*Article* **Identification of Cost-Optimal Measures for Energy Renovation of Thermal Envelopes in Different Types of Public School Buildings in the City of Valencia**

**María Esther Liébana-Durán 1,\*, Begoña Serrano-Lanzarote <sup>1</sup> and Leticia Ortega-Madrigal <sup>2</sup>**


**Abstract:** In order to achieve the EU emission reduction goals, it is essential to renovate the building stock, by improving energy efficiency and promoting total decarbonisation. According to the 2018/844/EU Directive, 3% of Public Administration buildings should be renovated every year. So as to identify the measures to be applied in those buildings and obtain the greatest reduction in energy consumption at the lowest cost, the Directive 2010/31/EU proposed a cost-optimisationbased methodology. The implementation of this allowed to carry out studies in detail in actual scenarios for the energy renovation of thermal envelopes of public schools in the city of Valencia. First, primary school buildings were analysed and classified into three representative types. For each type, 21 sets of measures for improving building thermal envelopes were proposed, considering the global cost, in order to learn about the savings obtained, the repayment term for the investment made, the percentage reduction in energy consumption and the level of compliance with regulatory requirements. The result and conclusions will help Public Administration in Valencia to draw up an energy renovation plan for public building schools in the city.

**Keywords:** public school buildings; energy efficiency; optimal cost; energy renovation; public buildings

#### **1. Introduction**

It is a fact that the European Union is embarked on a path towards the conversion of economy and society with the aim of locating both of them in a more sustainable territory. A strategic framework is determined to promote a thriving, modern, competitive and climate-neutral economy. Among long-term objectives, a reduction of 90% of emissions by 2050 is included, compared to the levels in 1990 [1]. Currently, 36% of the EU's CO2 gas emissions comes from the building stock, and almost 50% of final energy consumption is used for heating and cooling [2]. Therefore, to achieve these goals it is essential to renovate the building stock, by improving the energy efficiency and fostering total decarbonisation.

The current rate of building renovation is between 0.4% and 1.2%. This means that, in order to reach long-term European targets by 2050, it is necessary to double the rate of interventions in existing buildings [3]. Europe is driving a wave of renovation, prioritizing the improvement of the worst energy-efficient buildings, including schools and hospitals [4].

According to the 2018/844/EU Directive, 3% of public administration buildings should be renovated every year. However, the large number of properties, the lack of financing, information and planning are some of the obstacles found.

After checking some interventions in Spanish schools, the aforementioned drawbacks make performances consequently be carried out in two ways: a comprehensive renovation of each building or a phased renovation. The latter allows simultaneous performance in several buildings by improving a specific element, for example, windows, facades,

**Citation:** Liébana-Durán, M.E.; Serrano-Lanzarote, B.; Ortega-Madrigal, L. Identification of Cost-Optimal Measures for Energy Renovation of Thermal Envelopes in Different Types of Public School Buildings in the City of Valencia. *Appl. Sci.* **2021**, *11*, 5108. https:// doi.org/10.3390/app11115108

Academic Editors: Tiziana Poli, Andrea Giovanni Mainini, Mitja Košir, Juan Diego Blanco Cadena and Gabriele Lobaccaro

Received: 7 April 2021 Accepted: 28 May 2021 Published: 31 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

heating systems, lighting, etc., or by installing renewable energy equipment. Based on the mentioned points, a simultaneous enhancement in several buildings makes it possible to jointly promote performances, to save time in project preparation and processing, as well as favour a further provision of financial assistance, since the projects are promoted by the public sector.

The main issue is that public administrations do not always have enough data or studies on school buildings or potential improvement scenarios, so there are no results that could be obtained in terms of energy saving. This means that, for example, the same renovation measure is implemented in all types of buildings, without knowing that whether in some of them a reduction of the energy demand before renovating heating systems could be necessary. Moreover, another example is those building types in which improvements in facade insulation could be suitable instead of window replacement.

So as to establish those performances with the greatest reduction in energy consumption at the lowest cost, the Directive 2010/31/EU proposed a cost optimisation methodology. Regarding its implementation in schools, the cost-optimal reports in the EU countries during 2018 [5] show that, whereas for the residential building sector some reference buildings have been established in all countries, for those buildings in the tertiary sector, in particular school buildings, not all countries have drawn up reports on them. Moreover, in those studied, there is no building classification, for example, they are grouped as "educational buildings" or "schools," as in the case of Slovakia and Germany, in which only a single building type is studied. Another example can be found in the Czech Republic with a "nursery school" or in the United Kingdom, with a "secondary school." Ferrara et al. [6] made a review on 88 scientific works based on the implementation of optimal-cost based analysis of calculation methods for designing and optimizing nearly zero-energy buildings in Europe. They show that only 4% of the papers studied include school buildings as case study.

The implementation of this methodology in school buildings shows great potential of growth. In addition, it provides local authorities with specific data on energy saving, maintenance costs, interventions, repayment terms, etc.

Furthermore, some studies on energy renovation in school buildings are worth mentioning. Several of them propose renovation measures for thermal envelopes, heating and lighting systems, use of renewable energy sources, etc. For example, Stocker et al. [7] use a calculation method focused on a standard energy demand with life cycle cost methods. Their results show that the optimal performance according to costs represents a value around 50 to 60 kW h/m2p.a regarding heating and cooling energy demand. Likewise, Dalla et al. [8] implemented cost-optimal methodology in some existing school buildings located in the north-east of Italy. They propose 120 sets of measures, including interventions in thermal envelopes, in systems (photovoltaic system and lighting replacement) and replacement of thermal generators (condensing boiler, biomass boiler or electrical heat pump).

Other authors tried to identify measures that enable to reach nearly zero energy building (nZEB) through an analysis from the cost-benefit perspective, as in the case of Lou et al. [9] who look into energy saving and electricity production schemes in a specific school building by using the building energy set eQUEST. The results show that improvement measures such as high-performance in building thermal envelopes, energyefficient air-conditioning systems and lighting fixtures, as well as building-integrated photovoltaic panels (BIPV), allow to obtain zero energy buildings. Gaitani et al. [10] analysed some school buildings in terms of energy efficiency and cost optimisation, and designed a comprehensive action plan for renovation, a Technical and Financial Toolkit. Likewise, this study is framed within the European project ZEMedS, focused on the renovation of schools in the Mediterranean area to reach nZEB. With the aim of upgrading school buildings and turn them into nZEB, Ferrari et al. [11] focused their research on criteria laid down for the intervention on historical school buildings officially protected by the Italian Cultural Heritage. They assessed an Italian historical school building, and

proved that the nZEB goals could be reached by retrofitting the building itself through measures compatible with the constraint arising from the protection of cultural heritage, and significantly reducing primary energy consumption. Marrone et al. [12] state that a large number of the Italian school building stock has implemented energy retrofitting measures, but the strategies suggested are often taken according to the best and most common practices (considering average energy saving), but not supported by a proper energy research. They evaluated 80 Italian school buildings by using cluster analysis, so as to provide a methodology capable of identifying the best energy retrofitting measures from the cost-benefit viewpoint. Mora et al. [13] state that a large number of Italian schools were built before the entry into force of energy and seismic regulations. Therefore, they simultaneously studied energy retrofitting and seismic upgrading in one school building.

The European project SHERPA (Share knowledge for Energy Renovation in buildings by Public Administrations) [14], is aimed at strengthening the abilities of public administrations at regional and local level to improve energy efficiency in their public buildings' stock, and reduce CO2 emissions. Soto et al. [15] describe the general auditing protocol devised by SHERPA and illustrate by carrying out an audit in one school building. They conclude that in the case of school buildings, in order to reach nZEB, energy efficiency is not always profitable (unless photo-voltaic energy is produced in situ). However, there are other benefits, such as improving comfort and preparing for the climate change.

In order to ease decision-making in future interventions, Jradi [16] identifies the impact of renovation measures on buildings, once enhancements in school buildings are made.

Before proposing different improvement energy measures, some authors establish a classification of school buildings according to different types based on energy factors, year of construction, building geometry, etc., which enable to find renovation solutions for each type. For example, Arambuela et al. [17] suggest a cluster analysis method that supports the definition of representative architectural types, and the identification of a small number of essential parameters, to assess energy consumption for air heating and the production of hot water in 60 schools in Treviso, Italy. Dimoudi et al. [18] also look into the development of school building types over the time within a Greece region, identify the most representative building types and propose seven improvement scenarios. Likewise, in order to classify the public school buildings in Rome, Santoli et al. [19] make use of data on schools, such as composition, (in terms of number, type and size of buildings), energy label of buildings in property of the municipality, which describe quality in terms of energy consumption for building's thermal envelopes and energy consumption, as heat is transferred from several thermal power plants to school buildings. Katafyogiotou et al. [20] and Castro [21] are authors that should be mentioned as an example of classification models. They propose improvement measures in representative school building types in Cyprus and northern Spain.

Through their analyses, Ferrara et al. [6] define two different methods used for the selection of measures in cost-optimal studies. The first one is a manual approach (selecting a defined number of sets of measures and calculating and comparing the global cost values), the other is an automated search (using computer-generated optimisation algorithms). They also establish two methods for energy performance calculation: one simplified (using simplified methods, for example, the quasi-steady state method defined by the UNI EN 13790 standard, and national implementations) and another dynamic (using dynamic simulation tools that allow detailed and precise energy results). According to this classification, this article uses a manual selection method and a simplified performance calculation method.

This article shows the results of adopting the cost-optimal methodology for housing developed by the IVE (Instituto Valenciano de la Edificación, the Valencia Institute of Building), for school building assessment. Specifically, this study applies this methodology to 3 schools within the city of Valencia, looking into energy performance and proposing a series of sets of improvement measures in thermal envelopes. Each school building is representative of a group in the city. As a result, a tool is obtained to identify the typeenergy saving and CO2 emissions through each set of measures, as well as the global cost over 30 years.

On the other hand, Spanish energy saving regulation, the CTE DB HE [22], sets out a number of requirements or demands for retrofitted buildings. This article also highlights these requirements, and shows to what extent they would be complied with each set of measures proposed.

Finally, the tool or system used and the analysis of the results provide a series of indicators on its usefulness as instruments and data for Public Administration to enable decision-making and planning energy renovation in similar school buildings.

#### **2. Materials and Methods**

#### *2.1. Cost Optimisation Methodology*

The methodology used in this study is that established for building energy renovation by the Directive 2010/31/EU on energy efficiency in buildings [23], and the Delegated Regulation 244/2012/EU complementing such directive, in particular the cost optimisation methodology [24]. According to Annex 1 of the regulation, this methodology is structured in the following sections:


Likewise, in the study for the energy analysis of representative buildings and improvement measures, Ce3X v2.3 is used, the Spanish computer software for energy calculation that also verifies the compliance with the CTE DB-HE.

For global cost calculation, a tool developed by the IVE was used, which had been previously applied to different studies on residential buildings.

#### 2.1.1. Buildings under Study

In the city of Valencia there are approximately 90 public primary schools. For this research, general data regarding 135 school buildings was obtained, corresponding to 79 schools.

An analysis of construction and architectural features of these buildings has enabled to group them together into six different building types.

The study is focused on three building types (A, B and C). These were built before the entry of the first Spanish Regulation on thermal characteristics of buildings NBE CT 79 into force, so none of them has thermal envelope insulation, nor have they been recently renovated because of their relative age.

The main factors that differentiate these school building types are structure and date of construction. Type A building was built using brick load-bearing walls and metal joints, and types B and C were built using a concrete structure. In type A the roof was made of ceramic tile mounted on wood, whereas the roof in types B and C was built by using a slab flat or pitched under the layers that make up the roof. Type B and C buildings have wooden windows, whereas type C includes metal windows.

In addition to these construction differences, the design and interior spaces vary according to the three types. Type C buildings are elongated or L-shaped buildings, their facade has a historicist character, and were built between 1945 and 1955. Type B buildings were built in the 1960s and follow the designs of the Modern Movement. They have a greater number of floors and are elongated in shape. Type C buildings were built in the 1970s and they are X or XX-shaped (Figure 1).

**Figure 1.** Examples of X or XX-shaped buildings.

These three building types (A, B and C), represent a total of 6, 11 and 29 schools respectively, that is to say, 46 school buildings.

For each type, a representative model school building is selected (Figure 2). They were built from school prototypes, adapting the architectural design to the site itself. This makes selected school buildings be representative in the city of Valencia, and also in other towns and municipalities.

**Figure 2.** Representative school buildings in the city of Valencia built before 1979. (**a**) Type A school; (**b**) type B school; (**c**) Type C School.

Type A and B buildings have a high historical value (listed or officially protected), or a unique architectural design. This means that any energy renovation cannot alter the building geometry and exterior design.

Although some of them have undergone minor renovations, such as window replacement, the initial condition of the buildings is taken for the energy study as a reference, and former potential improvements are ignored, so that they serve as a baseline to any building type. Table 1 includes the main characteristics of each building type, and Table 2 shows the thermal transmittance of construction elements in the thermal envelope for each building type in its initial state considered for energy study.


**Table 1.** Specifications and characteristics of building types.

**Table 2.** Thermal transmittance, U (W/m2K), of construction elements in thermal envelope of representative school buildings in their initial state L0.


2.1.2. Energy Efficiency Measures and Sets of Measures

This study is focused on proposing passive renovation measures, that is to say, measures to implement in the thermal envelope, so renewing air conditioning system, ventilation, lighting, renewable energy, etc., is not considered.

The buildings selected represent a group of school buildings according to specific architectural aspects, but many of them are part of a school complex, where other buildings are introduced, such as classrooms, canteens, gymnasiums, etc. This involves that requirements differ according to different typology, although the design and construction time of the main building are similar.

On the other hand, facility renovations are driven by the time when the existing ones break down or when a necessary renovation due to obsolescence is convenient and affordable. It would be unrealistic to plan the sudden replacement of all the facilities existing in school buildings. For all these reasons, the energy renovation measures proposed are aimed at reducing the energy demand in buildings.

The passive measures outlined are window and door replacement (W), including solar protection elements, and insulation upgrading in facades (F) and roofs (R). These measures can be implemented separately or combined with each other, resulting in the improvement of seven elements or combinations of elements of the thermal envelope.

In addition, three levels of energy demand are considered in relation to the transmittance of thermal envelope elements (L1, L2 and L3). These values are set according to specific regulatory requirements.

In particular, the intermediate level, L2, includes the minimum values set by current Spanish regulations on energy efficiency, the CTE DB-HE 2019 [22]. Level L3 corresponds to the guideline values of transmittance provided in Annex E of the aforementioned regulation, for pre-dimensioning construction solutions in private residential buildings. With these values, the requirements established for the global heat transmission ratio through the thermal envelope are fully met.

The strategic energy renovation in school buildings introduces a first level, L1, whose transmittance requirements are less restrictive than those set by current regulations. Thus, transmittance values in this level meet minimum requirements set by the same regulations in its initial version CTE DB-HE 2006 [25]. This is proposed with the aim of analysing whether requirements established by the former regulation reach cost-optimal results similar to those obtained with the conditions currently required.

Transmittance for each requirement level is shown in Table 3.

**Table 3.** Thermal transmittance, U (W/m2K), of thermal envelope elements according to different energy demand levels.


<sup>1</sup> CTE DBHE-2006. Values according to Table 2.2.-HE1 for climate zone B3. <sup>2</sup> CTE DBHE-2019. Values according to Table 3.1.1a-HE1 for climate zone B. <sup>3</sup> CTE DBHE- 2019. Values according to Table a-Annex and HE for climate zone B.

In total, 21 sets of improvement measures are proposed for the energy renovation strategy, according to each building type, combining three energy demand levels (L1, L2 and L3) and seven sets of improvement measures for thermal envelope elements (Table 4).

**Table 4.** Set of measures for thermal envelope according to a combination of energy demand levels and elements in thermal envelope to be renovated.


The improvement measures proposed for representative school buildings, type A and B, whose geometry and facade design cannot be altered, are found in facades, introducing inner insulation plasterboard lining with metal framing, and on the inside of sloping roofs in type A buildings, through a removable plaster false ceiling with thermal insulation. Both for facades and flat roofs in type C buildings, different exterior thermal insulation systems are proposed.

The type of insulation and the thickness used for facades and roofs, as well as the characteristics of glazing are different, depending on the transmittance to be obtained.

#### 2.1.3. Calculation of Global Costs of Sets of Measures

The calculation of global costs of sets of measures is made for a period of 30 years, as established by the Delegated Regulation 244/2012/EU for public buildings.

The global costs include those related to the intervention itself, building consumption and maintenance during the calculation period. Following the regulation, for cost calculation of each set of measures, the initial investment is considered (CI), as well as replacement costs, disposal costs, annual energy costs and annual rise in energy price, the annual maintenance cost of measures, as well as the residual value of elements added.

The Equation (1) used for global cost calculation is:

$$\mathbf{C\_{\%}}\left(\tau\right) = \mathbf{C\_{I}} + \sum\_{\mathbf{i}} \left[ \sum\_{\mathbf{i}=1 \ \left(\tau\right)} \left( \mathbf{C\_{a,i}} \left(\mathbf{j}\right) \times \mathbf{R}d\left(\mathbf{i}\right) \right) - \mathbf{V\_{f,\tau}}\left(\mathbf{j}\right) \right] \tag{1}$$

In which: τ indicates the calculation period; Cg (τ) indicates global cost (referred to starting year τ0) over the calculation period; CI indicates initial investment costs for implementing measure or set of measures j; Ca,i (j) indicates the cost per year, i for measure or set of measures, j; Vf,<sup>τ</sup> (j) indicates residual value of measure or set of measures j at the end of the calculation period (discounted of the starting year τ0); and Rd (i) indicates discount factor for year i.

Consequently, the optimal cost of measures or sets of measures would be that with the lowest energy consumption at the lowest global cost per m2 and year. As an example, to facilitate understanding and subsequent interpretation of global cost graphs, a graph is included (Figure 3). It shows the resulting cost-optimal curve (orange line), the initial state of the building (L0), the global cost in the initial state (red line) and the optimal-cost sets of measures (green line).

**Figure 3.** Example of cost-optimal graph. Correlation between the 30-year global costs of sets of measures proposed per m2, and building's primary energy consumption per m2 and year.

The sets of measures with global cost above the optimal cost in the initial state (L0) have a period to recover initial investment longer than the calculation period itself, in this case over 30 years.

#### *2.2. Implementing Legislation*

The Spanish regulation on energy efficiency, the Technical Building Code DB-Energy Saving (CTE DB-HE) [22] contains basic requirements on the matter, which have been modified in accordance with the directives and goals set by the EU.

Currently, regarding energy demand levels for energy saving, the CTE DB-HE establishes maximum transmittance (Ulim) for thermal envelope elements, both new and renovated, and a global ratio of heat transmission through thermal envelope (Klim). It also limits consumption of non-renewable primary energy (Cep,nren) and total primary energy consumption (Cep,tot).

On the other hand, concerning renovation of specific buildings, the regulation allows greater flexibility in obtaining some values required, as in the case of buildings with significant architectural value. In the same way, it classifies interventions into small or large ones, and sets limits or requirements according to the type of performance.

This study also analyses requirements for each building type, and the level of compliance with regulation, based on the sets of measures to be implemented.

#### **3. Discussion on Results**

#### *3.1. Results on Global Costs of Measures and Primary Energy Consumption*

It should be emphasised that each school building is studied in the initial state at an energy demand level, L0, subsequently implementing sets of measures, as seen in Sections 2.1 and 2.1.2.

As a result of relating 30-year global costs per m2 to each set of measures and the consumption of primary energy per m2 and year, the graphs obtained show an optimal intervention cost for each school building type (Figure 4a–c).

Overall, it is noted that, in the three building types, for the same combination of measures, as in the WF thermal envelope elements, the energy demand levels (L1, L2 and L3) do not imply great differences in terms of global costs and resulting energy consumption. The graph clearly shows how different combinations of measures are grouped together according to construction elements enhanced.

Moreover, when comparing the graphs of representative building types it is clear what set of measures or thermal envelope elements obtains optimal costs.

For type A buildings, sets of measures introducing roof insulation obtain a greater reduction in energy consumption at the lowest global cost over 30 years. In this case, and depending on the energy demand level in terms of transmittance, consumption reduction regarding the initial state (L0) is between 24.5% and 25.3%, for interventions on the roof (R); between 28.1% and 30.2%, for improvements in facade and roof (FR); between 30.8% and 32.2%, for windows and roofs (WR); and between 34.8% and 38.1%, if the three thermal envelope elements (WFR) undergo improvements. The energy saving gained would enable to recover initial investment in such improvements within 4–5 years (R), 5–6 years (FR), 15 years (WR) and 14 years (WFR). The cost-optimal levels of interventions would be R and FR, thermal envelope elements, with a lower global cost. A greater saving is obtained through the OR and OFR, elements improved in the thermal envelope.

For type B and C buildings respectively, the sets of measures with the lowest global cost over 30 years include facade thermal insulation (F), and facade and roof thermal insulation (FR). These sets of measures represent a decrease in consumption between 15.8–18.6% (F) and 16.6–19.2% (FR) for type B buildings, and between 18.6–21.1% (F) and 20.5–22.9% (FR) for type C buildings. The repayment term is less than 7 years in type B buildings, and between 12–13 years (R) and 19 years (FR) in type C buildings.

(**c**)

**Figure 4.** Cost-optimal graphs. Correlation between 30-year global cost per m2 in the sets of measures proposed and building's primary energy consumption per m2 and year, after the intervention, assuming a price increase rate of 1%. (**a**) Type A school building; (**b**) type B school building; (**c**) type C school building.

In building types B and C, a greater reduction in energy consumption is obtained after replacing facades and windows (WF), as well as renovating all thermal envelope elements (WFR). In both sets of measures, the global costs increase, which means a longer repayment term for the investment made. In type B buildings, the global cost would be very similar to 30-year global cost, without necessary performance in the building. That is, the initial state L0, even exceeding it in some cases, which implies that the 30-year investment recovery is greater.

Table 5 is drawn up in order to provide accurate figures and facilitate comparison with some results included in the previous graphs. It shows 30-year global costs per m<sup>2</sup> corresponding to the most relevant sets of measures which include the full amount to pay for energy consumption in 30 years for each m<sup>2</sup> (living area), the implementation of measures taken and maintenance. It also includes global cost per m2 after 30 years of the initial state (L0), that is, if no action is taken, and identifies the full amount to pay for each m2, especially energy consumption expenses.

**Table 5.** 30-year global cost of initial state L0 per m2, according to type of school building, and global cost of sets of measures per m2, including those with better energy performance.


The fact that the global cost of specific sets of measures is higher than that in the initial state entails that the starting investment is not amortised in 30 years. These sets of measures could be implemented together with an enhancement of building's facilities, namely, by taking measures to be implemented in thermal installations. In this way, global costs would be minimised through a reduction in energy consumption due to improvement in system performance.

The annual savings generated after implementing sets of measures concerning energy renovation in each building can be expressed from the viewpoint of emission reduction (Table 6), and the subsequent economic saving after minimizing annual energy consumption per year (Table 7). Table 8 shows the reduction percentage in energy consumption and recovery period of initial amortisation for sets of improvement measures with lower 30-year global cost and a greater consumption reduction, according to building type.


**Table 6.** Emission reduction compared to the initial state per year, according to type of school building and sets of measures. Expressed in KgCO2 per year and according to building.

**Table 7.** Average annual saving according to type of school building due to reduction in energy consumption, according to sets of measures.


**Table 8.** Reduction percentage in energy consumption and recovery period of initial amortisation in sets of measures with lower 30-year global cost and a greater consumption reduction, according to type of school building.


If the results obtained for each building type were implemented in all representative schools, the result obtained by applying the lowest overall cost measures N3 FR (Type A) and N3 F (Types B and C) would be an average saving of 50,752.68 euros per year, 37,391.75 euros and 295,590.91 euros, respectively.

In addition, annual emission reductions would be 79,687.2 KgCO2, 56,640.1 KgCO2 and 583,828 KgCO2, respectively.

#### *3.2. Regulatory Requirements and Compliance*

Regarding Spanish Regulations on energy saving and compliance when it comes to building renovation, the CTE DB-HE 2019 [22] sets a global energy consumption limitation (non-renewable consumption of primary energy (Cep,nren) and primary energy total consumption (Cep,tot)) when there are interventions in over 25% of thermal envelope, as well as in thermal installations.

Specifically, within the climate zone corresponding to the city of Valencia, the regulatory limit value established for the Cep,nren is 55 kWh/m2 per year, and 80 kWh/m2 per year for the Cep,tot.

In the case of the school buildings studied, the Cep,nren value in the initial state of type A buildings (L0) is 351.3 kWh/m<sup>2</sup> per year, 256.9 kWh/m<sup>2</sup> per year for type B buildings and 192.1 kWh/m<sup>2</sup> per year for type C buildings. The greatest reduction in energy consumption would be obtained through the set of measures L3-WFR. In particular, this set of measures would allow the Cep,nren values to be 207.6 kWh/m<sup>2</sup> per year for type A buildings, 183.1 kWh/m2 per year for type B and 116.3 kWh/m2 per year for type C.

Regarding Cep,tot, its value in the initial state for (L0) type A buildings is 425.7 kWh/m<sup>2</sup> per year, 311.3 kWh/m<sup>2</sup> per year for type B and 205.3 kWh/m2 per year for type C. The set of measures L3-WFR would allow Cep,tot values to be reduced in 251.6 kWh/m<sup>2</sup> per year for type A buildings, 221.9 kWh/m2 per year for type B and 128.8 kWh/m<sup>2</sup> per year for type C.

As mentioned above, this study is focused on the renovation of thermal envelope elements, so this limitation is not mandatory. However, it should be considered in the case of performing in facilities.

Below, the study analyses the compliance with requirements on transmittance of thermal envelope elements.

In any intervention on thermal envelope, every single element renovated must meet requirements on transmittance set by regulations, for example, in the case of window replacement. These values partly correspond to those set for level L2 in Table 2. Level L1, as indicated in Section 2, does not meet the CTE DB-HE 2019 regulation.

Particularly, for major renovations over 25% of thermal envelope, the standard also sets a global heat transmission ratio (K). This depends on the climate zone where buildings are located and their compactness. According to the CTE DB HE, the K coefficient indicates the average value of heat transfer ratio for heat exchange surface of the thermal envelope (Aint).

As shown in Table 9, the Klim level set in the regulations is reached only by implementing one set of measures (L3-WFR) in type C buildings. Consequently, to reduce global ratio of the sets of measures proposed, it is necessary to minimise transmittance, that is, by setting more restrictive energy demand levels in facades (F), roofs (R) and windows (W). Another way to minimise building's energy demand is by performing in other elements, such as interior partitions and floors in contact with unheated rooms. This is not always technically or economically feasible.


**Table 9.** Global heat transmission ratio K (W/m2K). Regulatory requirements according to type of school building, building compactness and climate zone, Klim and ratios obtained for each set of measures and energy demand level.

In view of this situation, legislation provides for the fact that occasionally it is not possible to reach the level of benefit generally established. In these cases, some solutions may be adopted to achieve the highest level of adequacy. This is possible, as long as they are buildings with recognised historical or architectural value, when other solutions are not technically or economically feasible, or solutions involve substantial changes in elements of thermal envelope, or in thermal facilities without initial intervention.

For this study, type A and B school buildings could benefit from this flexibility criterion included in the standard, provided that measures implemented are close to limit values.

Regarding solar control, in the case of renovating over 25% of the total area of the final thermal envelope, the solar control parameter (qsol;jul) should not exceed the limit value 4 kWh/m2 per month, for uses other than private and residential.

According to the CTE DB HE, qsol;jul indicates the ratio between the solar gains of windows and doors on the thermal envelope during the month of July with mobile solar protection activated, and the useful floor area included in spaces within the thermal envelope (Auseful). Solar protection can be implemented in all the building or in part of it.

This solar control parameter is fulfilled in those sets of measures in which windows and doors (O) are replaced, since protection elements are included. In type A and B buildings, as it is not possible to alter facades, protection systems should be installed on the inside, for example by using shutters.

#### **4. Conclusions**

Through the implementation of optimum-cost methodology, the study aims at identifying the set of improvement measures with optimum intervention cost for each building type studied. It is found that for type A buildings, the most cost-effective intervention would be to renovate facades and roofs (L3-FR), whereas for types B and C, the improvement is only made in facades (L3-F). In all cases, the set of improvement measures that brings buildings closer to nZEB involves performing in all thermal envelope elements with the most restrictive values of thermal transmittance (L3-WFR).

All in all, the implementation of cost-optimal sets of improvement measures in 46 schools studied results in an average annual saving of 378,735.34 euros and an annual emission reduction of 720,155.3 KgCO2.

These results show Public Administration in Valencia that the most cost-effective solution is not always the same for all schools, and depends on building typology. This suggests that it is not advisable to renovate the same thermal envelope element simultaneously in all buildings for instance, by renovating windows in all schools. In order to save costs when performing in more than one element or school at the same time, the

typology classification proposed for the sample is suggested to be applied so that the same intervention is replicated for the same typology but not for all schools.

The results achieved allow school principals in Valencia to make decisions on carrying out priority renovations in buildings and potential strategies. For example, for those measures with a global cost similar or higher than that in the current state of the building, it is appropriate to perform a deep renovation, including enhancement of thermal envelope and heating and cooling systems, so that the 30-year global cost is reduced. The long-term cost reduction and the quick return of investment of some sets of measures may be a reason for public administrations in Valencia to invest in school renovation.

Regarding regulatory requirements, it is shown that an approach to building renovation with the aim of complying with current legislation for new buildings may not be the most cost-effective option.

In summary, the cost-optimal methodology applied to the renovation of school buildings studied provides quantitative data on costs and energy saving that can be obtained after implementing specific sets of measures in 46 school buildings in the city of Valencia. All this facilitates to identify, among other data, the initial cost of measures, consumption reduction gains and the return on investment periods. These data can provide public administrations in Valencia with criteria to design long-term intervention plans, which enable available resources to be efficiently invested.

Irrespective of the specific results reached, the adaptation of the methodology proposed to a wider scale (regional/national) can help to build support for deciding about the renovation of school buildings and designing long-term renovation strategies. The study can also be expanded to other buildings in the city, as well as other cities or regions.

**Author Contributions:** Conceptualization, M.E.L.-D.; Methodology, B.S.-L. and L.O.-M.; Writing original draft, M.E.L.-D.; Writing—review & editing, M.E.L.-D., B.S.-L. and L.O.-M. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**


## *Article* **Passive Solar Solutions for Buildings: Criteria and Guidelines for a Synergistic Design**

**Giacomo Cillari \*, Fabio Fantozzi and Alessandro Franco**

Department of Energy, Systems, Territory and Constructions Engineering, University of Pisa, Largo Lucio Lazzarino, 56126 Pisa, Italy; f.fantozzi@ing.unipi.it (F.F.); alessandro.franco@ing.unipi.it (A.F.) **\*** Correspondence: giacomo.cillari@phd.unipi.it

#### **Featured Application: Optimization of passive solar strategies to minimize building energy demand.**

**Abstract:** Passive solar system design is an essential asset in a zero-energy building perspective to reduce heating, cooling, lighting, and ventilation loads. The integration of passive systems in building leads to a reduction of plant operation with considerable environmental benefits. The design can be related to intrinsic and extrinsic factors that influence the final performance in a synergistic way. The aim of this paper is to provide a comprehensive view of the elements that influence passive solar systems by means of an analysis of the theoretical background and the synergistic design of various solutions available. The paper quantifies the potential impact of influencing factors on the final performance and then investigates a case study of an existing public building, analyzing the effects of the integration of different passive systems through energy simulations. General investigation has highlighted that latitude and orientation impact energy saving on average by 3–13 and 6–11 percentage points, respectively. The case study showed that almost 20% of the building energy demand can be saved by means of passive solar systems. A higher contribution is given by mixing direct and indirect solutions, as half of the heating and around 25% of the cooling energy demand can be cut off.

**Keywords:** solar energy; building energy performance; energy saving; passive solar design; synergistic design

#### **1. Introduction**

Energy use in the residential sector represents a great share of the global energy demand, attested between 20% and 40% of the total [1]. Each country has developed specific energy efficiency strategies for the civil sector. Firstly, the main attention concerned energy conservation, focusing on the building envelope insulation that can reduce energy demand by up to 28% [2]. Then the focus moved to increasing the efficiency of Heating Ventilation and Air Conditioning system (HVAC) systems, that are the main building energy consumption source and commonly do not operate efficiently [3]. In a nearly zero-energy building (nZEB) perspective, the integration of different strategies regarding envelope insulation, heat generation, shading, and control devices is fundamental to minimize building conditioning loads, so as to be able to maximize the share of energy demand covered by renewable energy sources. It must also be taken into account that residential space heating is responsible for 86% of building energy demand and can easily take advantage from renewable sources [4]. Among the various alternatives, solar energy represents the best option for buildings as one of the most accessible and easily exploitable, even if its current contribution to global energy supply is still imperceptible [5]: it can be directly exploited by heating up the building through solar irradiation, or indirectly by means of photovoltaic (PV) or solar thermal systems. As Table 1 data from International Energy Agency (IEA) [6] show, in a scenario where mandatory building energy codes will almost totally cover construction activity by 2030, with a nZEB share forecast of

**Citation:** Cillari, G.; Fantozzi, F.; Franco, A. Passive Solar Solutions for Buildings: Criteria and Guidelines for a Synergistic Design. *Appl. Sci.* **2021**, *11*, 376. https://doi.org/10.3390/ app11010376

Received: 14 November 2020 Accepted: 29 December 2020 Published: 2 January 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

50%, the sales of heat pumps, which can be coupled with PV as a renewable production system, are slowly but constantly increasing, between 0.3 and 0.5% on a yearly basis, with fossil fuel-based equipment that, after a peak in 2014, is gradually decreasing. These data highlight the core role that solar energy plays in building design in the near future: by properly combining photovoltaic and solar thermal systems, indeed, solar energy can provide at least 76% of the primary energy demand of a residential building, with a short payback period [7].


**Table 1.** (a) Heating technology sales, (b) global building construction area by type of building code.

Despite the main contribution in a modern building coming from active solar systems commonly integrated in a new building [8], passive solar strategies represent an energy reduction design feature with a high potential to dramatically reduce building energy demand [9] through energy promotion, buffering and prevention, influencing heating, cooling, ventilation loads, and building's system size. The main advantages of passive solutions include variety, versatility, simplicity, generally low initial and maintenance cost, and long lifetime [10] involving different building components, from walls to roofs. The effectiveness of passive solar solutions depends on a wide variety of design parameters [11]. Like all solar based devices, the performance is mainly related to the latitude, as it influences the average weather conditions and solar radiation on the collector surface. The maximum impact is expressed at medium latitudes, where cold winter temperature and long sunshine create the ideal conditions to exploit passive solutions. The benefit is also related to the interaction with the building and its users as heat delivery, shading, or ventilation must comply with the comfort requirements of the occupants: the magnitude of passive systems' gains becomes more relevant in highly energy consuming buildings like public or office ones.

The aim of the present paper is to provide a theoretical background of the parameters influencing the applicability and integrability of the various passive solar solutions in buildings and analyze how their synergy affects building energy performance. The scope of this analysis is to determine the impact of the different passive solutions while varying some controllable variables: the paper reports the first results of the investigation, where the most relevant influencing variables, such as latitude, orientation, building use, and shape factors, have been considered. Not much research has analyzed the topic from a general point of view in order to develop guidelines for passive solar application mainly providing a more qualitative outcome, describing the affecting parameters and defining rules of thumbs for sizing and related possible expected solar savings [12]. Other investigations focused on a specific topic, e.g., orientation, analyzing the effects by a deep theoretical background validated by measures and results from experimental activity [13]. The present paper follows a different approach as it intends to quantify the effects of passive solar strategies in terms of energy savings in different conditions: this will allow to determine the most suitable solutions in different cases and to define design guidelines according to the quantified impact of the variables analyzed.

The influencing parameters work together in defining the performance of a passive solar strategy: heating and cooling must be provided according to the living patterns that depend on building use, but also orientation that determines room distribution. Climate is linked to latitude and affects the energy balance and operativity by determining sun hours and lighting levels. Cost depends on the integrability in building design, thus, on the kind of structure and building shape: integration of massive systems in heavyweight buildings, for example, would be relatively easy, but could represent a high cost for lightweight ones. As all these elements work in synergy, a synergy of different strategies may achieve a better result in terms of energy saving. Recent investigations on passive solar systems and design integration in buildings have generally focused on spot solutions, either through a set of parametric simulation to verify and optimize the contribution of the asset to the building [14], or to characterize, evaluate, and maximize the performance of a specific device in individual applications [15]. The present paper intends to evaluate the efficacy of the synergy of different passive strategies and quantify the impact on building energy demand. Both direct, indirect, and isolated solutions can be designed to minimize each other's side effects. Direct systems that only provide heating, but faster than any other solution, are a perfect solution for a nonresidential building that needs to heat up quickly to reach indoor air comfort levels. On the other side, indirect systems can be exploited as solar chimneys to get ventilation and reduce discomfort due to overheating caused by wide glazed openings, or to provide cooling through roof ponds. In residential buildings, sunspaces can be used as a passive plenum of warmed air in winter, as a more manageable solution than high-inertia massive systems or direct systems with heat storage. By merging direct systems and sunspaces, more uniform heat delivery can be achieved, while a ventilated Trombe wall can be used in synergy with the sunspace to get higher indoor cross ventilation. A proper combination of direct, indirect, and shading systems can guarantee passive heating most of the winter season and minimize overheating in summer. Synergistic design must optimize the combination of different systems to minimize the need of HVAC contribution and promote the achievement of a zero-energy building. The paper analyzes the effect of synergistic, complementary strategies on a real office building, with different levels of intervention complexity, moving from simple, less expansive solutions, to composite and integrated ones, to quantify the reachable savings.

A brief description of the most common passive solutions is provided in Section 2, defining how extrinsic and intrinsic parameters work to determine the suitability of a specific passive system according to building kind. The influence of basic parameters affecting energy modelling of solar based devices is examined. Section 3 includes the methodology description and simulation settings of both the general investigation and the case study. Section 4 provides the results of the preliminary quantification of the impact of the different variables on building demand and then analyzes the outcomes of the case study of a public office building to evaluate the effect of possible combined passive strategies on a real building and determine the share of energy saving achievable through a synergistic design. Finally, after a brief discussion in Section 5 on the limit and contribution of the results achieved, the main conclusions are outlined, to show the potential of a structural, planned integration of passive solar systems in buildings in terms of energy demand reduction.

#### **2. Passive Solar Systems**

The action of a passive solar system for buildings can be summarized in a resistive and capacitive combined model, as the one described in Figure 1. According to this description, passive solar systems can be suitable both for increasing, during the summer period, or

reducing, in the winter season, thermal resistance of direct solar radiation as well as to introduce appropriate capacitive systems able to store a part of solar radiation.

**Figure 1.** Conventional equivalent thermal circuit for passive solar heating building systems.

#### *2.1. An Overview of the Common Solutions*

Common categorization classifies passive solar systems into three classes. Direct gain systems collect solar energy through wide south-facing glazed envelopes: low construction cost, widely available and common technology represent the main advantages. No thermal storage is needed when these systems are sized to provide a small fraction of the heating load, but this could generate high indoor air temperature fluctuations. The most relevant disadvantage is related to glare discomfort or possible degradation from ultraviolet radiation [16]. The integration of insulation systems, thermal storage, external reflective surfaces, and shading systems (Figure 2) are the main possible improvements but can hugely impact the total cost. Indirect gain systems include a thermal mass placed between the solar collector and the indoor space that prevents indoor glare and ultraviolet degradation. A main disadvantage that can affect the system's lifespan is the maintenance, as proper access to the wall cavity for dust and condensation removal may be hard to achieve. In isolated gain systems, the collector and the storage are thermally isolated from the building: the main advantage is the independence of the system from the building.

**Figure 2.** Example of a passive solar system, external adjustable blinds applied in the case study building: (**a**) external view, (**b**) interior view, (**c**) louvres detail, (**d**) connection detail.

Integration of shading systems and reflective surfaces are simple strategies for both new and existing buildings with a low economic impact. At low latitudes, blinds on the east and west windows reduce heat gain by around 20% more than on the south-faced windows, whose contribution increases with latitude [17]. Investigation carried out by Alhuwayil et al. [18] shows that self-shading envelope in a multistory building has a lower payback period, 2 years, than additional insulation and low-e windows, with an energy consumption decrease of 20%. In direct systems, U value and solar factors are the most relevant design parameters: for common glass, U values around 1–1.5 W/m2K and a minimum solar factor of 0.3 is needed to have positive gain [19]. Low thermal resistance of the glass represents a critical weakness: use of triple glasses is a relevant energy saving measure in cold climates. Night insulation methods, such as roller-shade devices, are profitable but determine a not negligible extra cost.

In massive wall systems, the wall works as a storage mass buffering heat transfer. The greenhouse effect guaranteed by the external glazing improves the performance of the system. The thickness of the wall must be chosen according to the wall's material properties such as periodic and steady-state thermal transmittance, which define heat transfer rate, time lag, and decrement factor. Trombe wall adds convective heat exchange to the massive wall system by adding bottom and top openings to the wall: with the integration of outdoor vents, it can be used as a solar chimney [20]. This kind of configurations have good performance both in warm climates, cutting off 71.7% and 36.1% of heating and cooling demand, respectively, and in warm weather [14]. By exploiting fluid in the storage, water wall's heat transfer occurs by convection and the system is quite isothermal. This solution presents lower heat loss during night-time due to a lower surface temperature, and faster achievement of steady-state operating conditions, compared to other massive systems. Tests on a passive solar house with integrated water thermal storage walls showed an energy consumption reduction of 8.6% [21]. Roof pond systems, Figure 3, integrate water bags inside the roof structure: the large ceiling surfaces assure a more uniform heating distribution, but the effectiveness is limited to single-story buildings with an efficiency around 45%, as less than half of the collected heat is transferred downward. The high structural loads and the low efficiency at medium-high latitudes due to the low horizontal irradiance represent the main disadvantages. Results from a field study of a roof pond report a reduction of the indoor temperature swing around 1/4th [22]. The Barra–Costantini system is based on the collector loop configuration, but the warmed air flows inside a cavity in the ceiling and is finally released at the non-sun-facing rooms: this system guarantees a diffuse heat distribution and storage suitable for multistory buildings and is exploitable for building ventilation. The main disadvantage is the hard maintenance due to dust or condensation in the cavity. In temperate climates, this configuration can reach an annual heating energy saving percentage from 60 to 70%, but with a payback period of 25 years [23].

**Figure 3.** Water systems: (**a**) roof ponds winter mode (day and night), (**b**) roof ponds summer mode (day and night); sunspaces: (**c**) integrated, (**d**) attached, (**e**) attached ventilated, (**f**) sunporch.

Collector loops are based on convective heat exchange: these systems are perfectly suitable for lightweight insulated structures as easily integrable by adding an external glazing to the south façade. Convective loops also contribute to indoor ventilation. Likewise, thermosyphon systems consists of solar-glazed collectors with a black metal absorber. The most common application of these kinds of strategies in buildings is ventilated facades: in summer, the ventilated air gap and the reflective covering reduce the heat entering in the building, decreasing the cooling demand, while in cold weather conditions, the air gap reduces heat losses through the envelope, guaranteeing high air conditioning related

savings. The system can also exploit the chimney effect to set up natural ventilation that helps in heat and moisture removal.

A sunspace layout is related to its use: as Figure 3 shows, integrated sunspaces act as large direct gain systems, while externally attached sunspaces work as indirect systems. A sunspace can be exploited to preheat external air [24], and works as a buffer zone. Although representing a possible additional living space is an advantage, the high construction cost and the compliance with local requirements limit sunspace implementation. The role of thermal storage is relevant: energy saving can be enhanced from 10–15% to 80% by adding a water-based storage system [15]. Achievable by installing windows or sheets in a south-facing balcony, sunporches represent a simple and cheaper solution for existing buildings, thus a valid energy retrofit strategy [25].

Building orientation and shape are basic passive strategies that highly affect both the base building energy load and the performance of other passive solutions by defining solar exposure. When designing a new building, difference in heating demand from a regular-squared to an irregular building can account for about 50%, while proper site orientation can save up to 40% [26].

#### *2.2. Standard Modelling*

As clearly evidenced in the models of Figure 1, the sizing of a distinct passive solar system with a defined objective appears to be a quite difficult task due to the synergistic effects of different parameters that act together in defining the effectiveness of a passive solar system. Therefore, energy performance can only be determined by considering this synergy. As Table 2 shows, parameters can be classified into extrinsic factors, external to the passive system, such as latitude or building shape, and intrinsic, such as collector inclination and orientation. These factors have a different impact on final performance: they act directly on the incident solar radiation or influence the operativity of the passive system and its integrability in building design. All these parameters contribute to the performance of passive solar systems at different stages of a project: while building orientation, shape, and position should be adapted to maximize the potential performance of passive solar systems, building use and latitude are usually given parameters, so they must be considered for a preliminary screening to limit the choice to the most suitable strategies. Then, another set of parameters allows to identify the most appropriate system for a specific building. The selection process is strictly country-dependent, as microclimatic conditions, architectural details, and related costs widely differ from place to place.

**Table 2.** Influence of design parameters.


The performance of each solar system is related to incident solar irradiance G (W/m2), that depends on the different position of the site, latitude and longitude, on the different seasons, on the hour of the day, and on the position of the surface exposed to solar radiation. Solar irradiance can be evaluated with the following law [27]:

$$G\_T = G\_{\text{on}} \times \text{tr} \times \cos \theta \tag{1}$$

with

$$\mathcal{G}\_{on} = \mathcal{G}\_{sc} \left( 1 + 0.033 \cos \left( \frac{360n}{365} \right) \right) \tag{2}$$

*cosT* = *sinδsinφcosβ* − *sinδcosφsinβcosγ* + *cosδcosφcosβcosω*+ <sup>+</sup>*cosδsinφsinβcosγcos<sup>ω</sup>* <sup>+</sup> *cosδsinβsinγsin<sup>ω</sup>* (3)

$$
\tau = \sigma^{-b\lambda^{-a}ma} \tag{4}
$$

where *GT* is global irradiance on a tilted surface, *Gsc* is the solar constant, *θ* is angle between surface normal and incident radiation (Figure 4a) and *τ* represents atmospheric attenuation of solar radiation. Figure 4b reports the maximum daily solar irradiance per month at different latitudes.

**Figure 4.** (**a**) Angles related to sun position; (**b**) maximum daily solar irradiance per month at different latitudes on a horizontal, h, and a vertical, v, surface.

As Equation (3) states, latitude and surface inclination are the most impactful parameters to determine solar irradiance on a surface. Latitude affects the number of hours of sunlight on the surface. The best performance can be achieved at medium latitudes: at low ones, high solar radiation guarantees a high amount of collectable energy, but the short heating season makes the integration less cost-effective with a higher risk of overheating; at high latitudes, energy saving can be higher, but the lower solar radiation and shorter daytime limit the operativity, with a need of insulation, due to the lower average temperatures, that increases the total cost.

#### *2.3. Synergy of Influencing Parameters*

A generic model for passive solar systems, like the one in Figure 1, is internally ruled by three main resistances related to heat exchange among room, ambient, and storage, and characterized by a capacitive massive element. It is also externally stressed by the incident solar radiation on the collector. In summer, shading systems represent the most relevant resistance, while in winter, all kinds of solar radiation contribute with specific resistances. In building applications, materials and structures work in synergy with the

elements previously analyzed to define passive system operativity. Glass properties are the first element that intervene. Once the incident solar irradiance has been determined with Equation (1), the energy transferred inside the building can be evaluated with the following balance:

$$H \times A = Q\_l + Q\_r + Q\_{a,out} + Q\_{a,in} \tag{5}$$

where *H* is global solar radiation on the window, *A* is windows surface, while subscript *t* represents the amount of energy transferred, *r*—the reflected share, *a,out*—the energy absorbed and retransferred outside, whereas *a,in*—the energy absorbed and transferred inside the building. The solar factor (*g*), the main parameter related to glass, can be defined as the percentage of solar energy incident on the glass that is transferred indoor, as showed in Equation (6).

$$\mathbf{g} = \frac{\mathbf{Q}\_t + \mathbf{Q}\_{a,\text{in}}}{H \times A} \tag{6}$$

The solar factor depends on the composition and properties of the glass: from single to low emission glasses, the solar factor is almost halved, due to highly reduced transmittance.

The type of building structure and envelope materials affect the system's integrability [11] and the opportunity of exploiting building elements for heat storage with no extra cost. Integrated heat storage reduces indoor temperature fluctuation and extends the performance of a passive system. Density, specific heat capacity, and thermal diffusivity influence the rate of heat storage and the useful thickness involved in the process: high density and mass guarantee high heat capacity, while the higher the thermal conductivity, thus the diffusivity, the more readily the storage system absorbs heat and the deeper the material thickness involved is. The minimum thermal storage surface recommended by Balcomb [28] is six times the solar collector glazing area. Passive solar design solutions can be grouped according to the integrability, as shown in Figure 5, based on the kind of structure, light or heavyweight, and the suitability to new or existing buildings.

**Figure 5.** Classification of passive solar design strategies.

The building use and occupant's activity schedule are another set of parameters affecting the operation of a passive solar system: living pattern that varies according to the building use defines the period of comfort and that of possible setback. In office buildings, the main activity is focused on the middle of the day, from 7.00 a.m. to 5.00 p.m., while in residential buildings the time slot shifts to evening and morning. Educational buildings and offices, with a prevalent daytime use, are the most suitable for directly exploiting the heat provided by the sun. In residential buildings, the efficacy of passive solutions is related to heat storage effectiveness to deliver heat during night or cloudy days.

#### **3. Performance Evaluation of Passive Solar Systems**

#### *3.1. General Investigation*

As the first investigation, a preliminary quantification of the impact of different parameters on the three classes of passive solar systems has been carried out through a set of simulations. The energy analysis has been carried out with the EnergyPlus™ simulation tool developed by US DoE. In order to properly compare the outputs, the simulations considered a standard application of different strategies: the same construction and structures have been used, with no specific optimization for different solutions. The simulations have been run during the winter period to evaluate the impact of the solar strategies on the building's heating demand. Two kinds of buildings, an office complex and an apartment building, have been analyzed with different surface to volume ratio, 0.4 and 0.6, respectively, and different heating demand schedules: from 8.00 am to 7.00 pm on the weekdays and turned off in weekends for the office, while the opposite was set for the residential building. Another difference between residential and office building simulation occurred in schedule and magnitude of internal gains such as from equipment and appliances. Simulations have been set at Rome, 41◦ 50 , and Frankfurt, 50◦ 06 , to evaluate the incidence of latitude. The three strategies, a direct system, a ventilated Trombe wall, and a sunspace, have been simulated both with a north-south building axis and at 90◦ rotation (r), with east-west building axis. Both the models contained common building constructions with an external wall U-value of 0.40 W/m2K. Base number and dimensions of the windows were set to comply with the minimum window-to-floor surface ratio of 1/8 required by Italian legislation: fenestration constructions have a U value of 1.76 W/m2K and a *g* of 0.56. With these settings and no passive systems installed, a benchmark value of energy demand of both office and residential buildings has been evaluated as a reference for energy saving of the passive solar strategies. The reference values for Rome and Frankfurt houses are 160 and 290 kWh/m2, respectively, while office building reference demand is 98 kWh/m2 in Rome and 112 kWh/m2 in Frankfurt.

Implementing the direct system, a wide glazed surface has been added on the southfaced wall or divided between the east and the west façade in the rotated case. Window extension was set at 15% of the floor, according to the common rule of thumb [29]: fenestration U-value and *g* are 1.06 W/m2K and 0.6, respectively, while a 10 cm concrete slab provides the ground floor construction with a heat storage mass. This simulation is the only one with a specific low emission window kind, as direct systems installed are part of the thermal zone and directly affect building energy balance. Regarding the indirect and isolated systems, they belong to a different thermal zone, which are not considered in building energy balance. In the indirect system simulation, the Trombe wall area accounted for 0.2 m2 per m<sup>2</sup> of floor area, with an air cavity thickness of 15 cm. The thickness of the external wall, 30 cm, already provided a good buffering of the heat wave. In this simulation, the same clear glass construction of other windows has been applied to the glazed face of the Trombe wall. Finally, the sunspace modelled in the isolated system was designed as a sunporch linked to the main building through a patio door: its envelope was glazed with the ordinary kind of window, except for the floor, which had the same construction as the indoor floor.

#### *3.2. Analysis of a Case Study*

After a general investigation to quantify the impact of the different variables on the performance of the three kinds of passive solar strategies, another simulation was run to define possible effects of the synergy of different solutions on a case study of a real building. The aim was to provide a quantification of the energy saving that could be obtained with the design of passive solutions in an existing building. The selection of the case study has been influenced by various elements, as the positive effects of passive solar systems can be evaluated referring to both specific civil buildings for residential or public use. Between residential and public buildings, the latter result to be more energy consuming: daily use and commonly wide glazed envelopes make them also the most suitable kind of buildings

for the implementation of passive solar systems. The European Directive 2010/31/UE [30], in fact, firstly focused its attention on public buildings, anticipating the requirement for nearly zero-energy buildings (nZEB) in new construction. For these reasons, the case study is based on the office building of the Department of Energy, Systems, Territory and Constructions Engineering of the University of Pisa, shown in Figure 6. The building hosts offices and research laboratories on two floors: the technical room for the building system at the ground level and the adjacent building with mechanical laboratories were not included in the simulation. It develops along the south-north axis, and is characterized by a wide glazed envelope, mainly equally east- and west-exposed with a gross window-to-wall ratio of 57.65%.

**Figure 6.** Case study building: (**a**) energy model; (**b**) standard floor plan

For energy modeling, people, lights, and equipment loads were considered; no mechanical system has been modelled, only natural ventilation to simulate the passive behavior of the building and its energy demand. Table 3 lists the main construction involved and internal gains used.



Zone ideal loads have been evaluated with a heating setpoint at 20 ◦C and a cooling one at 26 ◦C. Natural ventilation through existing windows has been set according to the occupancy pattern and with an outdoor air temperature range between 15 and 30 ◦C.

The first solution investigated shading systems: given the high-glazed surface, this results as the easiest and most cost-efficient kind of passive solar solution. Fixed overhangs and external adjustable blinds, as the ones installed, were both simulated to compare their efficacy. The simulation has been set to activate the blind closing when 500 lux have been reached over the working plan or indoor air temperature rises above 25 ◦C, with a tilt angle configured to block direct beam solar radiation. A second passive strategy to reduce heat losses through the glazed envelope, focused on the integration of solar-control low-emissivity glasses. The windows chosen for this simulation had a solar control glass layer replacing common 4 mm clear glass, with a solar transmittance at normal incidence of 0.166: window U value moved from 2.7 to 1.65 W/m2K while the solar heat gain coefficient

decreased from 0.764 to 0.617. To fully exploit the potential of passive solar strategies, different solutions must be combined and balanced to take advantage of the energy savings coming from each system, as they can act on distinct services and in distinct times: for this reason, a combined solution, with external blinds and low-e glasses, has also been investigated. With reference to the models in Figure 1, the strategies that are discussed with this simulation focus on intercepting the incident solar radiation by acting on solar resistance. In terms of equivalent circuit, shading and glass element defined a rheostat with a variable resistance, as shown in Figure 7: both the integration of fixed overhangs and adjustable blinds or solar control glasses determined variable heat gain for the building.

**Figure 7.** Conventional equivalent thermal circuit for passive strategies related to solar radiation resistance.

To get a deeper understanding of the combined effect of different solutions on the possible energy savings, a single module of the office building has been modelled, both in the basic case, in the combined case with a shading system activated, and in a Trombe wall configuration. In this last case, as shown in Figure 8, part of the external window has been replaced with the specified indirect system: while the direct gain system provides heating and lighting during the day, Trombe wall guarantees higher temperatures at night, leading to a lower demand in the morning when the HVAC system turns on. Moreover, the reduction of the glazed surface hugely reduces heat losses in winter or the unwanted heat gain in summer. The system has been modeled both as an unventilated Trombe wall with a full conductive heat exchange, and as a naturally ventilated one. Due to the high window-to-wall ratio, 50% substitution rate has been chosen, as it does not highly impact the needed lighting level on the working plan.

**Figure 8.** Single office module: (**a**) standard configuration; (**b**) Trombe wall configuration.

#### **4. Results**

Results of the general investigation on the impact of variables over passive systems performance have been analyzed both in terms of absolute values and by comparing the percentages of energy saving achievable. Figure 9 shows the results of the simulation: in terms of energy demand, the difference between the two latitudes, as shown in Figure 9a,b, increased as the surface-to-volume ratio increases, moving from the office to the residential buildings. For the office building, direct systems proved to be the most profitable solution

in terms of energy saving for both locations, as the highest savings, 28.2% and 38.5% for Rome and Frankfurt, respectively, occurred in the rotated direct system configuration, as described by Figure 9c. For the apartment building, Figure 9d, the Trombe wall rotated setting reached the highest saving in Frankfurt, 12.8%, and Rome, 22.3%. A very different trend can be defined for office and residential buildings in terms of passive system performance. Data collected confirmed that daily use office buildings prefer direct systems, as indirect and isolated systems showed much lower values. The trend highlighted an increase of the savings moving from Rome to Frankfurt, due to the higher demand of the Frankfurt facility that can better exploit solar radiation during its colder season, except for the sunspace simulation, and an increment from standard to rotated configuration certified the higher efficiency of south-faced passive solar systems. Quite the opposite trend can be detected in residential buildings, as the energy savings decreased from Rome to Frankfurt, and the variation among direct, indirect, and isolated systems percentages was lower. As in the previous analysis, however, the rotated configuration showed higher results for both locations, establishing again the higher performance of south-faced systems.

**Figure 9.** Heating energy demand in winter season: (**a**) office building; (**b**) apartment building; (**c**) percentage of energy saving in office building; (**d**) percentage of energy saving in residential building.

Even building destination and use affect the performance of passive solar systems. While at Rome latitudes the difference between the two kinds of buildings was quite constant, as it went to 7.6% in standard and 6.3% in rotated direct systems to 6.7% and 8.2% in indirect and 5.5% and 4.2% in isolated ones, it greatly varied for Frankfurt: direct systems efficacy changed around 28.6% in standard and 30.7% in rotated configuration due to the low performance in residential application, while the range of indirect and isolated systems was between 1–4%. Frankfurt values for residential buildings were generally lower than office ones, excluding the standard sunspace, while at Rome latitudes, except for the direct systems, residential values were higher than that of the office.

Latitude impact differs according to building destination: the office in Frankfurt showed higher energy saving potential than the Rome one, while the opposite occurred in the residential building analysis, where Rome percentages were higher than Frankfurt ones. The range of variation between the two latitudes was wider for direct systems, 12.5% and 10.3% in office or 8.5% and 14.1% in residential building, than in indirect and isolated solutions: for the north-south axis building, the gap was higher in the office application, around 12.5 percentage points in the direct system, 6 in indirect, and 1.2 in isolated, versus 8.5%, 2.8%, and 2.1% for residential building direct, indirect, and isolated solutions, respectively. In the rotated configuration, the opposite occurred, since the gap between Rome and Frankfurt in residential application was higher than the corresponding value for office buildings.

Looking at the orientation impact, south-facing systems showed the highest values, but they must deal with summer overheating risk. The sensibility decreases as the latitude increases, with Rome gaps between standard and rotated configurations higher than Frankfurt ones. The influence of different building axis depends on building use: for Frankfurt latitude, the impact of orientation moved from 7.7% of energy saving variation in direct systems, 7.9% in indirect, and 5.9% in isolated ones in the office study to lower values in the residential analysis, 5.6%, 6.1%, and 2.8% respectively. In Rome, the effect of orientation in residential application was higher than in office buildings, moving from 11.2% to 9.9% in direct systems and from 12.8% to 11.3% in indirect systems. Isolated sunspace solution represents an exception, as the residential gap of performance between standard and rotated configurations, 7.2%, was higher than the office one, 5.9%.

The lower residential building performance and the consequent lower sensitivity to orientation and latitude was attributable to the lack of optimization for the heat storage system. Analysing the results from the perspective of the systems, direct solutions showed the highest efficiency in reducing building energy demand, but they had higher sensitivity to orientation, 6 to 10 percentage points of variation, and latitude, 9–13%, than indirect or isolated solutions.

Moving to the case study of the office building, four different strategies have been studied and results are shown in Table 4. As a reference, the basic case, with no shading systems, determined an energy demand per total building area of 115.52 kWh/m2, with an almost equal energy consumption for heating and cooling purposes, 47.59 kWh/m<sup>2</sup> and 45.66 kWh/m2, respectively. Due to the east and west exposure, the effectiveness of fixed overhangs was negligible, while the impact of external blinds to reduce the summer undesired heat gain while guaranteeing proper lighting levels for office work was relevant. The results show that while fixed shadings led to a very low energy demand variation, with only 1.28% energy saving in cooling, blinds cut off one third of the cooling energy demand, with an impact of 12.58% on total energy consumption. This result highlights the hidden potential of passive solar solutions that can provide a reduction in embodied and operational energy requirements over a life cycle [31]. As shown in Figure 10, indoor air temperatures in the office zone in free running conditions rise compared to the basic case due to the higher thermal resistance of the windows: results show a reduction around 15% in heating demand, but the lower heat losses during the night generated a higher demand of energy in the cooling season. The analyzed synergy effect of the combined strategies individually, external blinds and low-e glasses, reduced by around a quarter the energy

demand of the building, with a share for heating and cooling close to the highest values previously detected, 14.91% and 32.74%, respectively.


**Table 4.** Energy demand for run simulations.

**Figure 10.** Indoor zone air temperature of the office zone in free running conditions.

Regarding the investigation of the office module, as in the previous analysis, the combined case showed a higher share of energy savings on the cooling side, with a reduction of 13.78% of energy demand, and zero effect on heating for the single office module. Replacing half of the wall-wide window with a Trombe wall drastically reduced the heating demand, more than half of the required energy in the basic case and cut off one third of the cooling demand. Figure 11a shows the results of the simulations. The lighting load moved from 2.28 kWh/m2 in the full window configuration to just 2.65 kWh/m<sup>2</sup> in the half-window one. The naturally ventilated indirect system reached a higher share of energy savings for building heating, around 62%, but without a proper control system, its integration could be counterproductive: the cooling energy demand, indeed, rose from 3.21 to 3.91 kWh/m2. This last configuration highlights the possible impact of an integrated passive solar design on building energy consumption, as the combined use of direct and indirect system could generate a reduction of 50% of a common office building's energy demand: a higher share could be achieved taking into account ventilation, by exploiting the Trombe wall cavity as a solar chimney during the cooling season. Assuming the office module as a functional unit, we compared a 10-units building, as a benchmark of a small office facility, with the department building previously analyzed, which contains 32 office zones. Results in Figure 11b confirm the impact on cooling demand of the combined case, whereas neglectable energy savings in terms of heating demand have been achieved, thus implying that the reduction of heating load, around 15%, achieved in the whole building analysis was mainly related to common spaces and wide laboratories.

**Figure 11.** (**a**) energy demand of the office module and (**b**) energy saving of a 10- and 32-modules office building for different strategies.

The integration of the indirect system had a relevant impact on building energy saving: on heating demand, 65 to 70 kWh/m<sup>2</sup> can be saved yearly in unventilated and ventilated configuration, respectively, for the department building. On the cooling side, the unventilated solution reached the highest saving, around 20 kWh/m<sup>2</sup> for the small facility and 60 kWh/m2 for the larger structure: the lower values of ventilated strategies are related to the lack of monitoring systems to prevent ventilation of warmed air from the Trombe wall cavity to cause overheating.

#### **5. Discussion**

As exposed in the paper, the interest on the promotion of passive solar system solutions is relevant to reduce the energy impact of civil/residential structures. Other studies investigated the impact of specific variables: Djordjevi´c et al. [31] developed a mathematical model to estimate the indoor temperature trend in a building with a combined passive solar system made of a direct and an unventilated Trombe wall. Their results show that an 80◦ rotation of the room with a combined indirect passive system installed leads to indoor air temperatures about 40% lower than the temperatures in the south-oriented room. Results of Pathirana et al. [32] on shape factor influence indicate that the rectangular shape provides the higher thermal comfort, while window-to wall-ratio influence on thermal comfort is around 20–55%. Investigations on specific passive solar solutions report results close to the ones showed in this paper. As showed by Owrak et al. [15] the installation of a sunspace can lead to a 10–15% energy saving with no optimization: if a storage tank is added, the reduction can reach from at least 37% up to 87%. Other optimized studies show energy saving percentage even higher than the present paper's data: the integration of a south-faced sunporch in China led to a coal saving rate of 51.9% [33], while a Trombe wallrelated saving on a residential building in Portugal was about 43% [20]. The difference in this case could both be due to the very low energy demand of the building, 14.95 kWh/m2, and the lower indoor comfort temperature setpoint, 18 ◦C. Nevertheless, one of the major limits of the investigations on passive solar systems is the generalization of the results. Comparison of performance and savings from different research must take into account the boundary conditions of the passive strategies, such as latitude or kinds of building, which can hugely vary the impact on the total building energy demand. Due to the high

number of variables defining the interaction of a building and a passive solar system, results from a specific case study or measurement from experimental activity cannot be generalized without proper assumptions. In addition, differently from common building systems, passive solutions deal with the building design at an architectural level to reach the high integration required, thus the sizing process and the optimization strategy of each solution must be tailored to the specific building. Thus, the main purpose of passive solar investigation should be to develop a general framework and guidelines for building design, or a protocol for the optimization process, as tools that can be adapted to different cases.

The sizing and design of a passive solar solution is not always simple. Moreover, the efficiency is related to multiple interconnected parameters, both on a technical and a climatic side, thus the evaluation and optimization of passive solar strategies needs to be carried out taking into accounts the different contribution of these factors to various elements: the energy balance, the cost of construction and maintenance, and the environmental impact. Another limit of passive solar analysis is proper technical and economic evaluation, usually based on a pure energy performance evaluation. As the synergy of intrinsic and extrinsic parameters defines the performance of passive solar solution, and the synergy of different systems can guarantee higher levels of energy savings as showed in the previous analysis, a synergy of evaluating factors determine the cost–benefit correlation to optimize this combination. Another element that can be considered in the analysis is the economic impact of the passive solar system, which is sometimes highly relevant. In general, the evaluation of the performance of a passive solar system can be carried out with different methods: an analysis exclusively based on energy balance or a life cycle analysis taking into account the environmental impact, with the related reduction of fuel consumption and greenhouses emissions, or economic analysis, to consider the payback time and the credit of original constructions elements replaced. A system design depends on the balance between the saving from energy consumption and the construction cost, during the lifespan. In these cases, as all the kinds of energy are equaled, the low available power and conversion efficiencies disadvantage the value of solar energy. In addition, this analysis is strictly country-dependent, as in some countries, the low price of energy, subsidized by the local government, results in even lower passive systems profitability [34]: in this perspective, the construction of passive solar systems strictly depends on the opportunity to exploit possible local benefits. As a result, a common economic analysis would not suggest the implementation of passive solar systems: to encourage the diffusion of this kind of strategies, the contribution to the reduction of greenhouse gas emissions or the energy degradation connected with the use of fossil fuels must constitute integral elements of the analysis. Possible alternatives may consist of two different approaches. A penalizing coefficient related to energy degradation could be introduced in the balance equation to promote the use of solar energy as a direct source: by counterbalancing the economic advantage of common energy vectors, this coefficient should enhance the use of natural energy. Otherwise, the evaluation must be based on a wider perspective through a multicriteria analysis that consider both technical, architectural, and energy stream-related issues.

#### **6. Conclusions**

Passive solar systems hide a huge potential as energy saving measures for buildings. The integration of different cooperating solutions in buildings is a relevant asset towards a nearly zero-energy building perspective. The design process is ruled by the synergy of various parameters, both intrinsic and extrinsic, that affect the performance and integrability of the passive solar system. In the paper, the authors have tried to define a general model for the definition of the performance of a passive solar system. The model is based on the combined consideration of direct and indirect thermal resistance and capacitive elements: it takes into account the massive capacitance of passive solar strategies in buildings and solar radiation variable resistances due to shading systems in summer and surrounding condition in winter, affecting the exploitation of diffuse and reflected solar radiation. As analyzed in the paper:


The integration of passive solar systems is hampered by performance evaluation: a simple energy balance disadvantages solar energy, characterized by low available power and low conversion efficiencies, while in an economic analysis, low energy costs, subsidized by some local government, makes them less cost-effective. Due to higher reliability and easier design, the integration of active devices has become a more common practice in the building market. In a long-term time frame, considering energy and carbon payback times, solar energy-based interventions, even for energy retrofit, proved to be profitable [7]. Future activity will continue both quantifying the impact of influencing parameters on passive solar system performance to develop a general framework useful to building design, analyzing combined solar systems. Research will focus on a proper way to evaluate the benefits of a passive solar design accounting on energy evaluation and energy degradation, by developing a multicriteria optimization function that considers each contribution of passive solar strategies.

**Author Contributions:** Conceptualization, A.F. and F.F.; methodology, A.F.; software, G.C.; writing original draft preparation, G.C.; writing—review and editing, A.F. and F.F.; visualization and supervision, A.F. and F.F. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in article.

**Conflicts of Interest:** The authors declare no conflict of interests.

#### **Nomenclature**


#### **References**


### *Article* **Simulating and Comparing Different Vertical Greenery Systems Grouped into Categories Using EnergyPlus**

**Alberto Arenghi 1,\*, Camilla Perra <sup>2</sup> and Marco Caffi 1,3**


**Abstract:** The use of vegetation for the energy efficiency of buildings is an increasingly widespread practice; therefore, the possibility of representing these systems correctly with the use of simulation software is essential. VGS performances have been widely studied, but currently, the lack of a unique simulation method to assess the efficiency of different types of VGS and the absence of studies evaluating the performances of all the systems available, proposing simulation models for each of them, leads to an incomplete energy representation. The aim of this study is to achieve a consistent and complete simulation method, comparing the different systems' performances. The research is made up of five main steps. Firstly, a classification to group these systems into specific categories was proposed; secondly an in-depth analysis of existing literature was worked out to establish the methods used for different types of VGS. The study of plant physiology allowed the definition of an energy balance, which is valid for all vegetated surfaces; then, each category was associated to a mathematical formula and finally integrated into the EnergyPlus software. The results achieved for each model were compared evaluating two important parameters for the termohygrometric conditions control: outside walls face temperatures and operative temperatures.

**Keywords:** Vertical Greenery Systems (VGS); classification; comparison of different types of VGS; mathematical modeling and thermohygrometric analysis; EnergyPlus

#### **1. Introduction**

The search for technological systems and materials for urban and building regeneration, especially in recent years, has paid particular attention to sustainability. The integration between vegetation and buildings responds effectively to this request, providing benefits proven by several studies: the reduction of CO2 emissions and the high temperatures that determine the "heat island" effect, modifying the urban microclimate [1–5], the increase in the quality of life [6,7] and the improvement of building hydrological [8] and thermal performances. Vertical Greenery Systems (VGS), especially, have a great potential, as buildings in urban areas develop mainly vertically, while Green Roofs (GR) only affect the higher floors in tall buildings [9,10]. Furthermore, GR do not include particularly diversified systems, a feature possessed by VGS instead, which in fact require different models.

Currently, the VGS are mainly included in projects carried out by internationally renowned architects, and have very high construction and maintenance costs. For example, Stefano Boeri designed a tower completely surrounded by trees in Milan [11] and Herzog & de Meuron integrated the Mur Vegetal, the system patented by the botanist Patrick Blanc [12], with the building envelope in their project at Caixa Forum in Madrid; the same system was chosen by Jean Nouvel for the Musée du Quai Branly in Paris. The design of systems with accessible costs, to allow a wider diffusion, can be encouraged through a more in-depth knowledge of VGS and their benefits on buildings. In fact, there are several

**Citation:** Arenghi, A.; Perra, C.; Caffi, M. Simulating and Comparing Different Vertical Greenery Systems Grouped into Categories Using EnergyPlus. *Appl. Sci.* **2021**, *11*, 4802. https://doi.org/10.3390/ app11114802

Academic Editors: Tiziana Poli, Luisa F. Cabeza, Andrea Giovanni Mainini, Gabriele Lobaccaro, Juan Diego Blanco Cadena and Mitja Košir

Received: 7 April 2021 Accepted: 20 May 2021 Published: 24 May 2021

**Publisher's Note:** MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations.

**Copyright:** © 2021 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

<sup>1</sup> Department of Civil, Architectural, Environmental Engineering and Mathematics (DICATAM), University of Brescia, 25123 Brescia, Italy; marco.caffi@unibs.it

technological solutions capable of providing different advantages, replacing traditional systems. The aim of the present study consists in identifying the contribution offered in the thermohygrometric field by the different types of VGS, translating the behavior of plants into a mathematical form that can be suitable for the EnergyPlus software. The validation of the methods proposed is obtained by a comparison between mathematical models and the experimental data, both as presented in the scientific literature.

#### **2. Classification**

The term VGS includes several systemic types that possess different characteristics and that are functional for specific plant varieties. Moreover, to build high-performance façades, it is necessary to act differently depending on the climate and the characteristics of the building [13], using the most suitable VGS. It is therefore necessary to provide a classification aimed at organizing plant verticalization into sets having common characteristics, which can be properly analyzed through accurate energy simulations and thus appreciate the differences. Some studies have proposed grouping, analyzing the scientific literature and systems characteristics, but without proposing a simulation method for each category [14–18]. On the contrary, in other research studies, such as the one conducted by Wong et al. [19], the field measurements for different VGS were analyzed but without proposing a classification.

In the present study, grouping into categories, based on the differences among the main technological solutions by considering both their geometrical and mathematical properties, is proposed. Each category has a different effect on the building envelope, based on its characteristics, through all or some of the following properties: shading, wind barrier, evaporation, transpiration and ventilated façade, as shown in Figure 1.

**Figure 1.** Proposed classification of VGS. Effects on buildings are specified for each category.

By re-elaborating the classification of VGS proposed by Bit [20], according to the energy benefits, three macro categories were defined: the Green Barrier Systems (GBS), the Green Coating Systems (GCS) and the Green Walls (GW). Each group interacts differently with the building envelope and therefore there are substantial differences in the approach to simulation. Further breaking down into sub-categories indicates differences in modeling or in the change of some parameters. GBS have the lowest level of integration with the building walls because there is no direct contact between them. The Green Barrier made up of trees (in the surroundings of the building or integrated with the structure) was defined as the Green Tree Barrier (GTB); systems composed by climbing species were defined as the Green Climbing Barrier (GCB).

The plant organisms that grow in adherence to a building closure or on a support system that forms a small gap with the wall were defined as the Green Coating Systems (GCS) divided into the Green Climbing Coating (GCC) and the Green Modular Coating (GMC). The main difference between these two sub-categories concerns the species of plants used: the first one is made up of climbing species and the second one consists in non-climbing species and requires particular modular systems in which a small amount of substrate is present. Finally, the Green Walls (GW) include systems which require greater technical specialization than the other categories. The technology package (which includes the plants and the substrate) is supported by a subsystem and forms a gap with the walls, thus behaving like a ventilated façade. In this case, three categories have been proposed: the Mur Vegetal (MV) that refers specifically to the system patented by the botanist Patrick Blanc [12] (in which the substrate is an inorganic fiber layer, and a PVC panel is present) and the Light Systems (LS) and the Heavy Systems (HS) that have a soil substrate and differ from each other in the soil thickness (less or greater than 15 cm, respectively).

#### **3. Literature Review**

In the literature, the topic of the Vertical Greenery Systems (VGS) has been faced with both experimental studies and through numerical modeling. Nevertheless, the authors have only considered one single type of VGS at a time in simulations, and therefore, a comparison among all of the different systems with a unique method is not available. The studies analyzed investigate different areas and types: the trees shading effect [21–27], the double skin façade with plants [28–32] and the Green Walls [3,8,33–36].

Table 1 shows the most significant studies for the model developed, which have the most compatible solutions with EnergyPlus, grouping the references according to the macro-categories identified.

**Table 1.** Studies about VGS divided into the three categories defined. The VGS effects on buildings considered in each study are specified.



**Table 1.** *Cont.*

From Table 1, it is evident that all the mentioned studies consider just one type of VGS at time performing numerical analyses with diverse codes that evaluate different terms in thermal balance. Therefore, a consistent comparison among different VGS systems cannot be properly evaluated.

#### **4. Methodology**

The mathematical model used in this study was obtained by integrating some of the formulas analyzed in the literature review into EnergyPlus. The equations used have already been validated by previous research and are reported and specifically defined in Section 4.1. Then, according to the effects on buildings indicated in Figure 1, the components of the energy balance were integrated into the numerical code of the software, as presented in Section 4.2.

#### *4.1. Study of Plant Physiology*

The analysis of several studies and publications regarding plant physiology [37–51] allowed the determination of the energy balances that occur on the surface of plants.

Vegetated surfaces interact with the environment through energy exchange, basically involving four terms: net radiation *R*n, sensible heat flux *H*, heat flux through soil *G* and latent heat flux *L*, that are linked together by the balance proposed by FAO [38]. In particular, *G* value is negligible on daily averages [34,38]. Moreover, the physical characteristics of the leaves influence the energy balance on vegetated surfaces [43], so the main parameters were analyzed.

#### 4.1.1. Radiation Balance

Net radiation is the difference between incoming and outgoing radiation, considering both shortwave and longwave radiation [47]. It can be defined as the difference between net solar radiation and net longwave radiation:

$$R\_n = R\_{ns} - R\_{nI} \tag{1}$$

and typically takes on a positive value during the day and a negative one at night. Net solar radiation *Rns* is the percentage of radiation that is not reflected by the surface, and its value is therefore related to albedo by the following relation, as leaves are primarily absorptive [47]:

$$R\_{\rm ns} = (1 - a) \ast R\_{\rm s} \tag{2}$$

where albedo (α) depends on different variables like density, thickness and the color of leaves [43].

The solar radiation transmitted to soil, beyond the foliage layer, was calculated according to the following equation:

$$R\_{us} = (1 - \alpha) \ast R\_s \ast e^{-k\_s \ast LAI} \tag{3}$$

that considers the geometrical properties of canopy.

#### 4.1.2. Sensible Heat Flux

The energy exchange on a surface, due to sensible heat flux, is perceived as an increase or decrease in surface temperature. Heat transport occurs through convection, and after a comparison (using the EnergyPlus simulation program) with other studies [37,43,52], the mathematical formula proposed by Stec et al. [32] appears as the one that best fits what is stated by FAO [38]:

$$Nu = 0.37 \left( Gr + 6.417 \text{ R}c^2 \right)^{0.25} \tag{4}$$

where *Nu*, *Gr* and *Re* are, respectively, the Nusselt, the Grashof and the Reynolds number. Thus, the convective heat transfer coefficient *h* can be expressed as follows:

$$h = \frac{k}{N\mu \cdot L} \tag{5}$$

#### 4.1.3. Latent Heat Flux

Latent heat flux allows a substance to affect a state change, by adding heat, without perceiving an increase in the temperature of the substance itself [47]. This type of heat exchange characterizes the vegetated surfaces: water vaporizes thanks to the transpiration from the leaves and evaporation from the ground. The whole process is known as evapotranspiration and results in a cooling effect of the surroundings [8,34,41]. Mass and energy flows are related by the following equation:

$$L = \lambda \ast ET\tag{6}$$

where *L* is the latent heat flux, λ is the latent heat of vaporization, and *ET0* is the evapotranspiration value, starting from the FAO Penman–Monteith equation [38], adapted to VGS by Davis and Hirmer [49]:

$$ET\_0 = \frac{0.408\ \Delta \ast (R\_{\rm II} - G) + \ \gamma \ast \frac{900}{T\_d + 2\mathcal{I}\lambda \cdot \Gamma 5} \ast \mathcal{U}\_2 (\varepsilon\_s - \varepsilon\_d)}{\Delta + \gamma (1 + 0.34 \ast \mathcal{U}\_2)}\tag{7}$$

To obtain the evapotranspiration value *ET* for a particular plant species, *ET0* value is multiplied by coefficient *KC*, depending on the plant species [36,38].

#### 4.1.4. Physical Parameters of Leaves

The physical characteristics of plants that influence the energy balance with the environment are essentially the LAI (Leaf Area Index) [53,54] and extinction coefficient *ks* that depends on the spatial distribution of leaves and on the angle between the leaves and soil. Both these parameters contribute to the result of Equation (3).

#### *4.2. Integration in the EnergyPlus*

The use of a software that operates in dynamic regime is necessary to guarantee a simulation as close as possible to reality related to plant organisms, which are a living component of the building envelope and therefore respond to environmental conditions in a very complex way. The use of advanced programming language, the EnergyPlus runtime language (Erl) combined with the Energy Management System (EMS), and other functions integrated into the software make it possible to simulate every component of the energy balance on vegetated surfaces. EnergyPlus provides a model (EcoRoof Model [31]) to simulate greenery systems, but it works only for horizontal vegetated surfaces, and it does not consider the change of the emissivity values of foliage and soil and of the convective heat transfer coefficient, both influenced by the inclination of the analyzed surface.

#### 4.2.1. The EMS Settings—The Solar Absorptance

The leaves can absorb long-wave radiation almost completely, so they are considered as perfect emitters [47]; consequently, the thermal absorptance value is equal to 1. Instead, the solar absorptance coefficient (ζ) depends on the specie's physical characteristics, according to [43]:

$$\mathcal{Z} = 1 - \varepsilon^{-k\_s \ast LAI} - \mathfrak{a} \tag{8}$$

and for each parameter a variation range was defined (Table 2).

**Table 2.** Variation range for the variable parameters that influence solar absorptance coefficient and related references.


The reference species, *Bergenia Crassifolia* and *Geranium Macrorrhizum* were associated with a LAI equal to 2.24 and 1.89, respectively. These values were obtained by the comparison with similar species analyzed by Candelari [55].

Equation (5) was integrated in the EMS, setting the solar absorptance coefficient as an actuator (i.e., value affected by programming) and the other variables in the formula as sensors (i.e., input values).

#### 4.2.2. The EMS Settings—The Sensible Heat Flux

Sensible heat flux related to VGS was simulated using EMS, this time setting the convective heat transfer coefficient as an actuator. Analyzing different methods proposed in the literature [23,24,43,52], and comparing the daily sensible heat flux values obtained with the values of the other terms involved in the energy balance [38], the formula proposed by Stec et al. [32] resulted as the most suitable as reported above in Equation (4).

#### 4.2.3. The Advanced Settings—The Latent Heat Flux

The EnergyPlus, among its advanced settings, provides the possibility to add another term to the traditional energy balance on the outer or inner surface of a wall. This function was to simulate the evapotranspiration effect. The hourly latent heat flux was calculated according to Equation (7). Different values of coefficient *KC* were used to represent different plant species [34] to compare the related *ET* term.

#### 4.2.4. The Advanced Settings—The Ventilated Façade

The Green Walls can be compared to a ventilated façade, due to the gap between the continuous surface of these systems and the building envelope. This effect was never considered in developing GW's models, despite having a significant effect in summer energy efficiency. Analyzing some studies about these systems [56–58] and their simulation methods in the EnergyPlus [39], the most suitable model was defined. The ventilated cavity was modeled as a separate thermal zone, and the setting *Zone Ventilation: Wind and Stack Open Area* was applied. This function allows the automatic calculation of the convective heat fluxes in the gap, considering wind and stack effects.

#### 4.2.5. The Layers' Properties

The Green Walls were represented as a simplified model, composed of two layers: foliage and substrate, spaced from the wall by an air gap. The foliage properties are different for each plant species, so two reference species have been analyzed: *Geranium Machrorrhizum*, associated with Light Systems because of its superficial roots, and *Bergenia Crassifolia,* linked to Heavy Systems because of the roots developing in depth. Thermal and physical properties were attributed to these layers comparing the results obtained by Jayalakshmy and Philip [45] and Merzlyak et al. [46] for some plant species' leaves. Table 3 shows the properties obtained for the two reference species.

The study of the thermophysical properties of the soil, whose contribution is substantial due to its thermal mass, was carried out after a literature review [59–65]. Three types of soil have been analyzed in this study: sandy loam, loam and clay loam, suitable for cultivation, and for each one, a defined density was fixed, thermal conductivity and specific heat. For the two species selected, the composition of soil was chosen according to the plant considered, to ensure its proper growth. The properties of soil are related to its water content, that must be included in a specific range to allow the plants to fulfill their vital functions: between 5% and 10% for sandy soils and between 40% and 50% for clay soils, as stated by Pitts [65]. These values were used to find a linear correlation between sandy and clay soils, to identify the correct saturation percentage of the simulated soils as shown in Figure 2.


**Table 3.** Variation range for the variable parameters that influence solar absorptance coefficient and related references.

Other properties related to each soil, were obtained analyzing the studies carried out by Clauser and Huenges [61], Abu-Hamdeh and Reeder [59] and Monteith and Unsworth [50]; the results are shown in Table 4.

**Figure 2.** The optimal range of saturation percentage for each type of soil, to guarantee plant survival, is represented by the rectangular boxes; instead, the values indicated as a line generate stress in plants.



#### *4.3. Mathematical and Geometrical Models*

Each category above defined was simulated in the EnergyPlus using simple models, by adopting small cubic samples (3 × 3 × 3 m) with 15 cm concrete walls. The concrete cubic sample was used as reference model in the comparisons with each category. The analysis of these models allowed the comparison between VGS categories and the execution of a large number of tests, avoiding the simulation of complex buildings. The dynamic simulations were performed in a free running mode, without plants. The meteorological data used refer to the Brescia–Ghedi weather file [66].

From the geometric point of view, GBS were modeled as shading objects: simplified trees for GTB and rectangular surfaces for GCB, both placed at a distance of 2 m from the walls of the sample. A transmittance schedule was associated with each shading object, to represent the different transmission of solar radiation in each season.

GCS were simulated adding two layers on the outer sample's surfaces: an anti-root membrane and a vegetated layer. The subcategory GMC also has a small layer of substrate, but its contribution can be negligible in terms of thermal insulation. In addition to the modification of the layers' properties, the behavior of the plants was reproduced through the modification of the solar absorptance, of the sensible heat flux and by adding the latent heat contribution. The latter, for the GCC only results from foliage transpiration, while for the GMC results from the whole process of evapotranspiration, due to the presence of soil.

The GW have the common feature of functioning as ventilated façades, and they were simulated as described in 4.2.4. The MV has a defined stratigraphy, and the outer layer was simulated respecting the characteristics of the system patented by Patrick Blanc [12]. The HS and LS can be composed of different types of plants and substrates, which determine a great variability in the results. Therefore, a parametric study was carried out to identify the most effective combination of variables in improving the thermohygrometric behavior of the sample. The parameters were analyzed one at a time, keeping the other characteristics of the system unchanged and applying only the setting concerning that specific variable. The variation of the extinction coefficient *ks*, the thickness of the air gap and the type of soil appears to be almost irrelevant in influencing the external surface temperatures; while the variation of LAI, as shown in Figure 3, influences the external surface temperatures which is reduced by about 2 ◦C in summer for a LAI equal to 5 compared to a LAI equal to 1, comparable to the results obtained by [43].

**Figure 3.** Effect of LAI on the surface external temperature of the walls. Model properties: Substrate in Loam (9 cm); *ks* = 0.70; air gap thickness = 4 cm.

#### **5. Results and Discussion**

The overall assessment of the thermohygrometric benefits on the simulated model was made by comparing the results obtained for the VGS models and the reference concrete model, analyzing external surface temperatures and operative temperatures, both in summer and winter. All the graphs refer to the south-facing walls, and the physical parameters used are consistent with the species suitable for the different systems, as indicated above and in [67].

The trends of outside face temperature for each category and for the concrete model, compared with outside air temperature, are shown in Figures 4 and 5, in summer and winter conditions, respectively.

The summer chart shows the data obtained during the simulation performed in the last week of July (25-31/07), the hottest day of the summer according to the meteorological data analysis [66].

**Figure 4.** Summer (25-31/07). Comparison between the external surface temperatures of the south wall for each category, the concrete model and outside air.

The GBS reduce concrete surface outside face temperatures by about 1.5 ◦C, due to the shading effect of trees and climbing species. There are no significant differences in the trends of the GTB and GCB models as both act only through shading and do not influence the temperature of the wall with the transpiration process. Hes [23] and Stec et al. [32] instead reported up to a 25% reduction in the outside surface temperatures for the GBS. The Different results could be due to the different height and position of the trees or climbing species or to a greater window area of the analyzed model. The GCC reduce the temperature of the concrete model on average by about 5 ◦C, confirmed by the empirical results obtained by [68], and the GMC by about 6 ◦C, due to the presence of soil, which also adds the evaporation process. The GW systems remarkably reduce the surface temperatures, also lower than the ones of outside air. The most performing systems are the LS and HS that reduce the maximum temperature of the concrete model up to 13 ◦C, included in the range of values obtained by Mazzali et al. [69]. These systems record higher evaporation values from the soil, having thick and continuous layers.

**Figure 5.** Winter (01-07/12). Comparison between the external surface temperatures of the south wall for each category, the concrete model and outside air.

The winter chart shows the data obtained during the simulation performed in the first week of December (01-07/12), the coldest day of the year. The trend of the external surface temperature of the GBS coincides with that of the bare wall, as in this season they only act as wind barriers; the latter effect could be more relevant with denser vegetation. The GCS increase the surface temperature by about 1 ◦C on average, during the day, similarly to the results obtained by [70], as they have a better behavior as wind barriers. The GW, instead, follow the trend of the outside air temperature, with negligible variations, increasing the external surface temperature up to 8 ◦C higher than the reference. No simulations were found in the winter period comparable with those carried out.

The influence of the different models on the summer and winter operative temperature is shown in Figures 6 and 7, respectively.

In summer (Table 5), the HS have the most significant impact in lowering the operative temperature: up to 9 ◦C less than the concrete model. These results derive from the higher thermal mass of the soil and from a higher LAI value than the other systems; in fact, the HS, thanks to the high thickness of the substrate, can host larger species and therefore greater foliar density. The LS, MV and GMC have similar trends, with a reduction in peak temperatures of between 4 and 8 ◦C, similarly to the field measurement on a living wall made by [71]. In these cases, the thermal mass of the soil, being less thick, has less effect on lowering temperatures. The GCC lower the temperatures between 3 and 6 ◦C, decreasing temperatures thanks to the transpiration of the foliage and shading. The GBS generally do not show a significant lowering in air temperature [72,73], even if in two of the days analyzed, there is a reduction in temperature of up to 4 ◦C, due to shading.

The best performing system in winter (Table 6) is the MV, which has 15 cm thick PVC panels in its stratigraphy, with a thermal conductivity lower than that of the soil, which allows a better insulation than the other systems; the operative temperature increases up to 4 ◦C compared to the bare wall. The LS and HS increase the operative temperature by about 1 and 2 ◦C, respectively, compared to the concrete model. In these systems, the soil provides thermal resistance but, being almost always wet, does not have a low enough

thermal conductivity to be insulating. The GCS have a very similar trend to that of the concrete model and the GBS trend coincides with the latter, as they shelter from the cold winter wind but do not isolate the wall.

**Figure 6.** Summer. Comparison between the operative temperatures obtained for each category and outside air.

**Figure 7.** Winter. Comparison between the operative temperatures obtained for each category and outside air.


**Table 5.** Summer. Comparison of the results obtained on the south wall of the sample during the daytime and evaluation of the main variables involved for each category.

**Table 6.** Winter. Comparison of the results obtained on the south wall of the sample during the daytime and evaluation of the variables involved for each category.


#### **6. Conclusions**

The subdivision of the VGS into categories turned out to be a fundamental step in setting up the entire work, allowing to compare the advantages of using different VGS. The variations in modeling and in the attribution of diversified energy balances on the same sample building allowed comparison of results about trends of the external surface temperatures and the operative temperatures for each system. The in-depth literature review produced mathematical models and allowed comparison of the results with those from empirical studies, demonstrating a good match. The HS (with a consistent substrate thickness) proved to be the best performing in the summer season, while the Mur Vegetal results to be the best performing system in winter. Compared to the concrete model, generally all categories improve the thermohygrometric performance of the sample building. In particular, the benefits on the outside face temperatures of the walls, which remain below the temperature of the outside air on hot summer days, are significant.

The results obtained refer to the simulated sample and therefore may vary in relation to the characteristics of the building analyzed (stratigraphy, number and size of windows, location, etc.) The simulation of a single sample and the non-determination of the contribution of each term of the energy balance in energy efficiency can be considered limitations of the present research that can be developed in further research with a parametric study.

**Author Contributions:** Conceptualization, A.A., C.P. and M.C.; methodology, A.A., C.P. and M.C.; software, A.A., C.P. and M.C.; validation, A.A., C.P. and M.C.; formal analysis, A.A. and C.P.; investigation, A.A. and C.P.; data curation, A.A. and C.P.; writing—original draft preparation, C.P.; writing—review and editing, A.A.; visualization, A.A. and C.P.; supervision, A.A. and M.C.; project administration, A.A. All authors have read and agreed to the published version of the manuscript.

**Funding:** This research received no external funding.

**Institutional Review Board Statement:** Not applicable.

**Informed Consent Statement:** Not applicable.

**Data Availability Statement:** The data presented in this study are available in Perra, C.; Arenghi, A.; Caffi, M. Verde Verticale: Analisi Termoigrometriche in Regime Dinamico. *DICATAM Technical Report* **2020**, *7*, 1–199, [67].

**Conflicts of Interest:** The authors declare no conflict of interest.

#### **References**

