{x}}_1}{2\cdot {\mathrm{k}}_1}+\frac{\mathsf{\Delta }{\mathrm{x}}_2}{2\cdot {\mathrm{k}}_2}}}={\mathsf{\rho }}_1\cdot {\mathrm{c}}_1\cdot \mathsf{\Delta }{\mathrm{x}}_1\cdot {\displaystyle \frac{{\mathrm{T}}_1-{\mathrm{T}}_1^{\mathrm{o}}}{\mathsf{\Delta }\mathrm{t}}}$$

(3)

The respective energy balance equation for the second node is given below:

$${\displaystyle \frac{{\mathrm{T}}_1-{\mathrm{T}}_2}{\frac{\mathsf{\Delta }{\mathrm{x}}_1}{2\cdot {\mathrm{k}}_1}+\frac{\mathsf{\Delta }{\mathrm{x}}_2}{2\cdot {\mathrm{k}}_2}}}-{\displaystyle \frac{{\mathrm{T}}_2-{\mathrm{T}}_3}{\frac{\mathsf{\Delta }{\mathrm{x}}_2}{2\cdot {\mathrm{k}}_2}+\frac{\mathsf{\Delta }{\mathrm{x}}_3}{2\cdot {\mathrm{k}}_3}}}={\mathsf{\rho }}_2\cdot {\mathrm{c}}_2\cdot \mathsf{\Delta }{\mathrm{x}}_2\cdot {\displaystyle \frac{{\mathrm{T}}_2-{\mathrm{T}}_2^{\mathrm{o}}}{\mathsf{\Delta }\mathrm{t}}}$$

(4)

The respective energy balance equation for the node (i) is given below:

$${\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}-1}-{\mathrm{T}}_1}{\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}-1}}{2\cdot {\mathrm{k}}_{\mathrm{i}-1}}+\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}}}{2\cdot {\mathrm{k}}_{\mathrm{i}}}}}-{\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}}-{\mathrm{T}}_{\mathrm{i}+1}}{\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}}}{2\cdot {\mathrm{k}}_{\mathrm{i}}}+\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}+1}}{2\cdot {\mathrm{k}}_{\mathrm{i}+1}}}}={\mathsf{\rho }}_{\mathrm{i}}\cdot {\mathrm{c}}_{\mathrm{i}}\cdot \mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}}\cdot {\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}}-{\mathrm{T}}_{\mathrm{i}}^{\mathrm{o}}}{\mathsf{\Delta }\mathrm{t}}}$$

(5)

Finally, the energy balance equation for the last node (N) is given as follows:

$${\mathrm{q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{i}\mathrm{n}}+{\displaystyle \frac{{\mathrm{T}}_{\mathrm{N}-1}-{\mathrm{T}}_{\mathrm{N}}}{\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{N}-1}}{2\cdot {\mathrm{k}}_{\mathrm{N}-1}}+\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{N}}}{2\cdot {\mathrm{k}}_{\mathrm{N}}}}}-{\displaystyle \frac{{\mathrm{T}}_{\mathrm{N}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n}}^{\mathrm{o}}}{\frac{\mathsf{\Delta }{\mathrm{x}}_{\mathrm{N}}}{2\cdot {\mathrm{k}}_{\mathrm{N}}}+\frac{1}{{\mathrm{h}}_{\mathrm{i}\mathrm{n}}}}}={\mathsf{\rho }}_{\mathrm{N}}\cdot {\mathrm{c}}_{\mathrm{N}}\cdot \mathsf{\Delta }{\mathrm{x}}_{\mathrm{N}}\cdot {\displaystyle \frac{{\mathrm{T}}_{\mathrm{N}}-{\mathrm{T}}_{\mathrm{N}}^{\mathrm{o}}}{\mathsf{\Delta }\mathrm{t}}}$$

(6)

where the indoor temperature has the value of the previous time node. The parameter (q_sol,in) is the quantity of solar irradiation that is absorbed by the indoor space through the windows.

Assuming that there is a quantity (Q_sol,in) that comes totally in the indoor space, then a part of it is directly absorbed by the air, a part is lost from the windows back to the ambience and the remaining part is absorbed by the internal structural elements. A uniform absorption of the energy in the structural elements is assumed by weighing it with the area of each wall, respectively.

The total view factor of the structural elements (f_se) is found by using the air absorbance factor (f_air) and the losses factor (f_loss) as follows:

$${\mathrm{f}}_{\mathrm{s}\mathrm{e}}=1-{\mathrm{f}}_{\mathrm{a}\mathrm{i}\mathrm{r}}-{\mathrm{f}}_{\mathrm{l}\mathrm{o}\mathrm{s}\mathrm{s}}$$

(7)

The air is assumed to absorb the f_air = 10% and no losses are assumed (f_loss = 0), which are the suggested values according to EN 15265:2007 [22].

The specific heat flux that every structural element receives from the solar irradiation on its internal surface is calculated as follows [22]:

$${\mathrm{q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{i}\mathrm{n}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{i}\mathrm{n}}}{{\mathrm{A}}_{\mathrm{s}\mathrm{e}}}}\cdot {\mathrm{f}}_{\mathrm{s}\mathrm{e}}\cdot \left({\displaystyle \frac{{\mathrm{A}}_{\mathrm{s}\mathrm{e}}}{{\sum }_{\mathrm{i}}{\mathrm{A}}_{\mathrm{s}\mathrm{e},\mathrm{i}}}}\right)$$

(8)

Finally, the combination of all the energy balance equations leads to the development of a tridiagonal matrix, and the respective equations can be written as below in a matrix format:

$$\left[\begin{array}{c}\begin{array}{ccc}\left({\mathrm{U}}_1+{\mathrm{U}}_2+{\mathrm{M}}_1\right)& -{\mathrm{U}}_2& 0\end{array} \begin{array}{cc}0& 0\end{array}\\ \begin{array}{ccc}& \ddots & \end{array} \begin{array}{cc}\ddots & \end{array}\\ \begin{array}{ccc}0& -{\mathrm{U}}_{\mathrm{i}}& \left({\mathrm{U}}_{\mathrm{i}}+{\mathrm{U}}_{\mathrm{i}+1}+{\mathrm{M}}_{\mathrm{i}}\right)\end{array} \begin{array}{cc}-{\mathrm{U}}_{\mathrm{i}+1}& 0\end{array}\\ \begin{array}{ccc}& \ddots & \end{array} \begin{array}{cc}& \ddots \end{array}\\ \begin{array}{ccc}0& 0& 0\end{array} \begin{array}{cc}-{\mathrm{U}}_{\mathrm{N}}& \left({\mathrm{U}}_{\mathrm{N}}+{\mathrm{U}}_{\mathrm{N}+1}+{\mathrm{M}}_{\mathrm{N}}\right)\end{array}\end{array}\right]\cdot \left[\begin{array}{c}\begin{array}{c}{\mathrm{T}}_1\\ ⋮\\ {\mathrm{T}}_{\mathrm{i}}\end{array}\\ ⋮\\ {\mathrm{T}}_{\mathrm{N}}\end{array}\right]=\left[\begin{array}{c}{\mathrm{M}}_1\cdot {\mathrm{T}}_1^{\mathrm{o}}\\ ⋮\\ {\mathrm{M}}_{\mathrm{i}}\cdot {\mathrm{T}}_{\mathrm{i}}^{\mathrm{o}}\\ ⋮\\ {\mathrm{M}}_{\mathrm{N}}\cdot {\mathrm{T}}_{\mathrm{N}}^{\mathrm{o}}\end{array}\right]+\left[\begin{array}{c}{\mathrm{U}}_1\cdot {\mathrm{T}}_{\mathrm{o}\mathrm{u}\mathrm{t}}\\ ⋮\\ 0\\ ⋮\\ {\mathrm{U}}_{\mathrm{N}}\cdot {\mathrm{T}}_{\mathrm{i}\mathrm{n}}^{\mathrm{o}}\end{array}\right]+\left[\begin{array}{c}\mathrm{a}\cdot {\mathrm{G}}_{\mathrm{T}}\\ ⋮\\ 0\\ ⋮\\ {\mathrm{q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{i}\mathrm{n}}\end{array}\right]$$

(9)

The parameter (U_i) expresses the thermal transmittance of every area between nodes, and these parameters can be found as below:

$${\mathrm{U}}_1={\displaystyle \frac{1}{\frac{1}{{\mathrm{h}}_{\mathrm{o}\mathrm{u}\mathrm{t}}}+\frac{{\mathsf{\Delta }\mathrm{x}}_1}{2\cdot {\mathrm{k}}_1}}}$$

(10)

$${\mathrm{U}}_{\mathrm{i}}={\displaystyle \frac{1}{\frac{{\mathsf{\Delta }\mathrm{x}}_{\mathrm{i}-1}}{2\cdot {\mathrm{k}}_{\mathrm{i}-1}}+\frac{{\mathsf{\Delta }\mathrm{x}}_{\mathrm{i}}}{2\cdot {\mathrm{k}}_{\mathrm{i}}}}}$$

(11)

$${\mathrm{U}}_{\mathrm{N}+1}={\displaystyle \frac{1}{\frac{{\mathsf{\Delta }\mathrm{x}}_{\mathrm{N}}}{2\cdot {\mathrm{k}}_{\mathrm{N}}}+\frac{1}{{\mathrm{h}}_{\mathrm{i}\mathrm{n}}}}}$$

(12)

The parameter (M_i) is the thermal mass of every volume between nodes, and it can be calculated as follows:

$${\mathrm{M}}_{\mathrm{i}}={\displaystyle \frac{{\mathsf{\rho }}_{\mathrm{i}}\cdot {\mathrm{c}}_{\mathrm{i}}\cdot \mathsf{\Delta }{\mathrm{x}}_{\mathrm{i}}}{\mathsf{\Delta }\mathrm{t}}}$$

(13)

The tridiagonal matrix is solved for every time step with the Thomas algorithm [23].

The energy input from the structural element to the indoor space is estimated by the following expression:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{e}}={\mathrm{A}}_{\mathrm{s}\mathrm{e}}\cdot {\mathrm{U}}_4\cdot \left({\mathrm{T}}_{\mathrm{N}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n}}^{\mathrm{o}}\right)$$

(14)

Thermal Transfer Through Transparent Building Elements

The thermal loads due to the conductivity through the transparent building elements are found as follows:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{e}}={\mathrm{A}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}\cdot {\mathrm{U}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}\cdot \left({\mathrm{T}}_{\mathrm{a}\mathrm{m}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n}}^{\mathrm{o}}\right)$$

(15)

The solar energy that goes into the indoor space through the window is described below:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{o}\mathrm{l},\mathrm{i}\mathrm{n},\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}={\mathrm{A}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}\cdot {\mathrm{g}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}\cdot {\mathrm{G}}_{\mathrm{T}}$$

(16)

Infiltration/Ventilation Thermal Losses

The infiltration thermal load (Q_inf) is calculated as follows:

$${\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{f}}={\mathrm{m}}_{\mathrm{i}\mathrm{n}\mathrm{f}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{a}\mathrm{i}\mathrm{r}}\cdot ({\mathrm{T}}_{\mathrm{a}\mathrm{m}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n}})$$

(17)

The mass flow rate of the infiltration can be computed by the following equation, by using the air changes per hour from infiltration (INF):

$${\mathrm{m}}_{\mathrm{i}\mathrm{n}\mathrm{f}}={\displaystyle \frac{\mathsf{\rho }\cdot \mathrm{V}\cdot \mathrm{I}\mathrm{N}\mathrm{F}}{3600}}$$

(18)

The ventilation thermal load (Q_vent) is expressed as follows:

$${\mathrm{Q}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}={\mathrm{m}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}\cdot {\mathrm{c}}_{\mathrm{p},\mathrm{a}\mathrm{i}\mathrm{r}}\cdot \left({\mathrm{T}}_{\mathrm{a}\mathrm{m}}-{\mathrm{T}}_{\mathrm{i}\mathrm{n}}\right)\cdot (1-{\mathsf{\eta }}_{\mathrm{H}\mathrm{R}\mathrm{S}})$$

(19)

The mass flow rate of the infiltration is calculated by using the air changes per hour from infiltration (VENT):

$${\mathrm{m}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}={\displaystyle \frac{\mathsf{\rho }\cdot \mathrm{V}\cdot \mathrm{V}\mathrm{E}\mathrm{N}\mathrm{T}}{3600}}$$

(20)

The heat exchanger effectiveness (η_HRS) is applied in cases with a heat recovery system. Moreover, during the cooling period (summer), when the free cooling is more effective, there is a bypass for the heat recovery system.

Internal Gains

There are three different internal gain types, which are described below. Specifically, there are internal gains of occupants, lighting, and equipment. The variations in the daily operating fractions are given in Figure 2.

The internal gains from the occupants (Q_occ) are calculated as follows:

$${\mathrm{Q}}_{\mathrm{o}\mathrm{c}\mathrm{c}}={\mathrm{q}}_{\mathrm{o}\mathrm{c}\mathrm{c}}\cdot {\mathrm{N}}_{\mathrm{o}\mathrm{c}\mathrm{c}}\cdot {\mathrm{f}\mathrm{r}}_{\mathrm{o}\mathrm{c}\mathrm{c}}\cdot \left({\displaystyle \frac{\mathrm{f}{\mathrm{r}}_{\mathrm{o}\mathrm{c}\mathrm{c},\mathrm{m}}}{\mathrm{f}{\mathrm{r}}_{\mathrm{o}\mathrm{c}\mathrm{c},\mathrm{n}\mathrm{o}\mathrm{m}}}}\right)$$

(21)

where the specific thermal load per occupant is selected at q_occ = 80 W/m² [24], the number of occupants is (N_occ), the operating fraction (fr_occ) is given by Figure 2, the mean daily fraction is (fr_occ,m = 0.75) and the nominal mean daily fraction for the present profile is (fr_occ,nom = 0.6625). The profile has been taken from Ref. [25].

The internal gains from the lighting (Q_ligh) are calculated as the following:

$${\mathrm{Q}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}}={\mathrm{q}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}}\cdot {\mathrm{A}}_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}}\cdot {\mathrm{f}\mathrm{r}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}}\cdot \left({\displaystyle \frac{\mathrm{f}{\mathrm{r}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h},\mathrm{m}}}{\mathrm{f}{\mathrm{r}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h},\mathrm{n}\mathrm{o}\mathrm{m}}}}\right)$$

(22)

where the specific lighting load per area can be selected at q_ligh = 5 W/m² [26], the floor area is (A_floor), the operating fraction (fr_ligh) is given by Figure 2, the mean daily fraction is (fr_ligh,m = 0.3) and the nominal mean daily fraction for the present profile is (fr_ligh,nom = 0.27625). The profile has been taken from Ref. [25].

The internal gains from the equipment (Q_dev) are computed by the following equation:

$${\mathrm{Q}}_{\mathrm{d}\mathrm{e}\mathrm{v}}={\mathrm{q}}_{\mathrm{d}\mathrm{e}\mathrm{v}}\cdot {\mathrm{A}}_{\mathrm{f}\mathrm{l}\mathrm{o}\mathrm{o}\mathrm{r}}\cdot {\mathrm{f}\mathrm{r}}_{\mathrm{d}\mathrm{e}\mathrm{v}}\cdot \left({\displaystyle \frac{\mathrm{f}{\mathrm{r}}_{\mathrm{d}\mathrm{e}\mathrm{v},\mathrm{m}}}{\mathrm{f}{\mathrm{r}}_{\mathrm{d}\mathrm{e}\mathrm{v},\mathrm{n}\mathrm{o}\mathrm{m}}}}\right)$$

(23)

where the specific devices load per area can be selected at q_dev = 2 W/m² [26], the floor area is (A_floor), the operating fraction (fr_dev) is given by Figure 2, the mean daily fraction is (fr_dev,m = 0.75) and the nominal mean daily fraction for the present profile is (fr_dev,nom = 0.675417). The profile has been taken from Ref. [25].

The total internal thermal gains are calculated as below:

$${\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{t}}={\mathrm{Q}}_{\mathrm{o}\mathrm{c}\mathrm{c}}+{\mathrm{Q}}_{\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}}+{\mathrm{Q}}_{\mathrm{d}\mathrm{e}\mathrm{v}}$$

(24)

2.2.2. Energy Systems Control for Heating/Cooling

In the case that the indoor temperature (T_in) falls outside the desired limits, the heating/cooling system is activated.

Heating Period (Winter)

During the heating period, the goal is to maintain the indoor temperature over the set point, thus:

$${\mathrm{T}}_{\mathrm{i}\mathrm{n}}\ge {\mathrm{T}}_{\mathrm{s}\mathrm{e}\mathrm{t},\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}$$

(25)

When this condition is not satisfied, then the heating system is activated, and it adds heat to the indoor space:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{y}\mathrm{s}}>0$$

(26)

The heating set point is T_set,heat = 20 °C.

Cooling Period (Summer)

During the cooling period, the goal is to maintain the indoor temperature under the set point, thus:

$${\mathrm{T}}_{\mathrm{i}\mathrm{n}}\le {\mathrm{T}}_{\mathrm{s}\mathrm{e}\mathrm{t},\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}$$

(27)

When this condition is not satisfied, then the cooling system is activated, and it removes heat from the indoor space:

$${\mathrm{Q}}_{\mathrm{s}\mathrm{y}\mathrm{s}}<0$$

(28)

The cooling set point is T_set,cool = 26 °C.

Energy Balance in the Indoor Space

The energy balance of the indoor space is given as follows:

$$\sum {\mathrm{Q}}_{\mathrm{i}\mathrm{n},\mathrm{t}\mathrm{l}}=\mathrm{F}\cdot (\mathsf{\rho }\cdot \mathrm{V}\cdot {\mathrm{c}}_{\mathrm{p}}{)}_{\mathrm{a}\mathrm{i}\mathrm{r}}\cdot {\displaystyle \frac{{\mathrm{T}}_{\mathrm{i}\mathrm{n}}-{{\mathrm{T}}_{\mathrm{i}\mathrm{n}}}^0}{\mathsf{\Delta }\mathrm{t}}}$$

(29)

The (F) parameter is set to two for typical furniture inside the space [27]. The symbol (V) is the volume of the indoor space.

The sum of the thermal loads is expressed as follows:

$$\sum {\mathrm{Q}}_{\mathrm{i}\mathrm{n},\mathrm{t}\mathrm{l}}={\sum }_{\mathrm{i}}{\mathrm{Q}}_{\mathrm{s}\mathrm{e},\mathrm{i}}+{\sum }_i{\mathrm{Q}}_{\mathrm{w}\mathrm{i}\mathrm{n}\mathrm{d}}+{\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{f}}+{\mathrm{Q}}_{\mathrm{v}\mathrm{e}\mathrm{n}\mathrm{t}}+{\mathrm{Q}}_{\mathrm{i}\mathrm{n}\mathrm{t}}+{\mathrm{Q}}_{\mathrm{s}\mathrm{y}\mathrm{s}}$$

(30)

where (Q_sys) is the heat input/output of the energy system for maintaining the indoor space temperature and the desired levels.

Domestic Hot Water (DHW) Demand Calculations

The demand calculations of the DHW load (Q_DHW) are based on the number of occupants (N_occ), the daily demand per occupant (DD_occ, e.g., 50 Lt/day [26]), the desired DHW temperature (T_DHW, e.g., 45 °C [26]), the water grid temperature (T_grid), the water density (ρ, e.g., 1 kg/Lt), and the water specific heat capacity (c_p, e.g., 4187 J/(kg·K)). The mass flow rate for the DHW (m_DHW) can be found below, by also introducing the hourly distribution fraction of the daily demand (f_DHW):

$${\mathrm{m}}_{\mathrm{D}\mathrm{H}\mathrm{W}}={\displaystyle \frac{{\mathrm{f}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\cdot \mathsf{\rho }\cdot {\mathrm{N}}_{\mathrm{o}\mathrm{c}\mathrm{c}}\cdot \mathrm{D}{\mathrm{D}}_{\mathrm{o}\mathrm{c}\mathrm{c}}}{3600}}$$

(31)

where the value “3600” in the denominator is used to convert hours to “seconds”, while the daily profile to the hour distribution is converted through the (f_DHW). The DHW daily demand distribution is depicted in Figure 3, and it has been created using data from Ref. [28].

The DHW demand (Q_DHW) is found as follows:

$${\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}={\mathrm{m}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\cdot {\mathrm{c}}_{\mathrm{p}}\cdot \left({\mathrm{T}}_{\mathrm{D}\mathrm{H}\mathrm{W}}-{\mathrm{T}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}\right)$$

(32)

The grid water temperature (T_grid) can be found below, for the case of Athens, Greece [19]:

$${\mathrm{T}}_{\mathrm{g}\mathrm{r}\mathrm{i}\mathrm{d}}=17.81+7.4\cdot \sin \left(3.925+0.205247\cdot \mathrm{t}\cdot {10}^{-6}\right)$$

(33)

where time (t) is measured in seconds.

Efficiency Definitions for the Heat Pump for Heating/Cooling/DHW

The heat pump consumes electricity to produce heating and cooling. The performance of the heat pump is estimated through the Coefficient of Performance (COP). The detailed modeling of the heat pump has been presented in previous studies [29,30]. Below, the basic definitions of the efficiency parameters are given.

The heating heat pump (COP_h) is defined as the following:

$$\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{h}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}}{{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}}}$$

(34)

The cooling heat pump (COP_c) is defined as the following:

$$\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{c}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}}{{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}}}$$

(35)

The DHW heat pump (COP_DHW) is defined as:

$$\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{D}\mathrm{H}\mathrm{W}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}}{{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{D}\mathrm{H}\mathrm{W}}}}$$

(36)

The seasonal (COP) values, which are called (SCOP), can be found as follows:

$$\mathrm{S}\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{h}}={\displaystyle \frac{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{Q}}_{\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}\cdot \mathrm{d}\mathrm{t}}{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}\cdot \mathrm{d}\mathrm{t}}}$$

(37)

$$\mathrm{S}\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{c}}={\displaystyle \frac{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{Q}}_{\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}\cdot \mathrm{d}\mathrm{t}}{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}\cdot \mathrm{d}\mathrm{t}}}$$

(38)

$$\mathrm{S}\mathrm{C}\mathrm{O}{\mathrm{P}}_{\mathrm{D}\mathrm{H}\mathrm{W}}={\displaystyle \frac{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}\cdot \mathrm{d}\mathrm{t}}{{\int }_{\mathrm{s}\mathrm{e}\mathrm{a}\mathrm{s}\mathrm{o}\mathrm{n}}{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{D}\mathrm{H}\mathrm{W}}\cdot \mathrm{d}\mathrm{t}}}$$

(39)

Practically, the COP is dependent on the ambient temperature and thus it has high variation during the year, a fact that shows the high importance of the SCOP parameters.

Electrical Heaters for Domestic Hot Water

The electrical heaters consume electricity, which is calculated as below, by considering their efficiency:

$${\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{D}\mathrm{H}\mathrm{W}}={\displaystyle \frac{{\mathrm{Q}}_{\mathrm{D}\mathrm{H}\mathrm{W}}}{{\mathsf{\eta }}_{\mathrm{e}\mathrm{l},\mathrm{D}\mathrm{H}\mathrm{W}}}}$$

(40)

Electrical Demand Calculations

The building’s total electricity demand is found as the sum of all the separate electrical demands. In the case that the heating, cooling and DHW are covered by electricity (e.g., heat pump), then it is expressed as the following:

$${\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{t}\mathrm{o}\mathrm{t}}={\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{d}\mathrm{e}\mathrm{v}}+{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{l}\mathrm{i}\mathrm{g}\mathrm{h}}+{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{h}\mathrm{e}\mathrm{a}\mathrm{t}}+{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{c}\mathrm{o}\mathrm{o}\mathrm{l}}+{\mathrm{P}}_{\mathrm{e}\mathrm{l},\mathrm{D}\mathrm{H}\mathrm{W}}$$

(41)

2.2.3. Thermal Comfort Analysis

The thermal comfort is strongly associated with air temperature; a multitude of personal and weather factors need to be considered for occupants’ comfort and satisfaction. Thus, ISO 7730 [31] introduced the PMV (Predicted Mean Vote) and the PPD (Predicted Percentage of Dissatisfied) indices, which rely on statements from a group of people regarding some uncomfortable conditions [32]. According to Fanger [33] and ISO7730 [31], the calculation of these indices is based on the specification of a group of environmental factors (i.e., air temperature, mean radiation temperature, air velocity, relative humidity) and a group of personal factors (i.e., clothing insulation and metabolic rate). In this work, Fanger’s thermal comfort model was used [33].

Predicted Mean Vote (PMV) forecasts the average value of the thermal comfort votes among a great group of people on a sensation scale from –3 to +3 (i.e., +3 = Hot, +2 = Warm, +1 = slightly warm, 0 = neutral, −1 = slightly cool, −2 = cool, and −3 = cold) [31]. The environmental input factors are computed through experimental research or simulations on the respective area, while the personal inputs are usually specified through standardized tables of ISO 7730 or ASHRAE 55. The PMV equation is given based on ISO 7730, as follows [31]:

$$\begin{array}{ll}\mathrm{P}\mathrm{M}\mathrm{V}=(0.303·& \mathrm{e}\mathrm{x}\mathrm{p}(-0.036·\mathrm{M})+0.028)·[(\mathrm{M}-\mathrm{W})-3.05·{10}^{-3}·(5733-6.99·(\mathrm{M}-\mathrm{W})-{\mathrm{P}}_{\mathrm{w}})\\ & -0.42·\left(\right(\mathrm{M}-\mathrm{W})-58.15)-1.7·{10}^{-5}·\mathrm{M}·(5867-{\mathrm{P}}_{\mathrm{w}})-0.0014·\mathrm{M}·(34-{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}})\\ & -3.96\times {10}^{-8}·{\mathrm{f}}_{\mathrm{c}\mathrm{l}}·({({\mathrm{T}}_{\mathrm{c}\mathrm{l}}+273.15)}^4-{({\mathrm{T}}_{\mathrm{r}}+273.15)}^4)-{\mathrm{f}}_{\mathrm{c}\mathrm{l}}·{\mathrm{h}}_{\mathrm{c}}·({\mathrm{T}}_{\mathrm{c}\mathrm{l}}-{\mathrm{T}}_{\mathrm{a}\mathrm{i}\mathrm{r}})]\end{array}$$

(42)

where (M) is the metabolic rate [W/m²], (W) the external mechanical work [W/m²], (T_air) is the air temperature [°C], (P_w) is the partial water vapor pressure [Pa], (v) is the air velocity (m/s), (f_cl) is the clothing surface area factor, (T_r) is the average radiant temperature [°C], (T_cl) is the clothing surface temperature [°C], and (h_c) is the convective heat transfer coefficient [W/(m²·K)].

Respectively, the clothing surface factor is given according to ISO 7730 [31]:

$${\mathrm{f}}_{\mathrm{c}\mathrm{l}}=1+1.29·{\mathrm{I}}_{\mathrm{c}\mathrm{l}}, \mathrm{f}\mathrm{o}\mathrm{r} {\mathrm{I}}_{\mathrm{c}\mathrm{l}}\le 0.078 {\mathrm{m}}^2\mathrm{K}/\mathrm{W}$$

(43)

$${\mathrm{f}}_{\mathrm{c}\mathrm{l}}=1.05+0.645·{\mathrm{I}}_{\mathrm{c}\mathrm{l}}, \mathrm{f}\mathrm{o}\mathrm{r} {\mathrm{I}}_{\mathrm{c}\mathrm{l}}>0.078 {(\mathrm{m}}^2\cdot \mathrm{K})/\mathrm{W}$$

(44)

where (I_cl) is the clothing insulation (m²·K/W).

In this work, the metabolic rate was considered at M = 1.0 Met (80 W/m²). For the thermal comfort analysis, the clothing factor (f_cl) is chosen at 0.75 clo in the winter and 0.50 clo in the summer (Thermal resistance of 1 clo = 0.155 (m²·K)/W).

The Predicted Percentage of Dissatisfied (PPD) provides a prediction of the percentage of a great group of people who probably stated that they feel “too warm” or “too cool”. Thus, the PPD is predicted based on the thermally dissatisfied people from the respective PMV, as follows [31]:

$$\mathrm{P}\mathrm{P}\mathrm{D}=1-0.95·\mathrm{e}\mathrm{x}\mathrm{p}\left(-0.03353·\mathrm{P}\mathrm{M}{\mathrm{V}}^4-0.2179·\mathrm{P}\mathrm{M}{\mathrm{V}}^2\right)$$

(45)

The acceptable thermal comfort is achieved for a range of PMV values from −0.5 to +0.5, which corresponds to a PPD percentage below 10%.

2.3. Developed Model and Followed Methodology

The present work is performed with a developed energy model in the MATLAB programming language, which is the digital twin of the studied building. This model simulates the dynamic thermal behavior of the building and of the energy systems in detail. Practically, the present simulation program belongs to the energy tool called “T-DEOS” (Thermal–Dynamic Energy Oriented Simulation), which is developed by the University of West Attica. This tool is an advanced MATLAB-based simulation toolkit that enables dynamic simulation of the building thermal behavior, energy systems performance (e.g., heat pumps), renewable energy systems production (e.g., solar thermal collectors, photovoltaics, etc.), as well as calculations regarding the indoor thermal comfort conditions. This tool also performs the proper calculations for the humidity of the indoor space, which are important for thermal comfort calculations. Lastly, it is important to add that this tool enables the thermodynamic analysis of the heat pumps and other installations, which can be performed in dynamic terms.

The weather data were obtained from the PVGIS database for the location Athens in Greece [21] and specifically, the outdoor temperature, the direct beam solar irradiation and the diffuse horizontal solar irradiation were used with an hourly step. The model examines all the external opaque structural elements by solving the heat conduction equation using the finite volume method (1-D analysis). Also, the external solar irradiation on the walls is considered in the model, and the heat convection coefficients were selected at 8 W/(m²·K) (internal side) and at 25 W/(m²·K) (external side) [34]. Regarding the transparent structural elements (windows), the heat conduction and the solar irradiation that reaches the indoor space are considered. It is assumed that 10% of the solar irradiation that passes through the windows is directly absorbed by the air and the rest is absorbed by the internal sides of the structural elements in a rational way [22]. The thermal mass of the indoor space is selected to be double compared to the respective indoor air, aiming to also consider the thermal mass of the furniture. In the energy balance that is conducted at every time step, the infiltration, ventilation, and internal loads are also considered. Also, there is a proper control system for keeping the indoor space temperature within the desired temperature limits. The time step is selected to 5 min, and every structural element was separated into 200 nodes; values that were found after the proper mesh independence analysis.

In this work, different retrofitting actions are examined to improve the performance of the studied building. Typical values for their energy parameters were used, as well as the costs from the local market are considered in this work, after conducting a survey. Below, the selected renovation actions are described:

(A) Addition of external insulation (INS): Adding external insulation was considered with an insulation material with a thermal conductivity of 0.033 W/(m·K). The cost of adding insulation was EUR 20 per m² for the installation process and the specific material cost at 2 EUR/(m²·cm). For the scenario of adding 7 cm insulation (optimal economic scenario according to the results), the U-value of the retrofitted structural elements becomes around 0.4 W/(m²·K) [26], which is in accordance with the Greek legislation, while the cost of adding external insulation is around EUR 10,500.

(B) Windows replacement (GLZ): Triple windows were considered to replace the existing ones with a U-value = 0.6 W/(m²·K) and a g-value = 0.5. The cost of replacing all the windows is selected at EUR 3000.

(C) Installation of shading system for the summer period (SHD): Movable shading systems for reducing the solar irradiation that reaches the openings were considered. A reduction of 50% was considered, and the cost of shading for all the openings was selected at EUR 1500.

(D) Use cool dyes on the roof (CRF): The roof is dyed with a proper cool coating that has an absorbance of 30% and reflectance of 70%, aiming to reflect solar irradiation to reduce the cooling loads in the summer. The cost of this action is selected at EUR 1500.

(E) Installation of a mechanical ventilating unit with heat recovery (HRS): A proper mechanical ventilation unit with heat recovery effectiveness of 80% is selected. The cost for this retrofitting action is estimated at EUR 3500, including the maintenance cost.

(F) Replacement of the energy systems (HP): High-efficiency (air-to-water) heat pumps were considered for covering heating, cooling and DHW. Fan coils will be used as terminal units. The average efficiency (COP) of the system was 4.2 for heating, 5.4 for cooling and 3.8 for DHW. These values were found after conducting a preliminary thermodynamic investigation, and they correspond to highly efficient designs with optimized control systems. The cost for the energy system retrofitting was considered at EUR 4500 for the case of the renovated scenario, including the maintenance cost.

The different renovation techniques are examined separately, one by one, and the results proved that the addition of insulation is the most appropriate technique without a doubt. Specifically, a sensitivity analysis was considered for selecting the optimal insulation thickness and the optimal economic solution, which is also in accordance with the Greek legislation, was selected to be applied. Thus, this technique was considered the basis and all the scenarios with combined retrofitting techniques include the addition of insulation. In other words, the scenarios with combined retrofitting techniques that do not include the addition of insulation were not examined in this work. All the rest of the combinations were studied. Overall, 27 scenarios were examined (26 retrofitted scenarios and 1 baseline scenario).

The evaluation of the different retrofitting scenarios is conducted by applying various criteria. The first one is the electricity demand reduction compared to the baseline, which must be maximized. The second one is the minimization of the life cycle cost (LCC) of the investment for all lifetimes. In this analysis, the lifetime is chosen at 25 years, the discount factor at 3% and the cost of the electricity at 0.2 EUR/kWh_el. The third one is the CO₂ emissions avoidance every year compared to the baseline scenario. The CO₂ emissions factor was 0.3543 kg_CO2/kWh_el [35]. Regarding the thermal comfort analysis, the usual indices of PPD and PMV were considered. Specifically, the mean yearly PPD value was calculated, and the mean yearly absolute PMV values were found. Finally, the simple payback period is reported, although it is not such a strong economic index because it does not consider the economic benefits for the entire lifetime period. The costs of the selected technologies are reported in

Table 2. Summary of the selected costs.

Parameters	Values	References/Calculation Method
Insulation placement specific cost	20 EUR/m2	[36,37]
Insulation material cost	2 EUR/(m2·cm)	[38,39]
Total insulation cost	EUR 10,500	Calculation
Windows replacement specific cost	EUR 3000	[40] (specific cost around 330 EUR/m2)
Shading cost	EUR 1500	[41] (for pieces)
Cool dyes cost	EUR 1500	[42] (specific cost 15 EUR/m2)
Mechanical ventilation unit cost	EUR 3500	[43]
Heat pump cost	EUR 4500	[44]

with the respective references from the local market.

The final multi-criteria evaluation is conducted by using a global objective function, which is the geometrical distance of the different retrofitting scenarios from the “ideal” point. The goal is to minimize this index (F), and the scenario with the minimal value of (F) is the overall optimal design. In this multi-criteria evaluation procedure, the selected criteria to be used are the electricity reduction (ER), PPD, and LCC. The subscripts “min” and “max” correspond to the maximum and minimum values, respectively, of the studied retrofitting scenarios. For the LCC and the PPD, the goal is to minimize them, while for the ER, the goal is to maximize them; thus, there is a different definition of these goals inside the index F:

$$\mathrm{F}=\sqrt{{\mathrm{w}}_1\cdot {\left({\displaystyle \frac{\mathrm{P}\mathrm{P}\mathrm{D}-{\mathrm{P}\mathrm{P}\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{{\mathrm{P}\mathrm{P}\mathrm{D}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-{\mathrm{P}\mathrm{P}\mathrm{D}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\right)}^2+{\mathrm{w}}_2\cdot {\left({\displaystyle \frac{\mathrm{L}\mathrm{C}\mathrm{C}-\mathrm{L}\mathrm{C}{\mathrm{C}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}{\mathrm{L}\mathrm{C}{\mathrm{C}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{L}\mathrm{C}{\mathrm{C}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\right)}^2+{\mathrm{w}}_3\cdot {\left({\displaystyle \frac{\mathrm{E}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{E}\mathrm{R}}{\mathrm{E}{\mathrm{R}}_{\mathrm{m}\mathrm{a}\mathrm{x}}-\mathrm{E}{\mathrm{R}}_{\mathrm{m}\mathrm{i}\mathrm{n}}}}\right)}^2}$$

(46)

For the main scenario, the same weights (w_i) among the criteria studied are selected. Variable weights are studied in a sensitivity analysis aiming to check the optimal solution when the decision-making priorities vary.

2.4. Model Validation

The developed tool was validated using the European Standard (EN 15265:2007) [22], where 12 different cases are suggested for making comparisons. Specifically, this procedure regards the validation of the calculations regarding the cooling and heating thermal loads. The proper modifications in the present code were applied, aiming to investigate the cases of the standard and use the same inputs, as well as the same weather data. According to the standard, the deviation of every load must be found using the sum of heating and cooling as a reference load. In this direction, the heating load calculation leads to an average deviation of 6.9% and for cooling to 5.3% among the examined scenarios. These are relatively low values, which indicate that the developed model is valid. Figure 4a shows the heating load calculation and Figure 4b the cooling load calculation for the twelve examined cases.

Moreover, Appendix A includes verification evidence of the developed tool by conducting a comparison with the EnergyPlus software [45]. This comparison is conducted in terms of thermal load analysis, as well as thermal comfort conditions.

3. Results and Discussion

The present section is separated into two parts. In the first one, a parametric analysis for variable insulation thickness is conducted, and in the second one, a detailed multi-criteria analysis is performed.

3.1. Optimal Insulation Thickness

The first part of the present analysis is a parametric investigation of the insulation thickness of the external structural elements. This analysis is very important because the addition of the insulation is a critical retrofitting action, and its thickness is a vital parameter for this work. The variations in the heating load, cooling load, and total electricity demand expressed in yearly energy quantities [kWh] are given in Figure 5. Moreover, Figure 6 depicts the influence of the insulation thickness (from 0 to 12 cm) on energy demand reduction and the LCC, and Figure 7 illustrates the mean annual PPD and the annual CO₂ emissions avoidance.

Higher insulation thickness leads to lower heating and cooling loads, as well as to lower electricity demand, as shown in Figure 5. These are reasonable results, and they indicate that the addition of a small insulation thickness is vital, while as the insulation addition increases, the impact on the results is significantly reduced. For high insulation thicknesses (e.g., over 7–8 cm), there is no significant reduction of the reported parameters. Only the heating loads have a greater reducing trend compared to cooling and electricity curves, but it is a relatively low reduction rate. In other words, this figure proves that adding a few centimeters of insulation is very important, but there is an “optimal” limit or an “optimal” insulation thickness, which can be defined by considering also economic factors.

Figure 6 and Figure 7 show that the increase in insulation thickness increases energy demand reduction and the CO₂ emissions avoidance and reduces the mean yearly PPD. All the previous variations are monotonic, while the LCC has a different behavior. Specifically, the increase in insulation thickness reduces the LCC by up to 7 cm, and after this limit, the LCC increases but at a low pace. Thus, there is an optimal insulation thickness that minimizes the LCC at EUR 34,419, and in this case, there is an optimal economic behavior. Also, it is valuable to state that in this case, there is a high energy demand reduction (61.39%), high CO₂ emissions avoidance (3858 kg_CO2/year) and low mean yearly PPD value (around 10%). Thus, this case with a 7 cm insulation thickness is selected to be the proper solution for consideration as a suitable design. Moreover, in this case, the U-value of the structural elements is 0.4 W/(m²·K), which follows the Greek legislation. Therefore, this design is acceptable. From the thermal comfort point of view, the increase in the insulation thickness clearly enhances the indoor space conditions by reducing the PPD, which reaches the desired levels around 10% with an insulation thickness of about 7 cm or more.

It is useful to comment on the previous result and to highlight the need for conducting energy and economic analysis simultaneously to select the proper insulation thickness in every case. Specifically, the increase in insulation thickness leads to better energy indices; however, after a limit, there is a slight improvement in energy indices, something that cannot be supported by the economic point of view. Practically, after the critical limit of 7 cm, the extra insulation thickness cannot be economically viable because its capital cost cannot be covered by the life cycle savings that exist due to the reduced electricity demand.

3.2. Multicriteria Evaluation of the Different Retrofitting Scenarios

This section presents the different retrofitting scenarios and their performance. Specifically, 26 different retrofitting scenarios are studied, and the baseline scenario (existing situation) is presented in this section. The results for the most critical indices are presented in Figure 8, Figure 9, Figure 10 and Figure 11.

Specifically, Figure 8 depicts the energy demand reduction of the 26 retrofitting scenarios compared to the baseline scenario. Figure 9 illustrates the LCC for all the scenarios (retrofitting and baseline), and Figure 10 shows the results for the mean yearly PPD for all the scenarios (retrofitting and baseline). Figure 11 shows the yearly CO₂ emissions avoidance for the retrofitting scenarios.

Practically, Figure 8 and Figure 11 do not include the baseline scenario because the reported results are based on the deviation compared to it. Figure 8 indicates that the electricity reduction compared to the baseline scenario ranges from 1.04% for the case (SHD) up to 77.57% for the case (INS + HP + GLZ + SHD + HRS + CRF). The one-solution retrofitting scenarios present generally low reduction percentages except for the use of the insulation (INS), where the reduction is 61.39% and the installation of new energy systems (HP) with 36.15%. Thus, the retrofitting action of (INS) is the most appropriate one, and all the remaining combined scenarios incorporate it. Generally, combining multiple retrofitting actions leads to a greater reduction in a building’s electricity demand. Figure 9 shows that the LCC of the baseline scenario is EUR 61.77 k, and it is greater than most of the studied retrofitted scenarios. The exception is the single solutions, including SHD, CRF, GLZ, and HRS, where a small increase is observed. This result shows that there is no economic reason to make the renovations in a building if it is uninsulated. The optimal economic scenario is the (INS + HP) with LCC = EUR 32.00 k. However, this scenario is not optimal energetically, presenting a 72.60% reduction in electricity, lower than the 77.57% for the case (INS + HP + GLZ + SHD + HRS + CRF). On the other hand, the scenario (INS + HP + GLZ + SHD + HRS + CRF) is more expensive with LCC = EUR 38.43 k than the (INS + HP).

Figure 10 shows the yearly average PPD for the studied cases. The baseline scenario presents a value of 14.82% and the minimum value (optimal) is found for the (INS + HP + GLZ + SHD + HRS + CRF) with 9.44%. The scenarios with combined retrofitting actions present a mean yearly PPD close to 10% and thus, there is a significant thermal comfort enhancement in these cases. Also, the application of insulation leads to thermal comfort enhancements, while the rest of the scenarios with one retrofitting action are not efficient from a thermal comfort point of view. The achievement of PPD values up to 10% is a milestone for creating acceptable thermal comfort conditions [46].

Figure 11 depicts the yearly CO₂ emissions avoidance, which is maximized for the (INS + HP + GLZ + SHD + HRS + CRF) scenario at 4874 kg_CO2/year. The rest of the scenarios with combined retrofitting actions also present significant CO₂ avoidance compared to the baseline scenario, except for the single retrofitting action scenarios of CRF, HRS, SHD, and GLZ.

Table 3. Summary of the main results for all the scenarios studied.

Scenarios	Heating Demand	Cooling Demand	Electricity Demand	PMV	PPD	SPP	LCC	CO2 Avoidance	ER
	(kWh)	(kWh)	(kWh)			(Years)	(EUR)	(kg/year)	(%)
Baseline	29,595	12,242	17,735	0.6295	14.82%	-	61,765	-	-
INS	4779	4394	6847	0.4566	10.00%	4.86	34,419	3857.8	61.39
GLZ	28,059	11,937	17,121	0.6286	14.79%	24.44	62,627	217.5	3.46
SHD	29,657	11,626	17,550	0.6259	14.71%	40.57	62,621	65.5	1.04
HRS	28,118	12,082	17,189	0.6283	14.80%	32.05	63,364	193.4	3.08
CRF	31,337	9289	17,331	0.6202	14.40%	18.57	61,858	143.1	2.28
HP	29,595	12,242	11,324	0.6295	14.82%	3.51	43,936	2271.6	36.15
INS + GLZ	3404	4107	6293	0.4609	10.04%	5.93	35,491	4053.9	64.52
INS + SHD	4818	3390	6525	0.4378	9.70%	5.39	34,799	3971.7	63.21
INS + HRS	3418	4234	6340	0.4473	9.88%	6.18	36,155	4037.2	64.25
INS + CRF	5025	3911	6768	0.4501	9.89%	5.50	35,645	3885.6	61.84
INS + HP	4779	4394	4860	0.4566	10.00%	5.85	31,998	4561.8	72.60
INS + HP + GLZ	3404	4107	4537	0.4609	10.04%	6.85	33,873	4676.2	74.42
INS + HP + SHD	4818	3390	4630	0.4378	9.70%	6.32	32,699	4643.1	73.89
INS + HP + HRS	3418	4234	4569	0.4473	9.88%	7.05	34,487	4664.7	74.24
INS + HP + CRF	5025	3911	4792	0.4501	9.89%	6.40	33,262	4585.9	72.98
INS + HP + GLZ + SHD	3424	3228	4333	0.4442	9.75%	7.30	34,664	4748.4	75.57
INS + HP + GLZ + HRS	2089	3947	4255	0.4485	9.89%	8.00	36,391	4776.2	76.01
INS + HP + GLZ + CRF	3634	3595	4459	0.4547	9.91%	7.37	35,101	4703.9	74.86
INS + HP + SHD + HRS	3441	3229	4336	0.4287	9.56%	7.49	35,176	4747.2	75.55
INS + HP + SHD + CRF	5071	2952	4574	0.4324	9.61%	6.87	34,004	4663.0	74.21
INS + HP + HRS + CRF	3643	3751	4497	0.4416	9.76%	7.58	35,736	4690.3	74.64
INS + HP + GLZ + SHD + HRS	2099	3066	4048	0.4311	9.57%	8.43	37,173	4849.2	77.17
INS + HP + GLZ + SHD + CRF	3665	2763	4268	0.4351	9.62%	7.82	35,938	4771.4	75.93
INS + HP + GLZ + HRS + CRF	2293	3435	4171	0.4425	9.75%	8.51	37,602	4805.6	76.48
INS + HP + SHD + HRS + CRF	3677	2791	4277	0.4227	9.47%	8.02	36,469	4768.3	75.88
INS + HP + GLZ + SHD + HRS + CRF	2307	2602	3978	0.4230	9.44%	8.93	38,426	4874.3	77.57

includes the main results for all the scenarios studied.

The next step is the application of the multi-criteria analysis, applying the objective function with the same weights among the selected criteria. Specifically,

Table 4. Summary of the results for optimal designs (applying the same weights among the studied criteria) and the baseline scenario. The ranking starts from the optimal scenario, continues with the next optimal designs, and includes the baseline scenario.

Scenarios	Eheat	Ecool	Eel	PMV	PPD	LCC	SPP	CO2 Avoidance	Eel Reduction
	(kWh)	(kWh)	(kWh)			(EUR)	(Years)	(kgCO2/year)
INS + HP + SHD	4818	3390	4630	0.4378	9.70%	32,699	6.32	4643	73.89%
INS + HP + SHD + CRF	5071	2952	4574	0.4324	9.61%	34,004	6.87	4663	74.21%
INS + HP + GLZ + SHD	3424	3228	4333	0.4442	9.75%	34,664	7.30	4748	75.57%
INS + HP + SHD + HRS	3441	3229	4336	0.4287	9.56%	35,176	7.49	4747	75.55%
INS + HP + CRF	5025	3911	4792	0.4501	9.89%	33,262	6.40	4586	72.98%
INS + HP + HRS	3418	4234	4569	0.4473	9.88%	34,487	7.05	4665	74.24%
INS + HP	4779	4394	4860	0.4566	10.00%	31,998	5.85	4562	72.60%
Baseline	29,595	12,242	17,735	0.6295	14.82%	61,765	-	-	-

includes the results of the seven most appropriate scenarios, starting from the best-case scenario (INS + HP + SHD) and continuing with the next choices (INS + HP + SHD + CRF, INS + HP + GLZ + SHD, INS + HP + SHD + HRS, INS + HP + CRF, INS + HP + HRS, INS + HP), while also including the baseline scenario in this table. The optimal scenarios present significant enhancements compared to the baseline scenario. For the global optimal choice (INS + HP + SHD), the electricity reduction is 73.89%, the yearly CO₂ avoidance is 4643 kg_CO2, and the LCC is EUR 32,699, which is significantly lower than the EUR 61,765 of the baseline scenario (47% reduction). Moreover, the simple payback period is 6.32 years, the mean yearly PPD is 9.70%, while in the baseline scenario, it is 14.82%, and the mean yearly absolute PMV is 0.4378, while in the baseline scenario, it is 0.6295. Keeping the PPD under 10% and the absolute PMV under 0.5 is evidence of having acceptable thermal comfort conditions in the indoor space [46].

Practically, it is useful to state that the global optimal scenario includes external insulation and energy systems replacement, which are the most efficient retrofitting actions individually, while it also includes a third one, which is the external shading during the summer. So, this result proves that summer shading is a very efficient technique, and it can be favorable to be combined with other retrofitting actions; thus, it must be selected as a secondary retrofitting action in the building retrofitting process.

It is very useful to state that the optimal scenario demands 4630 kWh of electricity on a yearly basis. In the case that photovoltaics are installed on the roof with zero azimuth angle and 30° slope, then 2.7 kW_p nominal power is required to cover this load with a net-metering strategy. This calculation was performed using the PVGIS tool [21] for crystalline silicon photovoltaics and 5% inverter losses. This capacity can be achieved with 15 m² of photovoltaic panels, which is a relatively small area that can be easily installed in the building. Therefore, there is the possibility of creating a zero-energy building by combining the renovation actions with a reasonable photovoltaic area.

3.3. Dynamic Analysis

The dynamic results regarding the energy and the thermal comfort indices for the baseline and the optimal renovated scenario (INS + HP + SHD) are presented in this section. This analysis aims to provide a clear image regarding the load reduction, the energy reduction, and the improvement of the living conditions.

Figure 12 shows the yearly variation in the heating load in [W] and of the cumulative heating energy demand in [kWh] for the baseline and the renovated scenario. It is obvious that there is a significant reduction in the load in the renovated scenario; a very interesting result that highlights the improvement of the building envelope as a favorable renovation action. Specifically, the maximum heating load in the baseline scenario is found at 17.6 kW, while in the renovation scenario at 3.8 kW, presenting a reduction of about 78%. Furthermore, the trend of the curves for both scenarios is similar because they are affected by the same factors and mainly by the ambient temperature and the solar insolation. The heating energy is found at 29,595 kWh for the baseline and at 4818 kWh for the renovated scenario, presenting a reduction of about 84%.

Figure 13 illustrates the yearly variation in the cooling load in [W] and of the cumulative cooling energy demand in [kWh] for the baseline and the renovated scenario. The curves follow similar trends, but the renovated scenario has significantly reduced values. Specifically, the maximum cooling load is found at 17.0 kW in the baseline and 3.6 kW in the renovated scenario, presenting a significant reduction of about 79%. The maximum cooling loads are observed during the summer and especially in July and August. The cooling energy is calculated at 12,242 kWh for the baseline and at 3390 kWh for the renovated scenario, presenting a reduction of about 72%.

Figure 14 exhibits the yearly variation in the electrical load demand in [W] and of the cumulative electrical energy demand in [kWh] for the baseline and the renovated scenario. There is reduced electrical load in the renovated scenario, with a maximum value at 1.3 kW, while the baseline presents 6.3 kW. The maximum electrical load reduction is found at 79% and this is a very interesting result because it leads to an important reduction of the peak demand by the grid. Regarding the electrical energy demand, it was found at 17,735 kWh at the baseline scenario, while the renovation scenario presents reduced needs at 4630 kWh, with an observed reduction of 74%. Furthermore, it is interesting to note that the electricity demand profile presents maximum values during the winter and during the summer, when there are high heating and cooling needs. It is not a smooth profile, but it has variations during the year. However, these variations are more intense in the baseline scenario, while the renovated scenario has a smoother profile. This is important because this fact leads to the elimination of huge peaks that lead to oversizing the system and to present peak load demands. Therefore, the renovation also leads to the development of buildings that are easier to manage by the electricity grid, and widespread implementation across a region can provide further advantages to the local electricity network.

The next presented parameters regard the thermal comfort analysis and specifically, Figure 15 and Figure 16 illustrate the yearly variation in PPD and PMV, respectively. These indices must be close to zero to achieve optimal thermal comfort standards. Both figures show that the renovated scenario has significantly improved indices, and this fact proves the clear superiority of the renovated scenarios from the thermal comfort point of view. Specifically, the mean yearly absolute value of the PMV was found at 0.6295 for the baseline and at 0.4378 for the renovated scenario, presenting a reduction of 30%. The mean yearly value of the PPD was found at 14.82% for the baseline and at 9.70% for the renovated scenario, presenting a reduction of 35%.

3.4. Sensitivity Multi-Criteria Analysis

The goal of this investigation is to examine the impact of the weights of the optimization objective function on the final determination of the global optimal choice. A total of 13 different combinations of weights are studied by considering symmetrical choices among the weights. The increased value of weight (w₁) corresponds to cases where thermal comfort is a priority, the increased value of weight (w₂) corresponds to cases where the cost is a priority, while the increased value of weight (w₃) corresponds to cases where the energy reduction is a priority.

Table 3 summarizes the results of this sensitivity analysis. The previous analysis of Section 3.2 used cases with the same weight, which is the optimization case 1 (OC1) in

Table 5. Summary of the optimal scenarios for different optimization cases by changing the weights of the criteria.

Optimization Cases	w1	w2	w3	Optimal Scenario
1	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	INS + HP + SHD
2	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	INS + HP + SHD
3	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	INS + HP + SHD
4	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$4$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	INS + HP + SHD
5	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	INS + HP + SHD
6	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	INS + HP + SHD + CRF
7	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	INS + HP + SHD
8	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	INS + HP + SHD
9	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	INS + HP + SHD
10	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$6$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$3$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	INS + HP + SHD
11	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	0	INS + HP + SHD
12	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	0	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	INS + HP + GLZ + SHD + HRS + CRF
13	0	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	${\displaystyle \raisebox{1ex}{$1$}\!\left/ \!\raisebox{-1ex}{$2$}\right.}$	INS + HP + SHD

. In this case, the optimal renovation scenario is the one with (INS + HP + SHD).

It is very interesting that this scenario is the optimal solution for 11 out of the 13 examined cases. Only in OC6, the optimal design is (INS + HP + SHD + CRF), which practically adds cool dyes. In this case, where the weight assigned to thermal comfort was higher, it is proven that, in terms of thermal comfort being the most important index, the application of cool dyes is a vital solution.

Moreover, OC12, which neglects the cost of the system, leads to the optimal scenario with all the renovation actions together (INS + HP + GLZ + SHD + HRS + CRF). This is a reasonable result because, as has been previously reported, adding extra renovation action enhances thermal comfort and reduces the electricity demand. However, this optimization scenario is not so interesting because the cost is a critical parameter that cannot be easily neglected in a real application. In cases with a great renovation subsidy, this scenario presents a high interest because, in these cases, the cost criterion is not a priority.

Overall, the sensitivity analysis confirms that the selected scenario is robust across different weightings. Thus, it is strongly recommended to include the proper shading system, insulate the external structural elements, and install efficient heat pumps in all renovation case studies.

4. Conclusions

The renovation of the existing building stock is a critical challenge for the near future, aiming to achieve sustainability. Retrofitting is vital for reducing the energy demand, decarbonizing the building sector and improving indoor living conditions. This work investigates different renovation scenarios in a systematic way, and the multi-criteria analysis is applied. This investigation is conducted with a developed dynamic simulation model in MATLAB for an uninsulated building in Athens, Greece, as the baseline scenario. Specifically, this energy model belongs to a new tool called T-DEOS, which simulates with accuracy the dynamic behavior of buildings and energy systems. The key findings of this paper are provided below:

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The optimum economic insulation thickness is found to be 7 cm (minimization of LCC), and this design leads to an acceptable U-value according to Greek legislation for the studied climate zone.

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Among the investigated single renovation action scenarios, the application of external insulation was found to be the most effective, while the replacement of the energy systems with an efficient heat pump is the second most effective solution. The rest of the renovation actions are not effective as stand-alone solutions if the building remains uninsulated.

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The renovation scenarios with combined actions, including the addition of insulation, present a significant enhancement in energy, thermal comfort, and economic terms. Important synergies among the studied retrofitting actions exist, and so the combined renovation scenarios are more beneficial than the single retrofitting action scenarios.

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According to the multi-criteria evaluation, the global optimal scenario is the one with external insulation, a new heat pump and summer shading (INS + HP + SHD). In this case, the calculated electricity savings were by 73.9% compared to the baseline scenario, the LCC was EUR 32.7 k, the simple payback period was 6.3 years, the yearly CO₂ emissions avoidance was 4.6 tn_CO2, and the mean yearly PPD was 9.7%.

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The sensitivity analysis proved that most of the studied cases led to the same optimal solution (INS + HP + SHD). In the case that thermal comfort was a priority, the cool dyes in the roof could be added. Also, if the cost was not considered as a criterion, then the application of all the renovation actions was the optimal design.

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Generally, the variation in the weights for the criteria in the objective function was not so important for the selection of the optimal renovation action. This fact proves that the (INS + HP + SHD) is a strong optimal solution for the present analysis.

The present analysis was conducted under the climatic conditions of Athens, Greece. Consequently, the extracted conclusions apply to locations with similar climatic characteristics. Mediterranean cities exhibit comparable climate conditions. Therefore, the findings of this study can be reasonably extended to such regions. Moreover, the present work considers a symmetrical building envelope, aiming to facilitate the generalization of the results to other building shapes that do not exhibit significantly different length-to-width ratios.

In the future, extra renovation actions can be applied to the building, such as the use of phase change materials, thermochromic dyes, thermochromic and thermoelectric windows, as well as the application of renewable energies. Moreover, a detailed environmental analysis, including the embodied emissions of the retrofitting technologies, can be carried out. Lastly, this multi-criteria evaluation can be conducted for different climatic conditions.