Energy Benchmarking in Educational Buildings Through Cluster Analysis of Energy Retrofitting

energies

Article Energy Benchmarking in Educational Buildings through Cluster Analysis of Energy Retroﬁtting

Paola Marrone 1, Paola Gori 2 ID , Francesco Asdrubali 2,*, Luca Evangelisti 2, Laura Calcagnini 1 ID and Gianluca Grazieschi 3 1 Department of Architecture, Roma TRE University, Via della Madonna dei Monti 40, 00184 Rome, Italy; [email protected] (P.M.); [email protected] (L.C.) 2 Department of Engineering, Roma TRE University, Via Vito Volterra 62, 00146 Rome, Italy; [email protected] (P.G.); [email protected] (L.E.) 3 Department of Engineering, Niccolò Cusano University, Via don Carlo Gnocchi 3, 00166 Rome, Italy; [email protected] * Correspondence: [email protected]

Received: 2 February 2018; Accepted: 9 March 2018; Published: 14 March 2018

Abstract: A large part of the stock of Italian educational buildings have undertaken energy retrofit interventions, thanks to European funds allocated by complex technical-administrative calls. In these projects, the suggested retrofit strategies are often selected based on the common best practices (considering average energy savings) but are not supported by proper energy investigations. In this paper, Italian school buildings’ stock was analyzed by cluster analysis with the aim of providing a methodology able to identify the best energy retrofit interventions from the perspective of cost-benefit, and to correlate them with the specific characteristics of the educational buildings. This research is based on the analysis of about 80 school buildings located in central Italy and characterized by different features and construction technologies. The refurbished buildings were classified in homogeneous clusters and, for each of them, the most representative building was identified. Furthermore, for each representative building a validating procedure based on dynamic simulations and a comparison with actual energy use was performed. The two buildings thus singled out provide a model that could be developed into a useful tool for Public Administrations to suggest priorities in the planning of new energy retrofits of existing school building stocks.

Keywords: cluster analysis; school buildings; energy efficiency; cost-effectiveness; retrofit interventions

1. Introduction The European Directive 2010/31/EU [1] introduces minimum energy requirements for buildings and in order to meet them, energy retroﬁts are usually necessary for existing buildings [2–4]. In addition, the European Directive 2012/27/EU [5] directs the member states to develop an intensive refurbishment of public buildings. Schools represent an important part of public building stock and, even if they are not a predominant percentage of the total public patrimony, their refurbishment represents an important issue, both for social and educational aspects. Therefore, in Italy, a high number of buildings (about 43,000, representing 58% of the stock of Italian educational buildings) were recently subjected to energy retroﬁts [6]. Several studies on the energy performance of schools estimated their medium normalized energy uses. This normalization procedure is necessary in order to compare the uses among different buildings. It can be achieved as a function of the volume of schools, the heated surface, the number of classes or number of students, and the external climate. Findings in literature show this normalization in terms of the heated surface but, since schools may have rooms with different heights, the normalization in terms of the heated volume can be considered more appropriate [7–9].

Energies 2018, 11, 649; doi:10.3390/en11030649 www.mdpi.com/journal/energies Energies 2018, 11, 649 2 of 20

Comparing such a huge amount of data, that includes schools located in different countries, cannot be useful if standard indoor comfort conditions are not guaranteed and a normalization as a function of the external climate is not performed [8]. Children attend schools for a long period and good indoor comfort conditions must be guaranteed with reduced energy uses. The external climate has a strong inﬂuence on the building energy requirements and its inﬂuence can be considered by the Heating Degree Day (HDD) [8,9]. Energy use in schools can be characterized by different performance indicators, depending on several parameters, such as:

• the school’s typology (kindergarten, primary or high school), which also reflects the different occupational schedules and the different facility buildings connected to the supplementary activities given outside of teaching hours (laboratories, sport facilities, canteens, etc.) [8,10]. Generally, space heating is not provided all day long but only in the morning during the teaching period. However, some schools also have afternoon activities with a longer time schedule for the heating system; • the ratio between external surface (S) and heated volume (V), which reflects how the geometric characteristics of the building influence energy use; • the construction period: new schools show lower energy use in comparison with buildings made during the absence of any energy regulation [10].

The comparison of different use patterns for schools and the definition of benchmarks for energy use is crucial when an energy requalification of the building stock must be undertaken. The importance of the energy upgrade of existing public buildings is underscored by Ascione et al. [11], with a focus on educational buildings. The role of public administrations is fundamental to meeting the European directives on greenhouses gas emissions and energy efficiency. Their role is to provide stimulus for private interventions, to give demonstrative examples, and good practice guidelines. Moreover, the central administrations of various countries also provide the financial incentives for all of the interventions. Financial stimulus often aims at reducing the dependence on imported energy and at increasing energy self-sufficiency. The aim of getting both economically convenient and thermodynamically efficient energy retrofit interventions has already been demonstrated to be effective by García Kerdan et al. [12], who propose a novel optimization methodology that was tested on a primary school located in London. The definition of the most cost-effective energy retrofit intervention is still one of the major challenges when studying the energetic requalification of buildings. Ma et al. [2] attempted a methodology able to identify the best retrofit option between the technologies and analysis models currently available. The costs of the retrofit interventions are usually affected by a wide range of uncertainty and probabilistic life cycle cost analysis would be the most suitable and realistic solution to check the economic effectiveness of alternative measures [13]. In this framework, the development of a tool to correlate significant characteristics of educational buildings with the best energy retrofit interventions from the point of view of a cost-efficiency ratio is here presented. Such an instrument can be useful for Public Administrations, for example at a regional scale, to establish a priority in the planning of new energy retrofits of school assets. Moreover, this contribution carries out a cost efficiency evaluation of the interventions done in the schools already refurbished and analyzes the obtained post-retrofit uses compared to the ones assessed before the interventions. The paper structure is as follows. In Section2, we introduce the state of the art in this research field. In Section3, we describe in detail materials and methods. In Section4, we describe, compare, and discuss the outcomes of the cluster analysis and the simulations results. In Section5, we draw the conclusions. Energies 2018, 11, 649 3 of 20 Energies 2018, 11, x FOR PEER REVIEW 3 of 21

2. State State of of the the Art Art Several works works about about the the energy energy performance performance of school of school buildings buildings can canbe found be found in literature. in literature. Dias PereiraDias Pereira et al. et[8] al. present [8] present a literature a literature review review abou aboutt the the energy energy uses uses of of worldwide worldwide schools schools with with the purpose of achieving energy benchmarks. Figure 11 showsshows anan elaborationelaboration ofof the annual heating energy use values in European countries considering data from [[8].8].

Figure 1.1. EnergyEnergy uses uses of schoolof school buildings buildings in European in Europe countriesan countries (varying from(varying about 52from to 197 about kWh/m 52 to2 year 197) 2 kWh/m(elaboration year) of (elaboration the authors fromof the [ 8authors]). from [8]).

According to other studies [14], Greek schools have an average heating use of 68 kWh/m2 year According to other studies [14], Greek schools have an average heating use of 68 kWh/m2 year that that represents the 72.4% of the total energy need. The overall calculated potential of energy represents the 72.4% of the total energy need. The overall calculated potential of energy conservation conservation is about 20% and the intervention that has the strongest influence on heating energy is about 20% and the intervention that has the strongest influence on heating energy savings is the savings is the envelope insulation with a reduction of space heating equal to 43%. In their research, envelope insulation with a reduction of space heating equal to 43%. In their research, Dascalaki Dascalaki and Sermpetzoglou [15] present similar values for the energy use of 500 Greek schools, and Sermpetzoglou [15] present similar values for the energy use of 500 Greek schools, reporting reporting 57 kWh/m2 year for heating and 68 kWh/m2 year as the total specific energy requirement. 57 kWh/m2 year for heating and 68 kWh/m2 year as the total specific energy requirement. In France, In France, a retrofit program regarding Parisian schools revealed a global energy use of 224 kWh/m2 a retrofit program regarding Parisian schools revealed a global energy use of 224 kWh/m2 year year of primary energy [16]. On the other hand, the annual primary energy use in Cyprus schools is of primary energy [16]. On the other hand, the annual primary energy use in Cyprus schools is 116.22 kWh/m2 year [17]. The addition of 5 cm of polystyrene on both walls and roof can reduce the 116.22 kWh/m2 year [17]. The addition of 5 cm of polystyrene on both walls and roof can reduce the energy use by 32%, while the most efficient solution for the air conditioning system in classrooms energy use by 32%, while the most efficient solution for the air conditioning system in classrooms and labs is the removal of the split-unit and its substitution with fans. Schools in Slovenia have a and labs is the removal of the split-unit and its substitution with fans. Schools in Slovenia have global energy requirement of 192 kWh/m2 year and for 83% of them the insulation of the envelope is a global energy requirement of 192 kWh/m2 year and for 83% of them the insulation of the envelope is recommended [8]. They identified this intervention as the principal measure to adopt in order to recommended [8]. They identified this intervention as the principal measure to adopt in order to reach reach the level of efficiency of neighboring countries. Luxemburg’s new schools have an average the level of efficiency of neighboring countries. Luxemburg’s new schools have an average value of value of heating demand of 93 kWh/m2 year [10] with potential energy savings in passive buildings heating demand of 93 kWh/m2 year [10] with potential energy savings in passive buildings ranging ranging from 17% to 35% respectively, when compared with the standard ones. from 17% to 35% respectively, when compared with the standard ones. Taking into account Italian schools, Desideri and Proietti [18] estimated a thermal energy use Taking into account Italian schools, Desideri and Proietti [18] estimated a thermal energy use from 15.7 kWh/m3 year to 21.7 kWh/m3 year after analyzing 29 schools located in the province of from 15.7 kWh/m3 year to 21.7 kWh/m3 year after analyzing 29 schools located in the province Perugia (central Italy), and estimated a potential reduction of the energy requirements of about 38%. of Perugia (central Italy), and estimated a potential reduction of the energy requirements of about The heating energy use represents 80% of the total energy requirements and generally the heating 38%. The heating energy use represents 80% of the total energy requirements and generally the systems are characterized by natural gas, oil boilers, and by radiators as emission system. The heating systems are characterized by natural gas, oil boilers, and by radiators as emission system. generators can be obsolete and, in many cases, they are oversized in terms of installed power with a The generators can be obsolete and, in many cases, they are oversized in terms of installed power with considerable drop of the efficiency as a consequence of their part load. The envelope of the buildings a considerable drop of the efficiency as a consequence of their part load. The envelope of the buildings located in that region can be divided into old structures located in the historic centers, characterized located in that region can be divided into old structures located in the historic centers, characterized by by load bearing walls, and prefabricated buildings often located in the outskirts of the towns. The load bearing walls, and prefabricated buildings often located in the outskirts of the towns. The highest highest thermal specific energy uses are detected for the second type of structures dated from 1970 thermal specific energy uses are detected for the second type of structures dated from 1970 to 1980, to 1980, with lower values for the same typologies built ten years later. Windows are the weakest part with lower values for the same typologies built ten years later. Windows are the weakest part of the of the envelopes and, in some cases, remarkable infiltrations through the frames are detected during the energy audit [18]. In their study, Sarto and Dall’O’ [19] provided an energy audit campaign investigating 49 schools in the Lombardia region (north of Italy). They found an average value of 47.1 kWh/m3 for the

Energies 2018, 11, 649 4 of 20 envelopes and, in some cases, remarkable infiltrations through the frames are detected during the energy audit [18]. In their study, Sarto and Dall’O’ [19] provided an energy audit campaign investigating 49 schools in the Lombardia region (north of Italy). They found an average value of 47.1 kWh/m3 for the heating energy demand. Some retrofit measures are proposed, based on three economic evaluations: a minimal investment scenario, a cost-effectiveness scenario, and a high-performance scenario, with the aim of reaching the standards of net zero energy buildings. The study demonstrates that it is not always convenient to pursue the high performance scenario [19]. Corgnati et al. [20], considering 100 schools located in the Piemonte region (north-west of Italy), showed an average heating value which ranges between 110 kWh/m2 and 115 kWh/m2, that corresponds to 37–38 kWh/m3. The paper shows how the definitions of specific indicators of space heating energy uses can be useful to predict the energy needs of a large building stock with a good approximation. Moreover, Walter and Sohn [21] have already demonstrated that it is possible to get energy saving estimations from the retrofitting of a large building’s stock, through statistical analysis. The application of a multivariate linear regression model, to foresee possible energy savings from different retrofits actions, results in a very interesting solution, particularly when the energy simulation is not cost or time feasible. Statistical methods are currently used for the prediction of the energy performance of buildings [22]. Recently cluster analysis has been employed to define homogenous classes and reference buildings within classes relying on data related to real energy uses [9,23,24]. In particular, Arambula Lara et al. [9] applied the cluster analysis to a sample of about 60 schools in the North-East of Italy, identifying reference buildings within the clusters in order to optimize the energy retrofit measures. The authors [9] correlated the real energy demands of the buildings’ stock to their geometrical and technical characteristics by means of proper statistical analyses. A fuzzy clustering technique has been used by Santamouris et al. [24] for the classification of energy data of 320 schools in Greece, clustered by similar characteristics. The clustering permitted the selection of representative schools for a more detailed analysis [23,24]. The definition of reference buildings has been promoted also by the European Commission [25] for cost-optimal analyses of energy retrofits in the existing building stock. Raatikainen et al. [26] use the k-means method for a data mining analysis on the average energy uses of six Finnish schools. The results show that the construction period has a strong influence on the energy requirements of the educational buildings: new schools are more efficient than older ones. Hong et al. [27] run a cluster analysis, using the decision tree method, of 6282 elementary schools located in South Korea. After the clustering, different combinations of methodologies were applied to evaluate the CO2 emissions from electric energy use, such as multiple linear regression, artificial neural networks, and case-based reasoning. The work shows that better accuracies and minor standard deviations can be reached when clustering is applied and all the available predictors are included in the analysis. Recently, Salvalai et al. [28] have proposed a methodology based on the cluster analysis, that defines the optimal cost-benefit retrofit action through an energy analysis of the reference buildings that represent every homogeneous group. In this paper, we present data on the energy uses (before and after retrofit interventions when available) of 80 schools located in the Lazio region (central Italy). By means of the available database and through our own surveys, it was possible to find data about the buildings’ geometry, their construction age, energy retrofit interventions typology and their costs, energy uses before the refurbishment, and the primary energy saving after the retrofit. Specifically, data about savings for the whole dataset are declared by the designers and only for 20% of the buildings. The savings are obtained thanks to the monitoring of energy uses after the interventions for the year 2016. Aiming at identifying representative buildings of the whole stock, the cluster analysis was applied. The definition of reference buildings, which are representative of the homogenous classes of building stock, can be useful to develop specific energy retrofit plans, based on the cost-optimal method, which can then be extended to the entire cluster. Energies 2018, 11, 649 5 of 20

3. Materials and Methods

3.1. Buildings’ Sample Description A large database composed by the refurbished buildings was provided by the Lazio region administrative ofﬁces. The sample includes 80 schools that are not uniformly distributed on the regional territory. The highest percentage (45%) is in the province of Rome, 22% are in the Latina province, and scattered cases are in the other provinces of Rieti, Viterbo, and Frosinone (see Figure2). Energies 2018, 11, x FOR PEER REVIEW 5 of 21 IncompleteEnergies 2018 and, 11,unreliable x FOR PEER REVIEW data were excluded from the cluster analysis. The schools composing5 of 21 the sample can be classiﬁed on the basis of the category of educational institution, as indicated by province,province, and and scattered scattered cases cases are are in in the the other other province provinces sof of Rieti, Rieti, Viterbo, Viterbo, and and Frosinone Frosinone (see (see Figure Figure 2). 2). Italian law: IncompleteIncomplete and and unreliable unreliable data data were were excluded excluded fr fromom the the cluster cluster analysis. analysis. The The schools schools composing composing the the sample can be classified on the basis of the category of educational institution, as indicated by Italian • sample9 kindergartens can be classified or daycare on the centers basis of (1–2the category years old); of educational institution, as indicated by Italian law: • law:1 kindergarten and nursery school; • • •22 nursery99 kindergartens kindergartens schools or (3–5 or daycare daycare years centers old);centers (1–2 (1–2 years years old); old); • 1 kindergarten and nursery school; • • 1 kindergarten and nursery school; 11• nursery and primary schools; • 2222 nursery nursery schools schools (3–5 (3–5 years years old); old); • 4•comprehensive institutes, including nursery, primary and secondary schools; • 1111 nursery nursery and and primary primary schools; schools; • • •18 primary44 comprehensive comprehensive schools (6–10institutes, institutes, years including including old); nu nursery,rsery, primary primary and and secondary secondary schools; schools; • • •2 institutes,1818 primary primary including schools schools (6–10 primary(6–10 years years schools old); old); and lower secondary schools; • • •13 lower22 institutes, institutes, secondary including including schools primary primary (11–13 sch sch yearsoolsools and and old). lower lower secondary secondary schools; schools; • • 1313 lower lower secondary secondary schools schools (11–13 (11–13 years years old). old).

Figure 2. Spatial distribution of the analyzed schools in the Lazio territory: (a) map and (b) number FigureFigure 2. 2. Spatial distribution of the analyzed schools in the Lazio territory: (a)a map and (b) bnumber of schoolsSpatial per distribution province (RM of = the Rome; analyzed VT = Viterb schoolso; FR in = the Frosinone; Lazio territory: LT = Latina; ( ) mapRI = Rieti). and ( ) number of schoolsof schools per province per province (RM =(RM Rome; = Rome; VT VT = Viterbo; = Viterbo; FR FR = = Frosinone; Frosinone; LTLT = Latina; Latina; RI RI = =Rieti). Rieti).

FigureFigure 3 3 shows shows that that the the analyzed analyzed buildings buildings were were mostly mostly built built before before 1976 1976 and and only only a a few few of of them them wereFigurewere built built3 shows in in recent recent that years years the analyzed(6%). (6%). 1976 1976 buildings is is the the year year were of of the the mostly first first publication publication built before of of an 1976an energy energy and law onlylaw in in aItaly Italy few [29] of[29] them wereand builtand from from in recent Figure Figure years 3 3 it it is (6%).is possible possible 1976 to to is notice thenotice year that that of 52% 52% the of ﬁrstof the the publication buildings buildings were were of an built built energy without without law any inany Italy energy energy [29 ] and fromregulation. Figureregulation.3 it is possible to notice that 52% of the buildings were built without any energy regulation.

Figure 3. Frequency distribution of schools in terms of construction period. Figure 3. Frequency distribution of schools in terms of construction period. Figure 3. Frequency distribution of schools in terms of construction period. ConsideringConsidering the the heating heating volume volume of of the the buildings buildings (Figure (Figure 4), 4), 57.1% 57.1% of of them them have have a a volume volume lower lower 3 thanthan 50005000 mm3. . LowerLower volumesvolumes occuroccur whenwhen thethe schoolschool consistsconsists ofof aa singlesingle building,building, oror smallsmall kindergartenskindergartens and and nursery nursery schools. schools. In In the the case case of of more more than than one one building building and and for for comprehensive comprehensive institutesinstitutes includingincluding bothboth primaryprimary andand secondarysecondary schools,schools, thethe volumesvolumes areare bigger.bigger. TheThe ItalianItalian legislationlegislation [30,31] [30,31] fixed fixed the the minimal minimal standards standards for for th thee number number of of students students per per class class and and for for the the gross gross surfacessurfaces per per student student for for every every typology typology of of school. school. The The Italian Italian Government Government has has significantly significantly tried tried to to

Energies 2018, 11, 649 6 of 20

Considering the heating volume of the buildings (Figure4), 57.1% of them have a volume lower than 5000 m3. Lower volumes occur when the school consists of a single building, or small kindergartens and nursery schools. In the case of more than one building and for comprehensive institutes including both primary and secondary schools, the volumes are bigger. The Italian legislation [30,31] ﬁxed the minimal standards for the number of students per class and for the Energies 2018, 11, x FOR PEER REVIEW 6 of 21 gross surfaces per student for every typology of school. The Italian Government has signiﬁcantly tried reduceto reduce the the number number of ofsmall small schools, schools, privileging privileging the the development development of of schools schools in in urban urban areas areas and and in cities with a high high density density of of population. population. Sometimes Sometimes the the consequences consequences of of government government action have been been the unionunion ofof two two different different schools schools in ain comprehensive a comprehens educationalive educational institution. institution. Alternatively, Alternatively, the merge the mergeof two of schools two schools of the sameof the typology same typology occurred occurre withd a reductionwith a reduction of the number of the number of buildings. of buildings.

FigureFigure 4. FrequencyFrequency distribution distribution of schools in terms of gross heated volume.

Figure 5 shows the distribution of schools as a function of the ratio between the external surface Figure 55 showsshows thethe distributiondistribution ofof schoolsschools asas aa functionfunction ofof thethe ratioratio betweenbetween thethe externalexternal surfacesurface and the gross heated volume (called S/V ratio). Only 6.5% of the sample is composed of very compact and the gross heated volume (called S/V ratio). ratio). Only Only 6.5% 6.5% of of the the samp samplele is is composed composed of of very very compact compact buildings with an S/V value lower than 0.3. A significant percentage of the studied buildings (44.2%) buildings with an S/V value value lower lower than than 0.3. 0.3. A A significant significant percentage percentage of of the the studied studied buildings buildings (44.2%) (44.2%) has a S/V ratio higher than 0.6 and this confirms the high presence of small single-floor buildings in has a S/V ratio ratio higher higher than than 0.6 0.6 and and this this confirms confirms the the high high presence presence of of small single-floor single-floor buildings in the sample. the sample.

16 100% 100% 90% 14 90% 91% 91% 80% 12 75% 70% 10 75% 10 60% 8 50% 8 56% 50% 40% Frequency 6 38% 40% Frequency 6 38% 30% 4 30% 4 20% frequencyCumulative 19% 20% frequencyCumulative 2 10% 2 6% 10% 3% 6% 0 3% 0% <0.2 >0.8 <0.2 >0.8 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 0.2-0.3 0.3-0.4 0.4-0.5 0.5-0.6 0.6-0.7 0.7-0.8 S/V S/V Figure 5. Frequency distribution of schools in terms of S/V ratio. Figure 5. Frequency distribution of schools in terms of S/V ratio. ratio. 3.2. Cost Framework 3.2. Cost Cost Framework Framework The cost of all the interventions on the school buildings, financed by European funds, sums to The cost of all the interventions on the school buildings, financed ﬁnanced by European funds, sums to approximately 19.3 million euros. Around 13.2 million euros have been spent on the energy retrofit approximately 19.3 million euros. Around Around 13.2 13.2 mill millionion euros euros have have been been spent spent on on the the energy retrofit retroﬁt of the building envelope and just slightly more than 6 million euros for interventions on building of the building envelope and just slightly more than 6 million euros for interventions on building systems and renewable energy sources. Over 50% of the interventions concern the building envelope, which accounts for approximately 70% of the costs. The first observations of these data drive us to deepen an evaluation of effectiveness of the interventions. In building envelope renovation, the material choices and the realization of the works have an important impact on both the environmental and the technological quality of buildings. 2 The cost of renovation per floor area is in most of the cases below 500 €/m2 (Figure 6). This figure is significant for an ordinary cost that could represent the use of traditional technological standards, linked to common (not best) practices and, supposedly, to traditional materials.

Energies 2018, 11, 649 7 of 20 systems and renewable energy sources. Over 50% of the interventions concern the building envelope, which accounts for approximately 70% of the costs. The first observations of these data drive us to deepen an evaluation of effectiveness of the interventions. In building envelope renovation, the material choices and the realization of the works have an important impact on both the environmental and the technological quality of buildings. The cost of renovation per floor area is in most of the cases below 500 €/m2 (Figure6). This figure is significant for an ordinary cost that could represent the use of traditional technological standards, linked to common (not best) practices and, supposedly, to traditional materials. Energies 2018, 11, x FOR PEER REVIEW 7 of 21

Energies 2018, 11, x FOR PEER REVIEW 7 of 21 Figure 6. Number of interventions as a function of cost per floor area (€/m2, (a)) and the cost per square Figure 6. Number of interventions as a function of cost per floor area (€/m2,(a)) and the cost per meter of the interventions’ surface area (€/m2, (b)). square meter of the interventions’ surface area (€/m2,(b)). 3.3. Retrofit Interventions 3.3. Retrofit InterventionsFrom the aforementioned database it was also possible to extract some information about the interventions carried out in the retrofits and the consequent improvement in energy class as defined Fromby the the aforementionedItalian legislation [32]. database The interventions it was can also be possible divided in: to extract some information about the interventions carried out in the retrofits and the consequent improvement in energy class as defined 1. envelope insulations (vertical walls insulation, roof insulation, windows replacement); by the Italian legislation [32]. The interventions can be divided in: 2. energyFigure service 6. Number upgrades of interventions (heating, as cooling); a function of cost per floor area (€/m2, (a)) and the cost per square 1. envelope3. renewable insulationsmeter energy of the (verticalinterventions’ sources implementation walls surface area insulation, (€/m2, (solar,(b)). roof thermal, insulation, photovoltaic). windows replacement); 2. energy serviceFigure3.3. Retrofit 7 upgradesshows Interventions the frequency (heating, distribution cooling); of the kind of interventions proposed in the energy retrofit phase. It is noticeable that the vertical walls insulation interventions represent approximately From the aforementioned database it was also possible to extract some information about the 3. renewablehalf (50.6%) energy of the sources total ones implementation and that 84.4% of (solar, the schools thermal, chose photovoltaic). to replace windows. Also, the interventions carried out in the retrofits and the consequent improvement in energy class as defined Figureintroduction7 showsby the of theItalian the frequency photovoltaiclegislation [32]. distribution system The interventions is very common of can the be divided kind and it of in:has interventions been implemented proposed at a frequency in the energy of 81.8% of the sample. The integration of renewable energy sources can also be carried out thanks to 1. envelope insulations (vertical walls insulation, roof insulation, windows replacement); retrofit phase.the installation It is noticeable of solar thermal that the systems, vertical but this walls happens insulation in a lower interventions percentage of representthe cases (29.9%). approximately 2. energy service upgrades (heating, cooling); half (50.6%)Finally, of3. the renewable interventions total energy ones regardingsources and implementation that the 84.4% plants (solar, ofinvolve the thermal, mainly schools photovoltaic). the choseheating to system replace with windows.a few Also, percentages implemented on the conditioning system. It is worth noticing that the interventions the introduction of theFigure photovoltaic 7 shows the frequency system distribution is very of common the kind of and interventions it has been proposed implemented in the energy at a frequency regarding the envelope, the energy systems, and the introduction of renewable energy systems were of 81.8% of theretrofit sample. phase. The It is noticeable integration that the of vertical renewable walls insulation energy interventions sources represent can also approximately be carried out thanks put in place by almost all the schools with percentages that are respectively 96%, 83%, and 86% of the to the installationhalf (50.6%) of solar of the thermal total ones systems,and that 84.4% but of thisthe schools happens chose to in replace a lower windows. percentage Also, the of the cases overall introductionschools considered of the photovoltaic in the study. system is very common and it has been implemented at a frequency (29.9%). Finally,of the 81.8% interventions of the sample. The regarding integration of therenewabl plantse energy involve sources mainlycan also be the carried heating out thanks system to with a few percentages implementedthe installation of on solar the thermal conditioning systems, but this system. happens in It a lower is worth percentage noticing of the cases that (29.9%). the interventions Finally, the interventions regarding the plants involve mainly the heating system with a few regarding the envelope,percentages theimplemented energy on systems, the conditioning and thesystem introduction. It is worth noticing of renewable that the interventions energy systems were put in place by almostregarding allthe envelope, the schools the energy with systems, percentages and the introduction that are of respectively renewable energy 96%, systems 83%, were and 86% of the put in place by almost all the schools with percentages that are respectively 96%, 83%, and 86% of the overall schools consideredoverall schools considered in the study. in the study.

Figure 7. Frequency distribution of retrofit interventions.

It is well-known that buildings energy efficiency can be determined by means of energy labeling procedures, in compliance with the Italian National Guidelines for Energy Labeling of Buildings [32].

Looking at the jumps in energy classes declared by the designers (Figure 8), 46.7% of the sample Figure 7. Frequency distribution of retrofit interventions. is characterized byFigure an improvement 7. Frequency of three distribution or four energy of retroﬁt classes, interventions. 26% by an improvement lower than three classIt is well-known jumps, and that 27.3% buildings by a energyjump ofefficiency five or cansix beclasses. determined by means of energy labeling procedures, in compliance with the Italian National Guidelines for Energy Labeling of Buildings [32]. Looking at the jumps in energy classes declared by the designers (Figure 8), 46.7% of the sample is characterized by an improvement of three or four energy classes, 26% by an improvement lower than three class jumps, and 27.3% by a jump of five or six classes.

Energies 2018, 11, 649 8 of 20

It is well-known that buildings energy efﬁciency can be determined by means of energy labeling procedures, in compliance with the Italian National Guidelines for Energy Labeling of Buildings [32]. Looking at the jumps in energy classes declared by the designers (Figure8), 46.7% of the sample is characterized by an improvement of three or four energy classes, 26% by an improvement lower thanEnergies three 2018, class 11, x FOR jumps, PEER and REVIEW 27.3% by a jump of ﬁve or six classes. 8 of 21

Figure 8. FrequencyFrequency distribution of jumps in energy cla classessses according to the energy retroﬁtretrofit projects.projects.

In 2013, the Lazio region published a call for proposals aiming at developing renewable energy In 2013, the Lazio region published a call for proposals aiming at developing renewable energy systems, energy efficiency, and a reduction of the pollutant emissions through interventions able to systems, energy efficiency, and a reduction of the pollutant emissions through interventions able to increase the energy efficiency of the public buildings located within the regional area. increase the energy efficiency of the public buildings located within the regional area. The funds were attributed by the regional administration following the criteria established in The funds were attributed by the regional administration following the criteria established in the the call: conformity with the Italian legislation, coherence with the topic of the call, requirements of call: conformity with the Italian legislation, coherence with the topic of the call, requirements of the the proponent subjects. The validity of the proposal was evaluated considering the energy data proponent subjects. The validity of the proposal was evaluated considering the energy data available, available, the impact of the interventions, the presence of constraints, the complexity of the the impact of the interventions, the presence of constraints, the complexity of the interventions, interventions, and the integration of the proposed retrofit action with initiatives about energy and the integration of the proposed retrofit action with initiatives about energy efficiency. Due to efficiency. Due to this, participants had to provide an energy consumption report in compliance with this, participants had to provide an energy consumption report in compliance with the Italian the Italian legislation, a description of the interventions to be actuated, and an estimation of the costs legislation, a description of the interventions to be actuated, and an estimation of the costs for each for each proposed intervention. proposed intervention. All schools proposed more than one intervention with the aim of achieving a deep improvement All schools proposed more than one intervention with the aim of achieving a deep improvement in in their primary energy uses. The typology of proposed retrofits is quite uniform for all the schools their primary energy uses. The typology of proposed retrofits is quite uniform for all the schools because because most of them put in place both interventions on envelope and on systems. The latter most of them put in place both interventions on envelope and on systems. The latter interventions interventions consisted of both the improvement of the efficiency of the existing heating systems and consisted of both the improvement of the efficiency of the existing heating systems and the introduction the introduction of renewable energy sources. Because the public administration fully financed the of renewable energy sources. Because the public administration fully financed the retrofit interventions, retrofit interventions, the main goal of the schools’ administrators and designers was to maximize the main goal of the schools’ administrators and designers was to maximize the savings and increase the savings and increase the number of possible interventions. the number of possible interventions.

3.4. Preliminary Input Data Processing When a comparison of the thermal energy uses has to be done, a normalization of the values of primary energyenergy uses uses against against the the climatic climatic conditions conditions is necessary. is necessary. The buildingsThe buildings included included in the samplein the aresample located are located in the different in the different cities and cities provinces and provin of theces Lazio of the region Lazio thatregion are that in three are in different three different Italian climaticItalian climatic zones, calledzones, C, called D and C, E D [32 and]. In E particular,[32]. In part 30%icular, of the 30% schools of the are schools in climatic are in zone climatic C, 48% zone in C, D, and48% 22%in D, in and E (see 22% Figure in E 9(see). The Figure climatic 9). The zones climatic deﬁne zones areas withdefine similar areas mean with externalsimilar mean temperatures external duringtemperatures wintertime during and wintertime consequently and similar consequently HDD. Certain similar areas HDD. in Certain the Lazio areas region in withthe Lazio lower region HDD arewith in lower climatic HDD zone are C, in and climatic the areas zone with C, and higher the valuesareas with are in higher climatic values zone are E. Thein climatic values zone of the E. HDD The canvalues be easilyof the found HDD forcan each be easily Italian found city and for town, each asItalian reported city inand the town, Italian as legislation reported [33in ].the Italian legislation [33].

Energies 2018, 11, 649 9 of 20 Energies 2018, 11, x FOR PEER REVIEW 9 of 21

Figure 9. Distribution of schools in the three climatic zones of Lazio Region.

In order to make the effects of the external weather conditions and gross heated volume In order to make the effects of the external weather conditions and gross heated volume negligible, negligible, it is possible to process the energy use data by employing the following equations: it is possible to process the energy use data by employing the following equations: HDD E E HDD (1) E = E HDDm (1) hn h HDD E E (2) EVhn Evhn = (2) where Ehn is the normalized value of the primary energyV use for heating, Eh is the measured primary whereenergy Eusehn isfor the heating, normalized HDD valueare the of heating the primary degree-days energy concerning use for heating, the location Eh is the of measured the school, primary HDDm isenergy the mean use forvalue heating, of the HDD of are all the the heating analyzed degree-days schools (equal concerning to 1677 thedegree-days) location of and the V school, is the grossHDD mheatedis the volume. mean value of the HDD of all the analyzed schools (equal to 1677 degree-days) and V is the grossFinally, heated it is volume.worthy to notice that the schools’ energy uses depend on the occupancy schedule. In particular,Finally, itthe is opening worthy tohours notice of care that centers the schools’ and nursery energy schools uses depend are established on the occupancy by the city schedule. council and,In particular, in Rome, the they opening open hours generally of care from centers 8 am and to nursery 5 pm, schoolsfrom Monday are established to Friday by thewith city only council few exceptions.and, in Rome, The they primary open generallyand secondary from 8 schools am to 5 pm,have from a more Monday variable to Friday opening with time only during few exceptions. the week Thebecause primary in some and cases secondary the afternoon schools education have a more is no variablet guaranteed. opening It was time not during possible the weekto determine because the in afternoonsome cases opening the afternoon hours educationfor these schools is not guaranteed. during the Itentire was not2012 possible year and to determineso the value the of afternoon primary energyopening uses hours was for not these normalized schools duringagainst the the entire heatin 2012g hours. year andHowever, so the this value fact of has primary a negligible energy influenceuses was noton normalizedenergy use againstbecause the in heatingmany cases hours. the However, building this is characterized fact has a negligible by central inﬂuence heating on workingenergy use also because in the inafternoon many cases for the the entire building building is characterized because it byis used central forheating non-educational working alsoactivities. in the Forafternoon this reason, for the it entire can be building stated becausethat the itworking is used forschedule non-educational of the heating activities. system For can this be reason, considered it can quitebe stated uniform that thefor workingall the schools schedule included of the in heating the sample. system can be considered quite uniform for all the schoolsAnalyzing included the in energy the sample. use of the whole investigated building stock, it is possible to observe an averageAnalyzing normalized the energyvalue of use the of specific the whole heating investigated energy use building of about stock, 23 kWh/m it is possible3 (in 2012), to observewith an averagean average evaluated normalized energy value saving of of the about speciﬁc 30%, heatingas reported energy in the use executive of about projects. 23 kWh/m Table3 1(in lists 2012), the withaverage an averageconsumptions evaluated and energythe energy saving savings of about as a 30%,function as reported of the building in the executives’ construction projects. years. Table 1 lists the average consumptions and the energy savings as a function of the buildings’ construction years. Table 1. Average consumptions and the energy savings of the buildings’ stock. Table 1. Average consumptions and the energy savings of the buildings’ stock. Construction Year Average Consumption [kWh/m3] Energy Savings [%] Constructionuntil 1950 Year Average Consumption24.91 [kWh/m3] Energy Savings21 [%] 1950–1975until 1950 25.23 24.91 2131 1976–19891950–1975 20.71 25.23 3130 1976–1989 20.71 30 since 1990 23.40 35 since 1990 23.40 35

Energies 2018, 11, 649 10 of 20

3.5. Cluster Analysis A cluster analysis can be a viable solution to provide the administrative institutions with a criterion for establishing which school building category the retrofit projects can prove most cost effective. The first step of the work was to run the cluster analysis in order to divide the school samples in homogenous groups. The analysis was run with the k-means partitioning method [34]. The k-means method is one of the most popular in cluster analysis and it allows the creation of K non-overlapping clusters using Euclidean distance to assign every element to the closest centroid. Once the initial values are randomly individuated, the method is characterized by a cyclic procedure that stops the iterations after minimizing the sum of squared Euclidean distances or the sum of squared errors (SSE) of the elements from the respective centroids. The analysis was implemented in the Matlab code (MathWorks, version R2017a, Natick, MA, USA) [35]. One of the useful parameters to select the projects (from a cost-benefit point of view) is the cost for saved kWh or the cost-benefits ratio (CBr). The value of the CBr has been calculated from the data declared in the executive projects presented in order to obtain the financing. In particular, the projects indicate the cost for every intervention and the cumulative savings obtainable from the sum of all of them. From these data it was not possible to determine the cost-benefits ratio for each single retrofit intervention and the overall CBr was calculated for every school refurbishment. This ratio was related with the different parameters available, such as those describing the building’s geometry, heating primary energy use, and retrofit intervention typology. In a first phase, the construction year of the buildings was considered as an independent parameter able to describe the envelope insulation characteristics. However, the first analysis showed a low significance of that parameter because of the remarkable uniformity of the construction period of the schools included in the sample. 84% of the schools were built between 1950 and 1990, before the main Italian law on energy efficiency in buildings was implemented [29]. Since the clustering seemed not to be deeply influenced by the construction period of the buildings, it was excluded from the analysis. The parameters considered for the cluster analysis are all the ones that were available and able to represent the energy and constructive features of the schools. Furthermore, these parameters are the most common and strongest indicators of energy use and cost-benefit in buildings. Different literature studies considered them in order to estimate energy consumption and to run a cluster analysis [9,36,37]. Such parameters, used to perform and validate the clustering, were obtained from the executive projects of the retrofits, and correlated with the cost-benefits ratio. They are:

• The shape factor of the school (S/V): it defines the ratio between the dispersing surfaces and the heated volume. • The heating primary energy use in 2012, normalized through the HDD of the climatic zone and the gross heated volume (Evhn, defined in Equation (2)): these values were provided by the administration office that manages the heating services of the schools. The available data includes domestic hot water consumption. However, data shows that the domestic hot water demand can be considered negligible if compared with the space heating. This is due to the fact that in Italy, pupils generally do not use the gym showers after training [38]. • The declared jumps in energy classes given by the designers (J): before the retrofit, all of the schools were classified either G or F, which are the higher consumption energy classes for the Italian Legislation. • The gross heated volume of the school building (V).

• The normalized primary saved energy for heating per year (ESn): both the primary energy saved and the heated volume were declared for the admission to public funding. This value also permits us to indirectly take into account the number of the retroﬁt interventions that were developed by the schools. The amount of heating primary energy reduction, in fact, can vary signiﬁcantly when multiple measures are implemented. Energies 2018, 11, 649 11 of 20

Energies 2018, 11, x FOR PEER REVIEW 11 of 21 Several tests were performed to check if the number of parameters could be reduced. Tests with 3, 4, andSeveral 5 parameters tests were led performed to a poorer to ch performanceeck if the number of cluster of parameters analysis could because be reduced. of the lower Tests with values 3,2 4, and 5 parameters led to a poorer performance of cluster analysis because of the lower values of of R adj. 2 R adjThe. cluster analysis was performed excluding the schools characterized by an incomplete dataset (missingThe a valuecluster of analysis at least onewas of performed the above-mentioned excluding the parameters); schools characterized the resulting by number an incomplete of schools dataset (missing a value of at least one of the above-mentioned parameters); the resulting number of was reduced from 80 to 60. schools was reduced from 80 to 60. In order to understand if linear correlations between the cost-benefits ratio and the five parameters In order to understand if linear correlations between the cost-benefits ratio and the five previously mentioned can be established, the multiple linear regression is applied. This regression is parameters previously mentioned can be established, the multiple linear regression is applied. This run for the elements belonging to each cluster, considering the cost-benefits ratio as a dependent output regression is run for the elements belonging to each cluster, considering the cost-benefits ratio as a of thedependent five independent output of the parameters five independent (called predictors).parameters (called Once the predictors). clustering Once and the the clustering regression and analyses the are run, the adjusted index of determination (R2 ) and the probability value (the so-called p-value) regression analyses are run, the adjusted index ofadj determination (R2adj) and the probability value (the areso-called calculated p-value) to validate are calculated the clustering. to validate The clustering the clusteri is notng. acceptedThe clustering until nois furthernot accepted improvement until no of 2 thefurther index Rimprovementadj is obtained of the after index a prescribed R2adj is obtained number after of trials a prescribed and a p-value number lower of trials than 5%and is a calculated, p-value sincelower this than limit 5% is is considered calculated, good since for this the limit rejection is considered of a null good hypothesis for the rejection [39]. of a null hypothesis [39].It is well known that the k-means clustering method is sensitive to the initial centroids. Consequently,It is well if aknown poor valuethat the of thek-means determination clustering indexmethod is calculated,is sensitive theto the clustering initial centroids. runs again, updatingConsequently, the initial if a centroids poor value that of were the determination randomly created. index Moreover, is calculated, the k-meansthe clustering clustering runs again, method is sensitiveupdating the to outliersinitial centroids since a that small were number randomly of elementscreated. Moreover, can substantially the k-means affect clustering the mean method value. Theis outlierssensitive areto outliers detected since through a small the number residuals of elements interval can of substantially confidence. affect The outliers the mean correspond value. The to theoutliers observations are detected of the through interval the that residuals does not interv containal of confidence. zero. The number The outliers of detected correspond buildings to the is justobservations three because of the these interval correspond that does to not the contain outliers zero. arising The number from multiple of detected linear buildings regression is just analyses. three Thebecause corresponding these correspond schools areto the not outliers considered arising in thefrom analysis multiple with linear the regression goal of obtaining analyses. aThe more robustcorresponding clustering. schools The exclusion are not bringsconsidered a tighter in the residuals analysis interval with the of goal confidence of obtaining and consequentlya more robust the clustering. The exclusion brings a tighter residuals interval of confidence and consequently the reduction of statistical error indexes. reduction of statistical error indexes. Only two clusters were considered because a higher number would have led to groups Only two clusters were considered because a higher number would have led to groups characterized by a low number of schools, not statistically representative. Moreover, considering characterized by a low number of schools, not statistically representative.2 Moreover, considering more than two clusters, the overall performance in term of R adj was severely degraded for at least more than two clusters, the overall performance in term of R2adj was severely degraded for at least oneone cluster. cluster. AfterAfter the the identification identification of of the the clustersclusters andand the centroids, two two real real schools schools (the (the nearest nearest to tothe the centroids)centroids) were were modeled modeled by by means means of of a dynamica dynamic simulation simulation code, code, in in order order to to assess assess if theif the declared declared and theand actually the actually achieved achieved energy energy savings savings are comparable. are comparable. ThisThis methodological methodological approach approach can can be be summarizedsummarized in the flow-chart flow-chart shown shown in in Figure Figure 10. 10 .

Input data Subsidies Cluster analysis Centroids dynamic Building stock ante operam Building stock post operam (centroids energy simulations identification)

Energy retrofit strategies

Steady state models results vs Dynamic models results vs Actual consumptions (Verify actual savings and possible benchmarking for similar interventions on building heritage) Output data

FigureFigure 10.10. MethodologyMethodology flow ﬂow chart. chart.

4. Results4. Results and and Discussion Discussion Two clusters composed of 39 and 18 schools respectively, were obtained as a result of the cluster Two clusters composed of 39 and 18 schools respectively, were obtained as a result of the cluster analysis described in Section 3.5. The index of determination and the p-value were calculated for both analysis described in Section 3.5. The index of determination and the p-value were calculated for clusters and for the whole sample, prior to cluster subdivision. The obtained values demonstrate that both clusters and for the whole sample, prior to cluster subdivision. The obtained values demonstrate

Energies 2018, 11, 649 12 of 20

Energies 2018, 11, x FOR PEER REVIEW 12 of 21 that the clustering is useful to reduce statistical errors, as seen in Table2. Good values of the p-value parameterthe clustering were is founduseful and to redu theyce guarantee statistical the errors, possibility as seen of in excluding Table 2. theGood H0 hypothesisvalues of the since p-value they areparameter lower than were 0.05 found [9]. Moreover,and they guarantee better determination the possibility coefﬁcient of excluding values the were H0 found hypothesis compared since to they the 2 Rarecalculated lower than before 0.05 [9]. the Moreover, clustering analysisbetter determin for the entireation sample.coefficient values were found compared to the R2 calculated before the clustering analysis for the entire sample. 2 Table 2. R adj and p-value calculated for each cluster and for the sample without clustering.

Table 2. R2adj and p-value calculated for each cluster and for the sample without clustering. 2 Clusters R adj p-Value Clusters R2adj p-Value No Clustering (57 schools) 0.303 0.0019 ClusterNo Clustering 1 (39 schools) (57 schools) 0.5700.303 0.0019 0.0012 ClusterCluster 2 (18 1 schools) (39 schools) 0.6900.570 0.0012 0.0481 Cluster 2 (18 schools) 0.690 0.0481 Once the centroids were identiﬁed,identified, the mean characteristics of the elements belonging to each cluster can be described with the centroids’ coordinatescoordinates (see(see TableTable3 ).3).

Table 3. The Centroids’ coordinates for every cluster. Variables for Clustering CLUSTER 1 (39 Schools) CLUSTER 2 (18 Schools) Variables for Clustering CLUSTER 1 (39 Schools) CLUSTER 2 (18 Schools) Shape factor (S/V) [1/m] 0.46 0.75 ShapeVolume factor (S/V) (V) [m [1/m]3] 8535.77 0.46 1906.00 0.75 3 VolumeClass jumps (V) [m (J)] [−] 8535.773.43 4.72 1906.00 Cost-benefitsClass jumps ratio (J) (CBr) [−] [€/kWh] 12.57 3.4325.61 4.72 Cost-beneﬁts ratio (CBr) [€/kWh] 12.57 25.61 Heating primary energy use (Evhn) [kWh/m3] 25.26 24.59 Heating primary energy use (E ) [kWh/m3] 25.26 24.59 Specific energy saving [kWh/mvhn 3 year] 6.12 10.09 Speciﬁc energy saving [kWh/m3 year] 6.12 10.09 Figure 11 represents a parallel coordinates plot of the normalized parameters describing the centroids.Figure Each 11 represents parameter awas parallel normalized coordinates compared plot ofto its the maximum normalized value. parameters The plot describinghighlights the centroids.centroids’ Eachcharacteristics parameter by was a visual normalized comparison compared of the to itsparameters maximum that value. correspond The plot to highlights the parallel the centroids’axis. characteristics by a visual comparison of the parameters that correspond to the parallel axis.

1.0 0.9 0.8 0.7 0.6 0.5 0.4 0.3

Centroid Coordinates Centroid 0.2 0.1 0.0 S/V V J CBr Evhn 2012 ESn Cluster 1 Cluster 2

Figure 11. Normalized coordinates of the centroids of the two clusters.

Cluster 1 represents the schools sample characterized by the lower S/V ratio and bigger volumes Cluster 1 represents the schools sample characterized by the lower S/V ratio and bigger volumes and the lower cost-benefits one. This cluster is composed by the largest schools. As the retrofits of and the lower cost-benefits one. This cluster is composed by the largest schools. As the retrofits of schools in Cluster 1 are less performing (only 6.12 kWh year/m3 against the 10.10 kWh year/m3 of schools in Cluster 1 are less performing (only 6.12 kWh year/m3 against the 10.10 kWh year/m3 of Cluster 2), also the energy class jumps declared in the design phase are lower. The declared savings Cluster 2), also the energy class jumps declared in the design phase are lower. The declared savings achievable by the retrofit interventions represent a mean percentage of about 24% of the normalized achievable by the retrofit interventions represent a mean percentage of about 24% of the normalized energy uses recorded in 2012. The cluster is mainly composed by primary, secondary and nursery energy uses recorded in 2012. The cluster is mainly composed by primary, secondary and nursery schools with a very low percentage of kindergartens (7%). The cluster 1 features are listed in Table 4. schools with a very low percentage of kindergartens (7%). The cluster 1 features are listed in Table4.

Energies 2018, 11, 649 13 of 20

Table 4. Cluster 1 features (39 buildings).

Variables for Clustering Typical Values Shape factor (S/V) [1/m] 0.29–0.74 Volume (V) [m3] 2682–41,633 Class jumps (J) [−] 0–7 Cost-beneﬁts ratio (CBr) [€/kWh] 1.33–34.97 3 Energies 2018Heating, 11, x FOR primaryPEER REVIEW energy use (Evhn) [kWh/m ] 7.82–49.79 13 of 21 Speciﬁc energy saving [kWh/m3 year] 0.24–15.48 Table 4. Cluster 1 features (39 buildings).

Variables for Clustering Typical Values Small volume schools with a higher shape ratio belong to Cluster 2. These schools are characterized Shape factor (S/V) [1/m] 0.29–0.74 by levels of heating energy use normalizedVolume per(V) [m unit3] of heated volume2682–41,633 that are comparable to the schools belonging to Cluster 1. The mean thermalClass jumps energy (J) [−] savings that can be obtained,0–7 instead, are higher and correspond to 40% of the normalizedCost-benefits heating ratio (CBr) energy [€/kWh] use. Consequently,1.33–34.97 the mean declared jumps of 3 energy classes are higherHeating than in primary the previous energy use cluster.(Evhn) [kWh/m The] schools belonging7.82–49.79 to cluster 2 are mainly Specific energy saving [kWh/m3 year] 0.24–15.48 nursery schools (45%), kindergarten (20%), and primary schools (34%) and there is no presence of secondary schools.Small The volume cluster schools 2 with features a higher are shape listed ratio belo in Tableng to Cluster5. 2. These schools are characterized by levels of heating energy use normalized per unit of heated volume that are comparable to the schools belonging to Cluster 1. The mean thermal energy savings that can be obtained, instead, are higher and Table 5. Cluster 2 features (18 buildings). correspond to 40% of the normalized heating energy use. Consequently, the mean declared jumps of energy classes are higher than in the previous cluster. The schools belonging to cluster 2 are mainly nursery schools (45%),Variables kindergarten for (20%), Clustering and primary schools (34%) Typical and there Values is no presence of secondary schools. The cluster 2 features are listed in Table 5. Shape factor (S/V) [1/m] 0.51–0.91 3 VolumeTable (V) 5. Cluster [m ] 2 features (18 buildings). 685–4156 Class jumps (J) [−] 1–7 Cost-beneﬁtsVariables ratio for (CBr) Clustering [€/kWh] Typical 5.76–69.89 Values Shape factor (S/V) [1/m] 3 0.51–0.91 Heating primary energy use (Evhn3 ) [kWh/m ] 6.97–58.56 Volume (V) [m ] 3 685–4156 Speciﬁc energyClass saving jumps [kWh/m (J) [−] year] 1.85–27.601–7 Cost-benefits ratio (CBr) [€/kWh] 5.76–69.89 Heating primary energy use (Evhn) [kWh/m3] 6.97–58.56 Figure 12 shows the energySpecific energy savings saving for [kWh/m both3 clustersyear] as a function1.85–27.60 of the buildings’ volume. Schools belonging to Cluster 2 are characterized by an average energy saving of 10.09 kWh/m3, while the educationalFigure 12 buildings shows the energy in Cluster savings 1for have both clus anters average as a function energy of the saving buildings’ of 6.12volume. kWh/m 3. It is Schools belonging to Cluster 2 are characterized by an average energy saving of 10.09 kWh/m3, while worthy to noticethe educational how the buildings smallest in Cluster schools 1 have belonging an average toenergy Cluster saving 2of are 6.12 characterizedkWh/m3. It is worthy in to almost half of the cases bynotice energy how savings the smallest higher schools than belonging 15% to and, Cluster on 2 are the characterized other hand, in almost the schools half of the that cases areby included in cluster 1 showenergy in allsavings cases higher anenergy than 15% savings and, on the percentage other hand, lowerthe schools than that 15%. are included in cluster 1 show in all cases an energy savings percentage lower than 15%.

Figure 12. Declared energy savings (kWh/m3) versus gross heated volume for the two clusters. Figure 12. Declared energy savings (kWh/m3) versus gross heated volume for the two clusters. This trend means that small buildings generally have the possibility of realizing a higher number of energy retrofit interventions. Usually in large buildings the retrofit interventions are more complex This trendto be means realized that because small of the buildings complexity generally of the building have shape the possibilityand of the building of realizing systems. a For higher number of energy retrofitexample, interventions. the roofs of large Usually multiple floor in large building buildingss can be characterized the retrofit by interventions the presence of thermal are more complex to be realizedmachines because and of thedistribution complexity canalizations. of the buildingThis fact causes shape many and problems of the building in the installation systems. of For example, the roofs of large multiple floor buildings can be characterized by the presence of thermal machines and distribution canalizations. This fact causes many problems in the installation of photovoltaic panels or insulation panels. Similarly, the façade can be very articulated with the presence of balconies, pilasters, Energies 2018, 11, x FOR PEER REVIEW 14 of 21

Energiesphotovoltaic2018, 11 ,panels 649 or insulation panels. Similarly, the façade can be very articulated with14 ofthe 20 presence of balconies, pilasters, string courses and cornices, and these elements increase the difficulties in the solution of thermal bridges and in the application of insulation on the outside skin. stringFor small courses single and floor cornices, building, and on these the contrary, elements increasethe retrofit the interventions difficulties in are the in solution general ofsimpler thermal to bridgesrealize and and can in the bring application higher energy of insulation savings. on The the outsidehigher potential skin. For of small energy single saving floor is building, caused onby the contrary,higher envelope the retrofit surface interventions per unit of are heated in general volume. simpler The toroof realize surface and of can a small bring building, higher energy for example, savings. Theis proportionally higher potential higher of energy in comparison saving is with caused theby roof the surface higher in envelope large buildings. surface per The unit considerable of heated volume.potential The of energy roof surface saving of of a small small building, schools is for also example, confirmed is proportionally by the higher higher number in comparison of energy class with thejumps roof that surface is 4.72 in for large the buildings.centroid of TheCluster considerable 2, and 3.43 potential for the centroid of energy of savingCluster of 1. small schools is also confirmedLooking at bythe the cost-benefits higher number ratio, ofthe energy analysis class shows jumps that that the is higher 4.72 for reduction the centroid of energy of Cluster uses in 2, andsmall 3.43 schools for the is centroidnot followed of Cluster by a 1.proportional increase of costs. The cost-benefits ratio, in fact, is higherLooking for schools at the belonging cost-benefits to Cluster ratio, the 2 in analysis compar showsison with that theCluster higher 1. This reduction fact discourages of energy uses the inretrofit small of schools the stock is notof small followed schools by and a proportional suggests a possible increase reduction of costs. The of the cost-benefits retrofit interventions ratio, in fact, to isimplement higher for in schools the future. belonging to Cluster 2 in comparison with Cluster 1. This fact discourages the retrofit of the stock of small schools and suggests a possible reduction of the retrofit interventions to implement4.1. Clusters in Reference the future. Building Assessment

4.1. ClustersAs mentioned Reference in Building Section Assessment2, several studies applied the cluster analysis to the buildings’ energy uses. This method has been employed to define homogenous classes and reference buildings within classesAs relying mentioned on inthe Section data 2connected, several studies to actual applied energy the clusterdemands. analysis In particular, to the buildings’ in [9] energythe authors uses. Thiscorrelated method the has real been energy employed demands to define of homogenousthe buildings’ classes stock and to referencetheir geometrical buildings and within technical classes relyingcharacteristics on the databy means connected of proper to actual statistical energy demands.analyses. Starting In particular, from inthis [9] study, the authors the novelty correlated of this the realwork energy deals demandswith the cluster of the buildings’ analysis application stock to their aiming geometrical at highlighting and technical the relationship characteristics between by means the ofcost-benefits proper statistical ratio and analyses. the five Starting parameters from this ment study,ioned the in novelty Section of this3.5, workwhich deals better with describe the cluster the analysiscorrelation application between aimingcosts and at highlightingbenefits. the relationship between the cost-benefits ratio and the five parametersOnce the mentioned clustering in Sectionhas been 3.5 ,performed, which better the describe Euclidean the correlationdistance of between all the costsschools and from benefits. the respectiveOnce centroids the clustering allows has to identify been performed, the ones that the are Euclidean the closest distance to the centroids. of all the These schools schools from can the respectivebe considered centroids the reference allows tobuildings identify for the the ones cluste thatr arethey the belong closest to, to since the centroids.their characteristics These schools best canapproximate be considered the mean the reference values represented buildings forby thethe clustercentroids’ they coordinates. belong to, sinceFor Cluster their characteristics 1 the lowest bestdistance approximate was found the for mean a school values located represented in the provin by thece centroids’ of Frosinone, coordinates. climatic zone For ClusterD, called 1 theBuilding lowest 1 distance(Figure was13). foundThis school for a school building located (primary in the province and nursery of Frosinone, education) climatic was zone built D, calledin 1930 Building and is 1 (Figurecharacterized 13). This by school an E shaped building plan (primary and is and two nursery floors education)high. The volume was built of in the 1930 school and isis characterized 5990 m3 and 3 bythe anS/V E ratio shaped is equal plan andto 0.41 is two1/m.floors The retrofit high. Theinterventions volume of involved the school theis heating 5990 m systemand theand S/V the ratioenvelope is equal of the to 0.41building 1/m. included The retrofit only interventions vertical walls, involved leading the to a heating declared system specific and energy the envelope saving ofequal the to building 4.53 kWh/m included3 with only an verticalexpected walls, improvement leading to in a energy declared classes specific from energy class savingG to class equal D. toIn 3 4.53particular, kWh/m thewith interventions an expected on improvementthe heating system in energy regard classes the replacement from class G of to classthe generator, D. In particular, which thewas interventions a traditional onboiler the heatingfueled with system natural regard gas, the eq replacementuipped with of a the new generator, hybrid system which wasthat ais traditional a 200 kW boilercondensing fueled boiler with naturalthat integrates gas, equipped a 50 kW with heating a new pump hybrid when system the temperature that is a 200 is kW between condensing 7 and boiler12 °C. ◦ thatMoreover, integrates when a 50the kW temperature heating pump goes whenbelow the7 °C temperature only the boiler is between provides 7 and thermal 12 C. energy. Moreover, The ◦ wheninterventions the temperature on the envelope goes below are related 7 C only to the the windows boiler provides replacement thermal and energy. is initially The interventionscharacterized onby thesingle envelope glass and are relatediron frames. to the They windows were replacement replaced with and double is initially low-emittance characterized 6-15-6 by singleglass filled glass andwith iron argon frames. and polyvinyl They were chloride replaced (PVC) with frames. double The low-emittance cost per saved 6-15-6 kWh glass of the filled interventions with argon is and6.86 polyvinyl€/kWh. chloride (PVC) frames. The cost per saved kWh of the interventions is 6.86 €/kWh.

Figure 13. The cluster 1 reference school building (Building 1): (a) actual view; (b) building ground Figure 13. The cluster 1 reference school building (Building 1): (a) actual view; (b) building ground floor map. ﬂoor map.

Energies 2018, 11, 649 15 of 20 Energies 2018, 11, x FOR PEER REVIEW 15 of 21

ConsideringConsidering thatthat thethe Cluster 2 building closest closest to to the the centroid centroid is is a aschool school located located near near Rome, Rome, in inclimatic climatic zone zone C, C, called called Building Building 2 2(Figure (Figure 14). 14). The The building, building, dated dated back to 1978,1978, hashas aa differentdifferent structurestructure comparedcompared toto the the previous previous one one (S/V (S/V ratioratio equalequal toto 0.79)0.79) andand itit isis characterizedcharacterized byby aa lowerlower volumevolume of of 4156 4156 m m3 3with witha atotal totalfloor floor area area equal equal to to 1100 1100 m m22over overtwo twofloors. floors. TheTheschool schoolincludes includes a a gym gym locatedlocated on on one one side, side, but but it it waswas notnot consideredconsidered for for thethe retrofitretrofit interventions.interventions. TheThe energyenergy retrofitretrofit project project regardedregarded bothboth thethe heating heating systemsystem andand the the envelope, envelope, with with interventions interventionson on vertical verticaland and horizontal horizontal surfacessurfaces (including(including thethe singlesingle glassglass windows windows replacement). replacement). RegardingRegarding thethe envelopeenvelope interventions,interventions, thethe traditional traditional aluminum-framed aluminum-framed windows windows were were replaced replaced with with better better performing performing double double glazing glazing 4-12-4 4- PVC12-4 framedPVC framed ones, andones, extruded and extruded polystyrene polystyrene (XPS) insulation (XPS) insulation panels werepanels integrated were integrated in the vertical in the wallsvertical and walls the roof. and On the the roof. other On hand, the theother heating hand, system the heating retrofit system was characterized retrofit was bycharacterized generator and by radiatorgenerator replacement. and radiator A replacement. new pressurized A new boiler pressuri withzed higher boiler efficiency with higher was installed efficiency to was replace installed the old to dieselreplace fueled the old generator, diesel fueled which suppliedgenerator, thermal which energysupplied to thermal the building energy before to the the building retrofit. Moreover,before the aretrofit. photovoltaic Moreover, system a photovoltaic was planned system in the was declared planned project. in the The decl declaredared project. specific The energy declared saving specific is equalenergy to saving 9.4 kWh/m is equal3 modifying to 9.4 kWh/m the3 energy modifying class the from energy G to B,class with from a funding G to B, with application a funding of 12.33application€ per savedof 12.33 kWh. € per saved kWh.

Figure 14. The Cluster 2 reference school building (Building 2): (a) actual view; (b) building ground Figure 14. The Cluster 2 reference school building (Building 2): (a) actual view; (b) building ground floor map. floor map. 4.2. Energy Performance Analysis of the Reference Schools 4.2. Energy Performance Analysis of the Reference Schools A dynamic energy simulation, employing the dynamic code TRNSYS (Transient System A dynamic energy simulation, employing the dynamic code TRNSYS (Transient System Simulation Tool) [40], was run for the two reference schools aiming at verifying the declared energy Simulation Tool) [40], was run for the two reference schools aiming at verifying the declared energy savings. It has been widely demonstrated that, employing this dynamic code, it is possible to correctly savings. It has been widely demonstrated that, employing this dynamic code, it is possible to correctly reproduce the building geometry and the external environmental conditions in order to accurately reproduce the building geometry and the external environmental conditions in order to accurately estimate energy uses. The TRNSYS Build allows us to generate the building model, and the external estimate energy uses. The TRNSYS Build allows us to generate the building model, and the external environmental conditions are applied by means of TRNSYS Studio (University of Wisconsin, environmental conditions are applied by means of TRNSYS Studio (University of Wisconsin, Madison, Madison, WI, USA). The energy audits and the information included in the schools’ official WI, USA). The energy audits and the information included in the schools’ official documents provided documents provided the needed parameters for the simulations. The temperature set point for the the needed parameters for the simulations. The temperature set point for the heating period was set heating period was set equal to 20 °C, according to the Italian Standard [41]. The data employed in equal to 20 ◦C, according to the Italian Standard [41]. The data employed in the simulation models are the simulation models are summarized in Table 6. summarized in Table6. The simulated heating energyTable needs6. Buildings of each model building data set were before compared retrofit. with the actual data related to the heating energy uses. The simulation can be considered calibrated according to the acceptance criteria definedSimulation in the data—ex American ante Society of Heating andBuilding Air-Conditioning 1 Engineers Building (ASHRAE) 2 Standard [42], takingLocation into account the Mean Bias Error (MBE),Arce (LT) and the Coefficient ofLadispoli Variation (RM) of the Main use Educational Educational Root Mean Squared Error (CV(rmse)). Occupancy 5.3 m2/student 4 m2/student AnalyzingInternal gains the measured (people)—latent and simulated energy uses,59 W/person for the Building 1 dynamic59 model W/person a MBE equal toInternal−4.8%, gains and (lighting)—sensible a CV(rmse) equal to 9.6% were obtained.73 W/person On the other hand, the Building73 W/person 2 model obtained a MBEDomestic value Hot equal Water to 0.42%, and a CV(rmse) value5 l/day equal person to 5.1%. 5 l/day person Average lighting power 10 W/m2 10 W/m2 Opening time (Monday-Saturday) From 8 am to 6 pm From 8 am to 6 pm Opening time on Sunday and holidays Closed Closed

Energies 2018, 11, 649 16 of 20

Table 6. Buildings model data set before retroﬁt.

Simulation Data—Ex Ante Building 1 Building 2 Location Arce (LT) Ladispoli (RM) Main use Educational Educational Occupancy 5.3 m2/student 4 m2/student Internal gains (people)—latent 59 W/person 59 W/person Internal gains (lighting)—sensible 73 W/person 73 W/person Domestic Hot Water 5 l/day person 5 l/day person Average lighting power 10 W/m2 10 W/m2 Opening time (Monday-Saturday) From 8 am to 6 pm From 8 am to 6 pm Opening time on Sunday and holidays Closed Closed 1.100 W/m2K (first floor) U-value walls 1.240 W/m2K (second floor) 0.950 W/m2K 0.998 W/m2K (bath walls) 1.590 W/m2K U-value roof 1.300 W/m2K 1.920 W/m2K (single floor parts) U-value foundation floor 0.706 W/m2K 0.900 W/m2K U-value windows 5.800 W/m2K 3.800 W/m2K Global COP of the heating system 70.6% 66.5%

These two reference buildings were retroﬁtted by improving the envelope performance, as mentioned before in Section 4.1. Table7 lists the data set employed to simulate the reference buildings after the refurbishment phase.

Table 7. Buildings’ model data set post retroﬁt.

Simulation Data—Ex Post Building 1 Building 2 1.100 W/m2K (first floor) U-value walls 1.240 W/m2K (second floor) 0.360 W/m2K 0.998 W/m2K (bath walls) 1.590 W/m2K U-value roof 0.430 W/m2K 1.920 W/m2K (single floor parts) U-value windows 1.800 W/m2K 2.000 W/m2K Global COP of the heating system 91.3 % 84.4%

Taking into account the reference building (Building 1) that is the closest to the Cluster 1 centroid, Table8 lists the data about the declared energy savings stated in the technical documents provided by the designers before the retrofit phase, the achievable savings estimated by the means of the dynamic simulations after the refurbishment and, finally, the actual measured energy uses in 2016. Weather-data files in the building energy models were relative to 2012, the energy use reference year, which allows making the simulated energy uses comparable. Observing the percentage of energy savings in Table8, it is possible to notice that the declared savings by the designer after the retrofit and the achievable energy savings obtained by means of the dynamic model are not far and the differences can be related to the different adopted simulation codes. The declared energy savings were obtained by means of steady-state simulation tools, less accurate than the dynamic one, yet able to fully reproduce hourly environmental boundary conditions and consider structural inertial effects [43]. These percentage differences can be also ascribed, to a lesser extent, to the modified weather conditions, which play an important role for calculating buildings energy demands. Indeed, temperatures in the winter period of 2016 were milder compared to the ones in 2012. Moving from the analysis of the 2012 energy use data to the 2016 ones, the actual energy needs after the retrofit confirm the reliability of the dynamic simulation model and the prediction obtained by the same model related to 2012, which indicates 24% energy savings in 2012 and 20% in 2016. Energies 2018, 11, 649 17 of 20

Table 8. Comparison between declared, achievable and actual energy uses (Building 1).

Actual Energy Need Declared Savings by Achievable Savings after Actual Energy Need Design and Realized before Retrofit the Designers after the the Retrofit (Dynamic after the Retrofit Interventions (2012) [kWh] Retrofit (2012) [kWh] Simulation, 2012) [kWh] (2016) [kWh] Air-conditioning system 75,146.58 22,605.80 18,153.58 59,853.96 and windows replacement Percentage of energy savings 30% 24% 20%

The same information related to Building 2 is provided in Table9. Also in this case, the declared savings and the achievable ones in 2012 are comparable, and the highlighted differences can be ascribed to the different simulation methods. Also in this case, moving from 2012 to 2016 data, the dynamic simulation model can be considered the most effective tool to properly reproduce the actual energy needs. In particular, comparing the actual energy need in 2012 and the achievable energy savings obtained by the dynamic code in 2012, it is possible to observe a percentage difference equal to 35% and this value is very close to the actual energy need after the retroﬁt phase in 2016 (33%).

Table 9. Comparison between declared, achievable, and actual energy uses (Building 2).

Actual Energy Need Declared Savings by Achievable Savings after Actual Energy Need before Retrofit Design and Realized Interventions the Designers after the the Retrofit (Dynamic after the Retrofit (2012) [kWh] Retrofit (2012) [kWh] Simulation, 2012) [kWh] (2016) [kWh] Air-conditioning system and 96,604.80 windows replacement Roof insulation 39,113.00 34,810.00 64,389.92 Wall Insulation Percentage of energy savings 40% 35% 33%

Analyzing data about Building 1, it is possible to observe that the real energy saving is lower than the declared one of about 10% and, considering the comparison between the simulated and the actual energy demand, a difference of about 4% can be noticed. The same findings can be noticed analyzing the values obtained through Building 2. In this case, the actual energy saving is lower than the declared one of about 7% and, comparing simulated and actual energy needs, they differ only by 2%. It is worth noticing that the above-mentioned energy savings could be more accurately estimated employing some indicators on the measures persistence [44]. However, due to the lack of documentation (only one year of post-retrofitting energy use was available), it has not been possible to prove the persistence of energy efficiency measures.

5. Conclusions Heating energy uses of school buildings are responsible for a significant part of the total energy demands and, due to this, proper cost-effective strategies for retrofitting are needed. In this framework, with the aim of improving the energy use of existing schools by means of proper retrofit interventions and of efficiently allocating public funds, an Italian school buildings’ stock was analyzed and classified through a cluster analysis. This approach was implemented to develop a methodology that can be useful to guide the selection of a building stock to be retrofitted from a cost efficiency point of view. A sample composed of 80 school buildings, located in the Lazio region (central Italy) and characterized by different features, construction age, and technologies was investigated. The refurbished buildings were classified in homogeneous clusters and, for each of them, an actual building, which best represents the cluster characteristics, was identified, simulated and verified. In particular, starting from a domain composed of several parameters able to properly describe the whole analyzed buildings’ stock, five of them, which are considered independent predictors, were selected to apply multiple linear regression with the cost-benefits ratio as the dependent variable. The regression was performed for the data sets belonging to all possible clusters. The analysis led to the identification of two clusters. The clustering was significant since an improvement of the index Energies 2018, 11, 649 18 of 20

2 R adj was found, and the model’s statistical significance was verified through the p-value. The clusters are characterized by two centroids for which two real reference buildings were identified. The adjusted 2 index of determination R adj is about 0.6 for Cluster 1, and about 0.7 for Cluster 2. The declared energy savings stated by the designers before the retrofit phase (as a predictive figure), the achievable energy savings calculated by means of dynamic simulations after the refurbishment, and the actual building energy demands were finally compared in order to validate the methodological approach. The implemented dynamic energy simulation, performed for the two reference schools, highlighted that the real energy saving is lower than the one declared by the designers after the refurbishment phase. Considering the comparison between the simulated and the actual energy demand, a very low percentage difference can be noticed in the Cluster 1 analysis, as well as the Cluster 2 one. These differences can be ascribed to the employment of different energy simulation codes. Steady-state and dynamic codes differ in their capability to describe physical phenomena over time (environmental climatic conditions and inertial effects) and, nowadays, it is well-known that transient system simulation tools can provide more effective and reliable simulation results. Beyond the differences between the two simulation approaches, we can say that the declared energy savings can be considered sufficiently reliable and representative of the actual performances of the retrofitted buildings. This constitutes an a-posteriori justification of the inclusion of declared energy savings in the group of predictors. The proposed methodological approach can be useful to define reference buildings, considered as representative of a building stock characterized by similar structural, technological and energy features. The reference buildings could be used as models for further simulations able to quantify the energy savings related to specific retrofit interventions and the corresponding cost-benefit analysis. The results could be extrapolated to each corresponding cluster and this could help the Public Administration in decision-making and prioritizing the energy retrofit of the buildings’ stock with the lowest cost-efficiency ratio. Future developments will therefore analyze more in detail the two reference buildings in order to evaluate the persistence over time of the energy savings, the cost-effectiveness of further retrofit interventions, and the effect of management measures.

Acknowledgments: The research leading to these results was supported by the Lazio Region administration under the project POR FESR LAZIO 2007/2013. Author Contributions: Paola Marrone and Francesco Asdrubali designed this research, analyzed the results and checked the manuscript throughout the whole revision process. Laura Calcagnini and Gianluca Grazieschi provided the statistical description of the schools’ sample. Paola Gori and Gianluca Grazieschi performed the cluster analysis. Luca Evangelisti and Paola Gori carried out the dynamic simulations. Laura Calcagnini, Gianluca Grazieschi and Luca Evangelisti wrote the paper and revised it. Conﬂicts of Interest: The authors declare no conﬂict of interest.

Nomenclature

CBr [€/kWh] Cost-benefits ratio COP Coefficient of performance CV(rmse) Coefficient of variation of the root mean squared error Eh [kWh/year] Measured primary energy use Ehn [kWh/year] Normalized value of the primary energy use Esn [%] Normalized saved primary energy saving per year Evhn [kWh/m3 year] Normalized value of the primary energy use over volume HDD [◦C day] Heating degree days ◦ HDDm [ C day] Average heating degree days J Declared jump in energy classes MBE Mean Bias Error p-value Probability value 2 R adj Adjusted index of determination S [m2] Dispersing building surfaces Energies 2018, 11, 649 19 of 20

U-value [W/m2K] Thermal transmittance V [m3] Gross heated volume

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