Optimisation analysis of PCM-enhanced opaque building envelope components for the energy retrofitting of office buildings in Mediterranean climates

Applied Energy 211 (2018) 929–953

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Applied Energy journal homepage: www.elsevier.com/locate/apenergy

Optimisation analysis of PCM-enhanced opaque building envelope components for the energy retrofitting of office buildings in Mediterranean climates

T

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Ylenia Cascone, Alfonso Capozzoli , Marco Perino TEBE Research Group, Department of Energy, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy

H I G H L I G H T S retrofit of an office building was studied with a multi-objective search. • Energy PCM properties and application in the opaque envelope were investigated. • Optimal of two PCM layers with different melting temperatures could be selected. • AThemaximum values which led to the Pareto optimal solutions were analysed. • The input • operation of the HVAC system implied non-trivial optimal retrofit solutions.

A R T I C L E I N F O

A B S T R A C T

Keywords: Energy retrofitting Multi-objective optimization Phase Change Material Building envelope Building energy performance Genetic algorithm

The energy retrofitting of existing buildings is of major importance to reach the energy sustainability target set by the European Union (EU) for 2020. Innovative retrofitting solutions can involve the adoption of Phase Change Materials (PCMs), but an effective use of PCM in buildings requires an appropriate selection of the thermophysical properties, quantity and position of the PCMs. To guarantee a good functioning of a PCM and ensure economic feasibility, an optimisation of PCM use is advisable. In the present paper, multi-objective optimisation analyses for the energy retrofitting of office buildings with PCM-enhanced opaque building envelope components are presented. A retrofitting intervention on either the external or internal side of the opaque envelope was considered, and a maximum of two PCM layers with different melting temperatures were selected and placed in different positions within the wall. Two sets of objective functions were minimised; first, primary energy consumption and global costs, and then the building energy needs for heating and cooling and investment costs. The search variables included the thickness and thermo-physical properties of the PCM layers, the window type, the insulation and internal lining materials, the wall configuration and U-value. In order to provide a robust methodology to drive designers towards an informed choice of the final retrofitting strategy, post-optimisation analyses were additionally carried out to investigate the variable values that led to the optimal solutions. Interesting and non-trivial information was obtained. The optimal thermo-physical properties of PCMs were found to be affected in particular by the operation of the HVAC system.

1. Introduction As commercial and residential buildings in Europe consume approximately 40% of primary energy and are responsible for 24% of greenhouse emissions [1], improving the energy performance of buildings is an important opportunity to satisfy the energy challenge set by the European Union for 2020 [2]. Because of the low replacement rate (around 1.0–3.0% per year) of existing buildings with new ones, the energy retrofitting of the existing building stock is of utmost

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importance to reach the EU targets and promote energy efficiency and environmental sustainability [3]. Innovative retrofitting solutions can involve the adoption of responsive envelope components, i.e. “design solutions that react to changes in external or internal conditions and to occupant intervention in order to maintain a balance between optimum interior conditions and environmental performance” [4]. Among the available responsive technologies, Phase Change Materials (PCMs) are substances that undergo a phase transition (in general solid-liquid) at their utilisation

Corresponding author. E-mail addresses: [email protected] (Y. Cascone), [email protected] (A. Capozzoli), [email protected] (M. Perino).

https://doi.org/10.1016/j.apenergy.2017.11.081 Received 28 July 2017; Received in revised form 10 November 2017; Accepted 18 November 2017 0306-2619/ © 2017 Elsevier Ltd. All rights reserved.

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Nomenclature C c EP fP,tot ,el fP,tot ,gas g k L QC ,nd Qel QH ,nd R T t U

ai Ref f G g I ins p pl w 1 2

cost (€/m2) specific heat capacity (J/(kg K)) primary energy (kWh/(m2y)) primary energy conversion factor for electricity (–) primary energy conversion factor for natural gas (–) solar heat gain coefficient (g-value) (–) thermal conductivity (W/(m K)) latent heat of fusion (kJ/kg) building energy needs for cooling (kWh/(m2 y)) electricity demand (kWh/(m2 y)) building energy needs for heating (k Wh/(m2 y)) thermal resistance (m2 K/W) temperature (°C) thickness (m) thermal transmittance (U-value) (W/(m2 K))

Acronyms AEEGSI DGU EU GA HVAC NSGA-II

Greek symbols

ΔT ηH ρ τl

melting temperature range (°C) efficiency of the heating system (–) density (kg/m3) visible transmittance (–)

PCM PEF SEER SHGC TGU

Subscripts

ae

internal air baseline (pre-retrofit building) frame global glazing investment insulation peak melting plaster window PCM1 PCM2

Autorità per l’energia elettrica il gas e il sistema idrico Double Glazed Unit European Union Genetic Algorithm Heating, Ventilation and Air Conditioning Non-dominated-and-crowding Sorting Genetic Algorithm II Phase Change Material Primary Energy Factor Seasonal Energy Efficiency Ratio Solar Heat Gain Coefficient Triple Glazed Unit

external air

renovation costs, by exploring different window-to-wall ratios and orientations. They found that the performance parameters for the renovation of existing buildings should be determined for each orientation. Asadi et al. [22] proposed a multi-objective optimisation methodology to optimise the retrofitting costs, energy savings and thermal comfort of a residential case study building. In a later work [23], they assessed the technological choices for the retrofitting of a school building by proposing a methodology based on genetic algorithms and artificial neural networks. They found that non-dominated solutions could prevalently be classified according to the type of windows, the HVAC system or solar collector. In order to achieve the best indoor thermal comfort, they found that investing in an expensive HVAC system was better than investing in additional insulation and other low energy measures. Shao et al. [24] developed a multi-criteria decision strategy to rank the Pareto-optimal solutions on the basis of the stakeholders’ concerns and needs. They applied the proposed methodology to retrofit an office building, for which they optimised the investment cost, the annual heating energy consumption and global warming potential. Penna et al. [25] investigated the relationship between the initial characteristics of residential buildings and the definition of optimal traditional retrofitting solutions. They searched for the optimal retrofitting measures of twelve building typologies by maximising the economic performance and minimising the energy consumption and thermal discomfort. They found that a zero energy target could be approached while maintaining economic convenience, but improving the energy efficiency led to a significant deterioration of the thermal comfort. They obtained cost-optimal solutions that were prevalently characterised by a large insulation thickness and substitution of the glazing systems with double glazing characterised by a high solar heat gain coefficient (SHGC). On the other hand, the insulation level of the opaque envelope in the comfort-optimal solution was not very important, but the substitution of the single glazings with lowSHGC ones and the introduction of a mechanical ventilation system seemed to be crucial. Wu et al. [26] performed a multi-objective energy hub optimisation for the retrofitting of a building envelope and the

temperature. They can store (during melting) and release (during solidification) large amounts of energy at an almost constant temperature by exploiting their latent heat of fusion. PCMs in buildings can hence be used to increase the heat storage capacity or to obtain a stabilising effect on temperature swings [5], therefore reducing building energy use, diminishing peak heating and cooling loads and improving thermal comfort [6]. PCMs can be applied both as passive strategies, when integrated within the building structure, and as active strategies, when integrated within the HVAC system. With regard to the passive utilisation of PCMs, its feasibility depends on the effectiveness of the PCM thermal cycles, which can be guaranteed by the diurnal temperature variability of the building site [7] or, for cooling applications, it can be enhanced by the use of night ventilation [8]. However, according to the intended application and to the building location, an effective use of PCM in buildings requires an appropriate selection of thermo-physical properties, quantity and position of the PCM [9]. Therefore, in order to guarantee good functioning of the PCM and ensure economic feasibility, optimisation of PCM use is advisable. An increasing amount of literature on optimisation analyses pertaining the improvement of the energy performance of buildings has been published in recent years [10–12]. Even though most of these studies focused on building design, the optimisation approaches were not limited to new constructions. Retrofitting analyses can be translated into multi-objective optimisation problems that are subjected to many constraints and limitations. Although the building shape is not included in the search process, the specific characteristics of the building need careful consideration. The optimal solution should be a trade-off between both energy and non-energy related aspects, such as economic and technical factors. For this reason, there has been increasing interest in the development of frameworks for the energy retrofitting of buildings, often aided by the application of optimisation algorithms [13–20]. Huang et al. [21] performed an optimisation of the thermal properties of an envelope in an energy-saving renovation of existing public buildings. They investigated the effect of the insulation thickness and the type of windows on the energy savings for heating and on the 930

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application of two different PCMs may be beneficial to improve the energy efficiency of buildings over the whole year [34]. Zhu et al. [35–37] presented numerical studies on the application of two layers of shape-stabilised PCM for buildings located in climates that required both heating and cooling. Their analysis was carried out for the south facing wall of an office case study building. The wall was characterised by an external PCM layer that was active during the cooling season, and by an internal PCM layer that was active during the heating season. The optimal thickness of the PCM layers was identified as being between 30 mm and 60 mm. Ascione et al. [38] numerically investigated the simultaneous application of two PCM layers to the inner and outer sides of the walls of a residential building, and found that the application of a PCM layer with a high melting temperature to the external side and a melting temperature of 25 °C to the internal side could help maximise the cooling energy savings. In this framework, the present paper has focused on the application of optimisation analyses for the energy retrofitting of office buildings. An archetype office building, constructed in Italy during the 1946–1970 period and located in Palermo and Turin, was chosen as a case study. Two retrofitting options were considered on the opaque envelope components; intervention on either the external or the internal side of the walls. In both cases, a maximum of two PCM layers with different melting temperatures could be selected and placed in different positions with respect to the insulation. The idea was that a “low-temperature” PCM could be effective during winter but not during summer, and vice versa for the “high-temperature” PCM. Two PCMs would therefore make it possible to exploit the latent heat of fusion of either one of the PCMs, more or less throughout the whole year. With regard to the optimisation objectives, the problem was faced from two points of view. On one hand, optimisations were run with three objectives: to minimise the building energy needs for heating and cooling and the investment costs. On the other hand, the optimisations were performed with two objectives: to minimise the primary energy consumption and global costs. Apart from emphasising the objective values that could be reached by means of the optimisation procedure, the analyses were mainly focused on the variable values that led to the optimal solutions. One of the most important differences between single-objective and multi-objective optimisation is that the former finds a single solution, whereas the latter provides multiple solutions that correspond to a trade-off between the objectives [39]. Since these solutions are all near-optimal, they can be analysed to search for common properties which can be seen as rules for the solutions to belong to the Pareto front.1 Relationships between optimal solutions can therefore provide useful design principles that can be applied to the problem under investigation. In order to carry out this process of knowledge extraction, a series of graphical, statistical and numerical analyses, such as box plots, a mapping of the values assumed by each variable on the Pareto front and an analysis of the extreme solutions, were performed. Moreover, additional analyses were carried out to investigate the reasons behind some of the choices—or lack of choices—of the optimisation algorithm. The temperature profiles within the building during representative weeks were analysed, the mutual influence of the thermo-physical properties of PCM was investigated, and the selection of the objective functions and the influence of the efficiency of heating and cooling systems were discussed for representative cases. Some design guidelines for PCM

energy systems of typical residential buildings in Switzerland, in which they minimised life cycle costs and greenhouse gas emissions. They found that a building retrofitting should be introduced together with a change in the heating system. Schütz et al. [27] presented a multi-objective optimisation to minimise the annualised costs and CO2 emissions of the energy retrofitting of a residential case study building by varying the structure, sizing and operation of the building energy systems together with the building envelope. They found that modifying the energy systems seemed to be more cost-effective than retrofitting the envelope. Fan and Xia [28] presented an optimisation analysis pertaining to the energy retrofitting of a residential case study, with the aim of maximising the energy savings and the net present value, while minimising the payback period of the investment. The problem—whose investigated variables involved the window type, the insulation materials of the walls and roof, and the potential installation of a solar panel power supply system—was converted into a single-objective problem through the weighted sum method. They found that priority should be given to retrofitting of the envelope components when a sufficient budget is available. As far as the application of PCMs for retrofitting purposes is concerned, Ascione et al. [29] carried out a study on the retrofitting of an office building in which they added a PCM plasterboard to the inner side of its exterior envelope. By fixing the phase change enthalpy, they performed a parametric analysis to find the optimal temperature of fusion, thickness and placement of the PCM for five Mediterranean climates, both in conditioned and unconditioned buildings. They found that a refurbishment, by means of PCM wallboards, seemed to be more appropriate for a semi-arid climate. Ramakrishnan et al. [30] performed a parametric optimisation for the retrofitting of a typical Australian residential building by installing bio-PCM mats on the ceiling. Through an assessment of performance indicators, they searched for the phase transition temperature, the thickness of the PCM layer and the night ventilation rate that guaranteed the best indoor thermal comfort, evaluated with the ASHRAE adaptive model. They found that, depending on the climatic condition, the optimal phase change temperature was about 3–5 °C higher than the average outdoor air temperature. However, it was also found that, in these conditions, PCM might not offer the best efficiency. The selection of a proper thickness and night ventilation resulted to be important to maximise PCM efficiency and minimise costs. Soares et al. [31], by means of single-objective optimisation analyses, investigated the effect of substituting the internal gypsum boards of a south-exposed living room with PCMdrywalls on the yearly heating and cooling energy savings. The position and thickness of the PCM-drywalls, as well as the thermo-physical properties of the PCM (enthalpy-temperature and thermal conductivitytemperature functions) and solar absorptance of the inner surfaces were investigated. The optimal melting temperature was found to be higher in warmer climates, whereas solar absorptance was found to be higher in colder climates. The energy saving effect was more evident for warmer climates. Saffari et al. [32] investigated the optimal peak melting temperature of a PCM integrated in a gypsum board by means of a single-objective optimisation to separately minimise the heating, cooling and total energy performance of a residential case study for a wide variety of climates. They found that significant energy savings could be achieved in many locations. Figueiredo et al. [33] investigated the optimal PCM solution and air flow rate that were necessary to apply during summer and winter seasons for the energy retrofitting of a real university department building, by minimising the annual heating demand and summer overheating rate. They found that the design of PCM solutions should always be aided by optimisation procedures, and that a simultaneous optimisation of the ventilation rate enhanced the performance of the PCM. The optimal PCM melting temperatures can differ in the winter and summer seasons according to the climate [6,29]. PCMs that perform well during the heating period may have only a marginal effect—if any—during the cooling period, and vice versa [9]. Therefore, the

1 The relationship among solutions of a multi-objective search can be studied through the concept of dominance [40]. If solution A outperforms solution B in at least one function and outperforms or equals solution B in all the other functions, then solution A dominates over solution B. If solution A outperforms solution B in one or more functions and at the same time solution B outperforms solution A in one or more functions, then solutions A and B do not dominate over each other. The Pareto front, also called the tradeoff set or non-dominated set, is the set of all non-dominated solutions in a given group. They represent the set of solutions where one cannot be said to be better than another if all the objective functions are simultaneously considered.

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(Fig. 1), to have no more than six floors, and to be located in an urban area where it was surrounded by lower buildings. For the present optimisation analyses, the building has been considered to have five floors and to be surrounded by four floor tall buildings at a distance of 14 m. Only the third floor was modelled. This choice is related to the need to make a compromise between a moderate influence of the urban context and the availability of solar radiation. The external wall and floor slab were selected according to the UNI/ TR 11552:2014 [48] national technical report, which provides a list of typical opaque building envelopes in existing Italian buildings. A typical wall in buildings built between 1930 and 1975 in the Piedmont region, where Turin is located, was selected. Since no region-specific information was provided in [48] for the Sicily region, the same kind of wall was also considered for Palermo. Details on the layers and thermophysical properties of the selected wall and floor slab are reported in Tables 1 and 2, respectively. A single glazing with an uninsulated metal frame (U-value of 5.7 W/(m2 K), g-value of 0.85) was selected for the transparent envelope according to the “National scientific report on the TABULA activities in Italy” [49]. A natural ventilation strategy was considered. No typical data for office buildings was found for the systems. Data for residential buildings were therefore used. On the basis of the efficiencies for emission, regulation, distribution and generation reported in [49], a seasonal efficiency of the heating systems of 0.63 was considered according to UNI/TS 11300-2 [50]. A seasonal energy efficiency ratio (SEER) of 2.5 was adopted for the cooling system. With a floor size of 18 × 12 m (external dimensions) and a floor height of 3 m, the net floor area before the retrofitting was 198.36 m2 and the net volume was 595.08 m3.

selection and application were also provided. To the best of the authors’ knowledge, no similar investigation on the layer distribution within a wall of either a new or existing building which includes PCMs has been proposed, especially considering the simultaneous presence of two PCMs with different thermo-physical properties. In the existing literature, investigations of the optimal application of PCMs for new and retrofitted buildings mostly involved parametric analyses [41,29,30]; when true optimisation processes were adopted, they mostly involved either analytical optimisation for specific applications (e.g. direct gain solar rooms [42,43]), single-objective analyses [31,32], or simulations explored only a short time window (e.g. a week [44]). Moreover, the comparison between several retrofitting strategies (i.e. investigating the optimal intervention in the case of retrofitting on either the internal or external side of the walls), the comparison between optimisation results according to the selected objective functions (i.e. investigating how the selection of the objective functions affects the results of the search process), as well as the postoptimisation analyses (i.e. investigating a methodology to extract useful information from the results of a search process), introduce an additional novelty to the present work. However, the main focus has been on the methodological approach rather than on the optimisation problem itself. 2. Methods and methodology The investigations focused on the application of optimisation analyses for the energy retrofitting of office buildings located in the Italian cities of Palermo (38.11°N, 13.33°E) and Turin (45.07°N, 7.67°E). The corresponding climate types, according to the Köppen classification [45], are Csa (hot-summer Mediterranean climate) and Cfa (humid subtropical climate), respectively. The annual heating and cooling degree days are 724 and 1022 °C day in Palermo, and 2506 and 381 °C day in Turin (18 °C baseline), respectively. The following retrofitting strategies were considered on the envelopes and systems: retrofitting of the external walls with the addition of insulation and PCM (up to two layers, referred to as PCM1 and PCM2 for lower or greater peak melting temperatures than 23 °C, respectively); replacement of the existing windows; substitution of internal movable shading devices with external ones (with the exception of the windows on the north façade); installation of a mechanical ventilation system with a night ventilation control strategy; revamping of the heating and cooling systems; installation of dimming lighting control. Moreover, the optimisation analyses were performed considering the following two retrofit options on the opaque envelope components: intervention on the external side of the walls (e.g. when interruption or relocation of the office activities is not possible during the renovation works) and intervention on the internal side of the walls (e.g. for buildings subjected to laws on the conservation of historical buildings—in Italy, for buildings older than 50 years). With regard to the optimisation objectives, the problem was faced from two different points of view. On one hand, the optimisations were run with three objectives: to minimise the building energy needs for heating and cooling (QH ,nd and QC ,nd , respectively) and the investment costs (CI ). On the other hand, the optimisations were performed with two objectives: to minimise the primary energy consumption (EP ) and to minimise the global costs (CG ).

2.2. Parametric model for the optimisation analysis A parametric model was developed in order to consider two possible retrofitting options, i.e. intervention on either the external side of the opaque envelope (referred to as RTe) or on the internal side (referred to as RTi). In both cases, the optimisation algorithm could select a maximum of two PCM materials. 2.2.1. Opaque envelope The retrofitted walls were described by the following variables: wall configuration, U-value of the wall, insulation material and internal lining material. Wall configuration According to the considered type of retrofitting, two sets of wall configurations were selected. The retrofitting configurations were chosen in order to test all the combinations of layer

2.1. Description of the case study (baseline) The investigations were carried out considering the energy retrofitting of an archetype office building constructed in Italy during the 1946–1970 period. According to the researches of Margiotta [46] and Rollino [47], until 1970, the representative office building in Italy was considered to have a cellular plan with a moderate amount of glazing

Fig. 1. Plan of the archetype office building.

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to comply with the national standard [52]. The maximum U-value for walls is 0.45 W/(m2 K) in Palermo and 0.30 W/(m2 K) in Turin. The lower bound for the U-value was set equal to 0.15 W/(m2 K), which is the upper limit for Passive Houses [53]. Insulation material The insulation material was chosen from a set of eight options, whose thermo-physical properties are reported in Table 3. The insulation thickness was calculated in order to obtain the U-value selected each time by the optimisation algorithm. Internal lining material In the case of retrofitting on the inner side of the walls, the internal lining material was also selected. The thermophysical properties and thickness of the possible options are reported in Table 4. Additional notes In the case of retrofitting on the external side of the walls, the existing render on the external side of the walls was considered to have deteriorated and was hence removed. Moreover, when the retrofitting intervention was performed on the internal side of the walls, a vapour barrier was considered to prevent interstitial condensation. In addition, thermal bridges were assumed to have been solved through an accurate installation of the insulation layer.

Table 1 Description of the external walls of the archetype building (baseline). Material

External render Bricks Air cavity Hollow bricks Internal plaster

t [m ]

ρ

c

[kg/m3 ]

[J/(kg K) ]

k [W/(m K) ]

[m2 K/W ]

0.02 0.12 0.06 0.08 0.02

1800 1800 – 800 1400

1000 1000 – 1000 1000

0.90 0.72 – – 0.70

– – 0.18 0.20 –

R

U-value: 1.30 W/(m2 K), thickness: 30 cm. Table 2 Description of the floor slabs of the archetype building (baseline). Material

Floor tiles Cement mortar Lightened screed Cement mortar Slab Internal plaster

t [m ]

ρ

c

[kg/m3 ]

[J/(kg K) ]

k [W/(m K) ]

0.015 0.02 0.06 0.02 0.24 0.02

1700 2000 900 2000 900 1400

1000 1000 1000 1000 1000 1000

1.47 1.4 0.58 – – 0.70

R [m2 K/W ] – – – 0.35

2.2.2. PCM properties The optimisation variables for each PCM included thickness, t, peak melting temperature, Tp , melting temperature range, ΔT , latent heat of fusion, L, and thermal conductivity, k. Details on the PCM modelling are reported in Appendix A. The thickness was allowed to vary between 0.5 cm and 4 cm. The peak melting temperature ranged from 15.5 °C to 23 °C for PCM1 and from 23.5 °C to 39 °C for PCM2. The melting temperature range for both PCMs was allowed to vary between 0.5 °C and 8 °C, the latent heat of fusion from 80 kJ/kg to 230 kJ/kg, and the thermal conductivity was allowed to span between 0.15 W/(m K) and 0.9 W/(m K).

–

U-value: 1.56 W/(m2K), thickness: 37.5 cm.

positions with no more than one insulation layer and one layer of the same PCM. These wall configurations were mathematically described according to the use of PCM (none, only PCM1, only PCM2, both PCMs) and by three position variables, which acted as switches for the selection of the wall configuration (i.e. either 0 or 1). The full list of possibilities is reported in Fig. 2 for retrofitting on the external side and in Fig. 3 for retrofitting on the internal side. It is important to mention that the wall configurations are not always described by all the position variables. For example, in Fig. 2, if PCMuse is 0 (no PCM), the wall will be “ext0000”, regardless of the values of the PCM position variables. In the same way, if PCMuse is either 1 or 2 (only PCM1 or only PCM2), only PCMpos1 will affect the selection of the wall, regardless of the values assumed by PCMpos2 and PCMpos3. This lack of uniqueness in the search space—i.e. several sets of variables can generate equivalent solutions—introduces a certain degree of epistasis to the problem. The higher the epistasis, the more difficult the problem is to solve [51]. U-value of the wall The U-value of the new wall was chosen in order

2.2.3. Transparent envelope The complete list of the new glazing types is reported in Table 5. The optimisation algorithm for each location could choose from four different windows, with a maximum U-value of 3.2 W/(m2 K) in Palermo (ID from 0 to 3) and 1.9 W/(m2 K) in Turin (ID from 4 to 7) in order to comply with the national standard [52]. The U-values, g-values and visible transmission coefficients were evaluated with the WINDOW 7.4 [54] software. To evaluate the overall U-value of the windows, Uvalues of the frame equal to 2.0, 1.8 and 1.2 W/(m2 K) were considered for windows from 0 to 3, 4 to 5, and 6 to 7, respectively. Fig. 2. Wall configurations for retrofitting on the external side.

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Fig. 3. Wall configurations for retrofitting on the internal side.

Legend Existing wall Insulation PCM1 PCM2

south to east, external shading devices were installed on all the windows with the exception of those on the north-facing façade. Twenty-five mm wide and 1.5 mm thick slats with a separation of 19 mm, characterised by a thermal conductivity of 0.9 W/(m K) and solar and visible reflection coefficients at a normal incidence of 0.7, were considered.

Table 3 Thermo-physical properties and costs of the insulation materials. ID

0 1 2 3 4 5 6 7

Material

EPS Rock wool XPS Sheep wool Cork Wood-fiber board Cellulose fiber panels Aerogel mats

k [W/(m K) ]

ρ

c

CI,ins

[kg/m3 ]

[J/(kg K) ]

⎡€ / m ⎤ ⎣ cm ⎦

0.042 0.040 0.033 0.037 0.044 0.038 0.039 0.0135

13 36 35 20 130 160 40 150

1250 1030 1250 1720 850 2100 2150 1000

0.34 0.58 1.02 1.77 2.01 2.15 2.22 65.28

2

2.3. Description of the objective functions 2.3.1. Building energy needs The energy analyses were performed with EnergyPlus 8.0.0 [55,56]. EnergyPlus is an open source software whose modules work with a simulation core that is based on fundamental heat balance principles. Assuming a uniform air temperature in the thermal zone, a uniform temperature of each surface, diffusive surface irradiation and one-dimensional heat conduction through the surfaces, and neglecting the heat transfer due to infiltration and inter-zone air mixing, the air heat balance can be written as

Table 4 Thickness, thermo-physical properties and costs of the internal lining materials. ID

0 1 2 3

Material

t

k

ρ

c

CI,pl

[m ]

[W/(m K) ]

[kg/m3 ]

[J/(kg K) ]

[€/m2 ]

0.02 0.02 0.04

0.70 0.90 0.26

1400 1800 1800

1010 2100 2100

18.05 19.50 31.31

0.05

0.091

400

1000

48.78

Lime and gypsum plaster Clay plaster Mineralised wooden board Thermo-plaster

Cz

dθz = dτ

Nsurface

N

∑

Qċ ,i +

i=1

∑

̇ hi Ai (θsi−θz ) + ṁ v cp (θe−θz ) + Qsys

i=1

where N is the number of convective internal loads, Qċ ,i , the term hi Ai (θsi−θz ) is the convective heat transfer from the i-th surface at temperature θsi to the air in the zone at temperature θz , ṁ v cp (θe−θz ) is ̇ is the the heat transfer due to ventilation with the outside air, and Qsys system output. The capacitance, Cz , takes into account the air in the zone as well as the thermal masses, which are assumed to be in equilibrium with the air in the zone.

2.2.3.1. Shading devices. In order to comply with the Italian standard [52], which requires the SHGC when the shading device is in use to be lower than 0.35 for windows with expositions ranging from west to Table 5 Glazing specifications and costs. ID

0 1 2 3 4 5 6 7

Type

4/12/4 4/12/4 4/12/4 6/16/4 4/12/4 4/12/4 4/12/4/12/4 4/12/4/12/4

Coating

None Low-e (3) Low-e (2) Selective (2) Low-e (3) Low-e (2) Low-e (3,5) Low-e (3,5)

Gap

Air Air Air Ar 90% Ar 90% Ar 90% Air Ar 90%

Ug

g

τl (S-N)

(E-W)

(S-N)

(E-W)

(S-N)

(E-W)

[W/(m2 K) ]

[–]

[–]

[W/(m2 K) ]

[W/(m2 K) ]

[€/m2 ]

[€/m2 ]

[€/m2 ]

[€/m2 ]

[€/m2 ]

2.84 1.61 1.61 1.07 1.28 1.28 0.94 0.72

0.75 0.58 0.40 0.26 0.58 0.40 0.49 0.49

0.81 0.80 0.71 0.61 0.80 0.71 0.71 0.71

2.77 1.93 1.93 1.54 1.64 1.64 1.23 1.07

2.72 1.81 1.81 1.39 1.51 1.51 1.11 0.94

37.55 38.77 38.77 70.08 44.67 44.67 74.33 81.48

154.38 154.38 154.38 154.38 278.93 278.93 306.82 306.82

138.72 138.72 138.72 138.72 271.53 271.53 298.68 298.68

191.93 193.15 193.15 224.46 323.60 323.60 381.15 388.30

176.27 177.49 177.49 208.80 316.20 316.20 373.01 380.16

Uw

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CI,f

CI,w

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In order to obtain the building energy needs for heating and cooling, the system was modelled as IdealLoadsAirSystem, with an infinite heating and cooling capacity; QH ,nd and QC ,nd were obtained from the ̇ , respectively. yearly sum of the positive and negative values of Qsys In the building energy model, the set-point air temperatures were set at 20 °C for heating and 26 °C for cooling, according to the Italian regulation [57]. The systems were only active from 7.00 AM to 6.00 PM during weekdays. Considering the high number of simulation runs required for the search process, the space was treated as a single thermal zone in order to reduce the calculation run time. Internal partition walls were taken into account as internal mass. The solar absorption coefficient of the external opaque surfaces was set equal to 0.6. A fixed ground reflectance value of 0.15 was assumed [58]. External shading devices were operated when the solar irradiance on the window was higher than 300 W/m2; a fixed slat angle of 45° was considered. Schedules were set according to ISO 13790:2008 [59], which assumes 20 W/m2 for internal gains in office rooms derived from the activity of people and electric equipment during daytime, and 2 W/m2 during night-time. In the other spaces, 8 W/m2 was assumed during occupied hours and 1 W/m2 during unoccupied hours. Since a single zone was modelled, the following average values, with respect to the floor area, were given as input to EnergyPlus: 7.5 W/m2 for internal gains derived from the activity of people, and 8.3 W/m2 for internal gains derived from electric equipment during daytime and 1.7 W/m2 during night-time. Occupancy time was considered from 8.00 AM to 6.00 PM during weekdays. Daylighting control was operated with a dimming option. Two control points were placed along the longitudinal axis of the building in the middle of the office rooms. The illuminance setpoint was set at 500 lx. The maximum lighting level was set at 10 W/m2 per zone floor area. The lighting schedule was set equal to the occupancy one. A mechanical ventilation strategy was adopted with sensible heat recovery (70% efficiency). According to UNI 10339:1995 [60], the ventilation rate was set at 0.792 air changes per hour during the occupation time. During the rest of the day and during weekends, the ventilation rate was set at 0.25 h−1 [61]. During the summer season, night-time ventilation was allowed from 11.00 PM to 7.00 AM [59,62] when the internal temperature was above 24 °C and the difference between the internal and external air temperature was greater than 2 °C. The night cooling air change rate was set at 6 h−1. A fan pressure rise of 75 Pa and a total fan efficiency of 0.5 were selected with a balanced ventilation type. The indications from Tabares-Velasco et al. [63] were followed to model the PCM, i.e. a timestep equal to 3 min and a space discretisation constant equal to 1. The ConductionFiniteDifference algorithm was adopted to model the walls with PCM, whereas the ConductionTransferFunction model was used in the absence of PCM in order to reduce the calculation run time. The enthalphy-temperature curve of the PCMs was obtained by integrating the c (T ) curve in Eq. (A.1). A maximum of 16 points were chosen as input values, due to the intrinsic limitation of EnergyPlus. The selection of these points was performed in order to guarantee the minimum discrepancy from the analytical curve.

EP = fP,tot ,gas ·

QC,nd QH ,nd + fP,tot ,el ·⎛ + Qel⎞, ηH ⎝ SEER ⎠

where primary energy factors (PEF) of 1.05 and 2.42 were adopted for natural gas and electricity, respectively, according to the values reported in the D.M 26 giugno 2015 decree [52]. This PEF value for electricity includes both renewable and non-renewable shares. 2.3.3. Global cost The cost analyses were performed according to EN 15459:2007 [64], where the global cost is defined as the sum of the initial investment cost and the annual costs for each component or system, minus their value at the end of the calculation period. Therefore, τ

CG (τ ) = CI +

∑ ⎧⎨∑ j

⎩ i=1

⎫ [Ca,i (j )·Rd (i)]−Vf ,τ (j ) , ⎬ ⎭

where CG (τ ) is the global cost, which is a function of the calculation period, τ ; CI is the investment cost; Ca,i (j ) are the annual costs for year i of component j ; Rd (i) is the discount rate for year i; and Vf ,τ (j ) is the final value of component j at the end of the calculation period. The initial investment cost was calculated considering only the material and installation costs related to the building envelope. The installation cost of the HVAC systems—as well as the costs for design, etc.—were not considered, since their value was assumed to be the same for all the candidate solutions in the same location. For the same reason, only the energy costs were considered as annual costs. To evaluate the final value, a lifetime of the building of 50 years after renovation and a calculation period of 30 years were assumed. The lifespan of the opaque envelope was considered equal to the lifetime of the building, whereas lifespans of 30 and 25 years were considered for the transparent envelope and the shading devices, respectively. A rate of development of the price for products of 0.02, a market interest rate of 0.045 and an inflation rate of 0.02 were considered. 2.3.3.1. Investment costs. With the exception of the PCM, the data source adopted to evaluate the investment costs was the official Regione Piemonte price list for public works [65]. Although prices change according to the location, the material and installation costs were assumed to be unvaried. The highest accuracy for the investment cost was hence obtained for the analyses performed in Turin. The unit costs of the insulation and internal lining materials are reported in Tables 3 and 4, respectively. The costs of the insulation were the raw material costs, which in [65] are given in €/m2 for predefined thicknesses. Starting from those data, a linear regression was found to describe the relationship between cost and thickness. Therefore, insulation prices in €/m2 per unit of thickness were estimated and used in the calculations. Installation costs of 42.47 €/m2 and 51.65 €/ m2 were considered for insulation installed on the external and internal side of the walls, respectively. The costs of the internal lining materials include both the raw material and installation. According to [65], the reference surface for the cost calculation was the total area of the wall, regardless of the presence of windows; when the wall had smaller openings than 4 m2, the area of the openings was not removed in order to account for the extra work and material needed to build the opening sides. When the retrofitting intervention required operation on the external side of the walls, the cost for removing the existing render was set at 6.31 €/m2. Moreover, an additional cost of 9.31 €/m2 was considered for the scaffolding, plus 1.59 €/m2 for each month after the first one. Two months of installation of the scaffolding were estimated. When the retrofitting intervention required operation on the internal side of the walls, a vapour barrier was added to prevent interstitial condensation,

2.3.2. Primary energy In order to evaluate the primary energy consumption, the energy vectors and system efficiencies after the retrofitting needed to be defined. Natural gas was assumed as the energy vector for the heating; the system was considered to have a seasonal efficiency, ηH , of 0.8. Cooling was considered to be provided by means of a chiller with an SEER of 3.0. Electricity use included lighting, equipment and the energy required to operate the ventilation system fans. The primary energy was hence evaluated as

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with a cost of 17.04 €/m2 for both the raw material and installation. The costs of glazing, of the frame and of the installation are reported in Table 5, together with the total costs of the window. The costs of glazing include raw-material costs, whereas the frame costs include the costs of the frame material and the costs of installing the window. Two values are reported for frame/installation costs, in consideration of the different sizes of the windows; 1.92 m2 ( < 2 m2) along the south and north façades, and 3.84 m2 ( > 3.5 m2) on the east and west façades. In addition, the costs for removing the existing windows were set equal to 12.14 €/m2. The costs of the shading devices were set equal to 59.10 €/ m2. The price of PCMs varies widely, according to their type, melting temperature and purity (which affects the melting temperature range and latent heat of fusion) [66]. Unfortunately, it is impossible to take all of these factors into account to accurately estimate the price of PCM. An average price was thus estimated from values reported in the literature (Table 6). Costs for commercial amounts (> 500 kg) were considered whenever known. An average price (with the exclusion of the laboratory-grade PCM) of about 40 €/m2 for each cm of thickness was chosen for the raw material. An additional 20% was considered for macroencapsulation [66]. The total estimated price of PCM was hence 48 €/ m2/cm, plus 4.36 €/m2 for installation [67].

Minimise f1 (x ) = EP ⎫ Problem 1, or Minimise f2 (x ) = CG ⎬ ⎭ Minimise f1 (x ) = QH ,nd ⎫ ⎪ Minimise f2 (x ) = QC,nd Problem 2 ⎬ Minimise f3 (x ) = CI ⎪ ⎭ subject to gi (x ) = xΔTi ⩽ (300−x Li )/15 i = 1,2 0 ⩽ x winType ⩽ 3 0.15 ⩽ xU − value ⩽ Ulim 0 ⩽ xInsulationType ⩽ 7

2.3.3.2. Energy costs. In Italy, according to the “Autorità per l’energia elettrica il gas e il sistema idrico” (AEEGSI) [72], the cost of electricity is calculated from the sum of three amounts; a fixed share, a power share and an energy share. The shares of the electricity prices for nondomestic users with a power request of 10 kW were 286.32 €/y, 31.77 €/kW/y and 0.1742 €/kWh, respectively (prices for the third trimester, 2016). According to AEEGSI, the price of natural gas in Italy is calculated from the sum of two amounts; a fixed share and an energy share. Considering a lower calorific value of 9.6 kWh/m3 and the estimated yearly gas consumption for each location, the fixed and energy shares for Palermo were set equal to 119.25 €/y and 0.2676 euro/kWh, and equal to 399.45 €/y and 0.5864 €/kWh for Turin (prices for July, 2016). All the prices include taxes and levies but exclude VAT. A VAT equal to 22% was applied to the electricity costs and natural gas in Turin, whereas a VAT equal to 10% was applied to the costs for natural gas in Palermo.

where i refers to either PCM1 or PCM2. The genetic algorithm inputs, including the domain of each variable, are reported in Table 7. NSGA-II explored 100 generations for all the simulations, with 100 individuals in each generation. Moreover, the constraint on the PCM properties reported in Appendix A.1 was considered. The constraint, gi (x ) , was handled with a repair algorithm which introduced modifications of the non-complying individuals. In detail, the melting temperature range was set equal to the limit value defined in Eq. (A.5). An always replacing approach was chosen. It was verified that transforming infeasible solutions into feasible ones did not introduce an important bias in the search [75,76].

0 ⩽ xPlasterType ⩽ 3∗ 0 ⩽ xPCMuse ⩽ 3 0 ⩽ xPCMpos1 ⩽ 1 0 ⩽ xPCMpos2 ⩽ 1 0 ⩽ xPCMpos3 ⩽ 1 0.005 ⩽ x ti ⩽ 0.04 0.5 ⩽ xΔTi ⩽ 8 80 ⩽ x Li ⩽ 230 0.15 ⩽ x ki ⩽ 0.9 15.5 ⩽ xTp,1 ⩽ 23

∗RTi

i i i i

= = = =

only

1,2 1,2 1,2 1,2

23.5 ⩽ xTp,2 ⩽ 39,

2.5. Post-optimisation analyses A series of graphical, statistical and numerical analyses were performed to carry out the knowledge extraction process. First, box plot Table 6 PCM costs (1 $ = 0.9033€).

2.4. Optimisation procedure The analyses were carried out by coupling a Python implementation of the NSGA-II optimisation algorithm [73] with the building energy model developed in EnergyPlus (see Section 2.3.1), according to the procedure described in [74]. Among the various genetic algorithms (GAs), NSGA-II is considered the most efficient multi-objective genetic algorithm [10]. Separate optimisation runs were performed for each problem to consider the two possible retrofitting options (RTe and RTi). The total time required to perform a single optimisation run was approximately eight days on computers with at least 8 Gb of RAM. It was possible to launch each optimisation run in parallel, with a limit that depended on the maximum number of simultaneous EnergyPlus instances that each computer could handle.

2.4.1. Genetic inputs Overall, the investigated optimisation problems can be explained by the following expression:

PCM type

€/kg

€ / m2 cm

Ref.

Organic, paraffins Paraffin wax Eicosan, laboratory-grade (> 99%) Eicosan, technical-grade (90–95%) PCM products Rubitherm RT20 Rubitherm RT (23, 25, 27 °C) Rubitherm RT27 Rubitherm RT28HC

1.75 48.69 6.36 6.00 14.74 0.62 5.00 8.25

13.32 428.45 55.96 52.80 110.56 5.46 38.00 63.53

[66] [66] [66] [68] [69] [67]

Organic, fatty acids Oleic acid Biodiesel crude glicerine PureTemp (min) PureTemp (max) PureTemp (max) BioPCM

1.55 0.23 1.49 4.97 9.96 1.18

13.79 2.88 12.82 42.73 85.63 10.13

[66] [66] [66] [66] [70] [71]

Inorganic, salt hydrates PCM Energy P. Ltd (min) PCM Energy P. Ltd (max)

2.78 4.47

41.73 67.07

[66] [66]

a

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Table 7 Genetic inputs. Population Size

100

Number of variables

17 for RTe

18 for RTi

Number of binary digits

2 for Window Type 2 for PCMuse

4 for U-value 1 for PCMpos

3 for Insulation Type 3 for PCM thickness

2 for Plaster Type 4 for Tp,1

5 for Tp,2

4 for ΔTi

4 for Li

4 for ki

Variable domains

xWindowType ∈ [0,3]

xU − value ∈ [0.15,Ulim]

xInsulationType ∈ [0,7]

xPlasterType ∈ [0,3]

xPCMuse ∈ [0,3]

xPCMpos ∈ [0,1]

x ti ∈ [0.005,0.04]

xTp,1 ∈ [15.5,23]

xTp,2 ∈ [23.5,39]

xΔTi ∈ [0.5,8]

x Li ∈ [80,230]

x ki ∈ [0.15,0.90]

Mutation probability

0.2

End condition

End after 100 generations

categorical variables are involved. Additionally, the mutual relationships between the variables were quantitatively identified according to the procedure proposed in [77] and detailed in [78]. Finally, the extreme solutions in the Pareto front were depicted. These solutions are particularly interesting because they represent the optimal solution for a single objective. If the objectives are contrasted, it is likely that the best solution for one objective corresponds to the worst solution for another.

analyses were carried out with a twofold aim. On one hand, the objective was to obtain information on the relative importance of the input variables within the set of Pareto front solutions. On the other hand, information on the possibility of reducing the number of input variables could be inferred [74]. Moreover, wide spanning variables can relate either to a randomness in the results (i.e. limited influence on the objective) or to a relationship between a variable and the objective (i.e. high influence on the objective). Therefore, in order to explore how the variables in the search space (domain) affected the results in the objective space (codomain), the values assumed by each variable were mapped on the Pareto front. This mapping was obtained by superimposing, onto the Pareto front, a colour-scale representation of the values assumed by each variable, one at a time. This representation allows simple relationships between a variable and the objectives to be qualitatively identified. When constant values are assumed by a variable, the Pareto front is represented by a single colour. A chromatic scale can identify direct or inverse relationships between a variable and the objectives. Variables mapped by random colours next to each other may signify that they have little influence on the objective functions. Moreover, clusters in the Pareto front are likely to be identified when

3. Results 3.1. Pareto frontiers The Pareto frontiers are illustrated and described hereafter. All the energy related values are expressed in kWh/(m2y), whereas all the cost values are reported in €/m2 (both refer to the gross floor area). 3.1.1. Two-objective analyses The Pareto fronts of the two-objective investigations are reported in Fig. 4. The retrofitting on the internal side (RTi) allowed a lower

Fig. 4. Pareto frontiers of the two-objective (2Obj) and three-objective (3Obj) analyses.

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operation and the worse lighting performance of the retrofitted windows with external movable shading devices, the electricity demand was still reduced overall as a result of the dimming lighting strategy. The major reduction was obtained for the solutions of the two-objective optimisation analyses. In the best case, the EP consumption was reduced by almost 25%. Both the cooling and particularly the heating energy needs could be significantly reduced in Turin. The solution which ensured the lowest EP had a similar energy performance to that which ensured the lowest heating energy need, but it was characterised by a significantly lower investment cost in the RTi case. In the best case, the primary energy consumption was reduced by 33%. In general, the solutions characterised by the lowest investment costs were characterised only by a slightly higher global cost compared to the solutions with a minimum CG . However, their performance, in terms of EP , was much lower.

primary energy consumption to be achieved with a lower global cost for both locations, whereas the retrofitting on the external side (RTe) resulted to be the worst option. The solutions in the A group represent those individuals that are characterised by the lowest primary energy consumption for each case. As a result of the contrast between objectives, they were also the solutions that presented the highest global costs. On the other hand, the solutions in the B group represent the individuals that are characterised by the lowest global costs (cost-optimal solutions of the Pareto fronts), and therefore by the highest primary energy consumption. However, the variation in the primary energy consumption between the best and worst solutions within each Pareto front was very small, ranging from 2 kWh/(m2y) to 5 kWh/(m2y). The difference, in terms of global costs, was much more significant. 3.1.2. Three-objective analyses The Pareto fronts of the three-objective investigations (minimisation of the building energy needs for heating and cooling and investment costs) are reported in Fig. 4. These fronts were represented as two-dimensional projections onto each plane (with blue squares for RTi and red dots for RTe), where the large markers highlight the bi-dimensional Pareto front. Intervention on the internal side showed an advantage in terms of both the energy performance and costs for both Palermo and Turin. However, the difference between the RTe and RTi fronts in Palermo was less pronounced than in Turin. As can be expected, a certain degree of contrast was found between all the objective functions. A remarkable contrast was observed in particular between the investment costs and both the cooling energy needs in Turin and the heating energy needs in Palermo. Moreover, the investment costs were found to increase dramatically beyond a limit value (the knee point in the 2D projections of the Pareto fronts) when the heating energy needs in Turin and the cooling energy needs in Palermo were minimised. The Pareto fronts in Palermo seemed to be divided into two main clusters, which are particularly noticeable from the projection onto the (Qh,nd,Qc,nd ) plane. The reasons behind this characteristic are discussed in Section 4. Even though less pronounced, the Pareto fronts for Turin were also clustered into two groups of solutions. The solutions in the C group represent those individuals that were characterised by the lowest building energy needs for heating for each case. They also correspond to the solution with the highest investment cost in the RTe case in Palermo and in the RTi case in Torino. The solutions in the D group represent the individuals that were characterised by the lowest building energy needs for cooling, whereas the solutions in the E group represent the solutions with the lowest investment costs. The greatest variation between the best and worst optimised solutions was observed for the investment costs. Only a small difference was observed for the heating energy needs in Palermo and the cooling energy needs in Turin.

4. Post-optimisation analyses Information on the search variables of the optimised solutions is presented hereafter. 4.1. Wall type and PCM selection The frequency analyses of the wall types selected for the nondominated solutions are reported in Fig. 5. Regardless of the type and number of PCM layers, the PCM tended to be placed between the existing wall and the external insulation in the RTe cases, whereas it was placed close to the internal environment in the RTi cases. With regard to the PCM selection, PCM1 was clearly preferred over PCM2 in the two-objective investigations. In Palermo, which has a cooling-dominated climate, choosing the low-temperature PCM may appear strange. However, after analysing the temperature profiles within the building (see Section 5.1), PCM1 was found to have a stabilising effect on the internal temperature for a longer period of time, because the climatic conditions in winter, and particularly during the mid-season, are mild. Moreover, the high temperatures in summer tended to be too extreme for even PCM2 to work effectively. On the other hand, this result could be expected in Turin, since minimising the primary energy consumption in a heating-dominated climate basically implies reducing the heating energy consumption. However, when analysing the wall types of the three-objective investigations, different results were obtained. PCM1 was still preferred in Palermo, whereas PCM2 was predominantly selected in Turin. Even though the heating energy needs was the most important aspect to minimise, PCM2 was able to work more effectively in Turin than in Palermo, due to the Table 8 Energy performance of the extreme solutions, the RTe cases. Solution

QH ,nd

3.2. Energy performance of the extreme solutions

QC ,nd

Qel

EP

CI

[€/m2 ]

[kWh/(m2 y) ]

The energy performance of the baseline and of the best-performing solutions, with respect to each objective function, are reported in Tables 8 and 9 for the RTe and RTi cases, respectively. The electricity share in the pre-retrofit building in Palermo accounted for most of the primary energy consumption (67.3%). Space heating and electricity accounted for almost half of the EP consumption in Turin (47.1% and 46.2%, respectively). In the best case (RTi solutions), the improvement in QH ,nd in Palermo, after retrofitting, spanned from 41% to almost 74% over the reported solutions. The energy needs for cooling were reduced by 31% when QC ,nd was minimised, and by 28% when the lowest EP was ensured. However, in absolute terms, a higher cooling energy reduction was obtained. In spite of the greater electricity demand due to fan 938

CG

Baseline Sol. A (min EP ) Sol. B (min CG ) Sol. C (min QH ,nd ) Sol. D (min QC ,nd ) Sol. E (min CI )

7.75 3.07 4.98 2.07 3.81 4.67

32.94 24.89 24.26 26.51 23.11 26.35

Palermo 38.15 36.61 36.63 36.30 37.27 36.26

137.19 112.70 114.74 111.96 113.84 115.13

– 604.68 172.15 858.18 549.26 171.87

– 793.23 445.08 997.98 750.85 446.01

Baseline Sol. A (min EP ) Sol. B (min CG ) Sol. C (min QH ,nd ) Sol. D (min QC ,nd ) Sol. E (min CI )

58.13 37.43 42.11 37.19 44.12 42.11

14.28 9.89 9.99 9.85 7.98 9.99

Turin 39.43 37.47 36.90 37.47 37.25 36.90

206.63 147.78 152.63 147.43 154.50 152.63

– 789.37 205.44 769.68 521.88 205.44

– 1012.43 545.52 996.01 803.41 545.52

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of both PCMs varied over a small range, and the latent heat of fusion of PCM1 tended towards the upper bound. The low range of variation of these variables implies that they had an important influence on the optimisation results. The melting temperature range of PCM1 was characterised by a slight tendency towards medium/low values, while that of PCM2 tended to assume higher values. The only exception was found for the three-objective analyses in Turin, where the trends were inverted due to the overall preference for PCM2. The thermal conductivity in the two-objective investigations varied over a relatively low range, whereas it spanned over the whole domain in the three-objective analyses. These aspects concerning both the melting temperature range and thermal conductivity are investigated in more detail in Section 5.2. Overall, it can be anticipated that a tendency towards minimisation of the melting temperature range was representative of the effectiveness of the selected PCM, together with the simultaneous tendency towards maximisation of the latent heat of fusion (whose influence on the building energy performance was more significant). Convergence towards a target value of thermal conductivity instead resulted to be easier when a single energy-related objective was addressed (i.e. in the two-objective problems).

Table 9 Energy performance of the extreme solutions, the RTi cases. Solution

QH ,nd

QC ,nd

Qel

EP

CG

CI

[€/m2 ]

[kWh/(m2 y) ]

Baseline Sol. A (min EP ) Sol. B (min CG ) Sol. C (min QH ,nd ) Sol. D (min QC ,nd ) Sol. E (min CI )

7.75 2.90 4.28 2.05 4.53 4.48

32.94 23.89 24.17 26.72 22.58 25.98

Palermo 38.15 33.27 34.00 35.06 35.90 35.43

137.19 103.59 107.39 109.10 111.04 112.56

– 373.06 121.13 523.07 358.47 116.79

– 582.45 384.06 714.99 583.24 389.77

Baseline Sol. A (min EP ) Sol. B (min CG ) Sol. C (min QH ,nd ) Sol. D (min QC ,nd ) Sol. E (min CI )

58.13 36.62 38.78 36.03 39.73 41.40

14.28 9.42 10.06 9.83 7.71 8.76

Turin 39.43 34.20 34.14 35.90 33.93 35.95

206.63 138.44 141.63 142.10 140.47 148.41

– 352.43 152.39 587.83 431.82 149.35

– 635.66 476.41 832.55 699.22 485.36

milder summer conditions, thus providing a longer stabilising effect on the internal air temperatures during the mid-seasons and a more effective coupling with night ventilation during summer. On the other hand, due to the harsher conditions in winter, PCM1 was not as effective in reducing the building energy needs for heating. However, when the primary energy was considered directly, the system efficiencies and PEF values were such that reducing the building energy needs for heating was more important.

4.3. Mapping of the input variables 4.3.1. Two-objective analyses The variable mappings on the Pareto fronts for the two-objective investigations are reported in Figs. 7 and 8 for the Palermo and Turin case studies, respectively. The small black dots refer to points belonging to the Pareto front where the PCM (either PCM1 or PCM2) was not applied. Only window types 2 and 1 (air-filled double glazed units (DGUs) with low-e coating) were selected in Palermo; since they were characterised by the same cost, choosing one instead of the other only had an impact on the primary energy consumption. In particular, those windows were found to provide the best trade-off between good thermal properties and a high visible transmission coefficient in order to reduce the electricity consumption for artificial lighting. Basically, only window type 7 and window type 4 were selected in Turin. Window type 4 (90% Ar-filled DGU with a low-e coating on face 3) was one of the two cheapest options, but had a low winter performance (but not the worst), whereas window type 7 (90% Ar-filled triple glazed unit (TGU) with low-e coatings) was more expensive, but was also the best option to reduce the heating energy consumption. The preferred insulation materials in the RTe cases were XPS and EPS, and the best performing but most expensive solutions adopted aerogel mats. The reason behind this choice is detailed in Section 4.3.2. The preferred insulation material in the RTi cases resulted to be EPS, i.e. the cheapest option. Thermo-plaster was mostly selected as internal lining material in Turin. As is evident from the box plots, all the solutions in the RTi case

4.2. Box plot analyses The box-plot representations of the values assumed by the non-categorical variables are reported in Fig. 6. Their cardinality is generally equal to the number of non-dominated solutions. However, the PCMrelated variables could be characterised by a lower cardinality, depending on whether one or both PCMs were considered. For this reason, the grey plots in Fig. 6 refer to cases that apply to less than 20% of the non-dominated solutions. A few evident results can be observed from the box plots. First, all the solutions of the two-objective investigations with a retrofitting intervention on the internal side shared a constant U-value of 0.15 W/ (m2 K), i.e. the lower bound. In Palermo, even though the primary energy consumption for heating was lower than that for cooling, the EP reduction derived from a lower U-value was greater than the consequent increase in primary energy consumption for cooling and the night ventilation fans. In Turin, low U-values were preferred to reduce the heat losses through the opaque envelope in winter. Heating energy consumption was the most important aspect to minimise, and it was in fact effectively reduced. In all the cases, the peak melting temperature

Fig. 5. Frequency analyses of the wall types (the wall codes are reported in Figs. 2 and 3).

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Fig. 6. Box plots of the non-dominated solutions (1 and 2 refer to PCM1 and PCM2).

shared a constant U-value of 0.15 W/(m2 K). On the other hand, in the RTe cases, decreasing U-values were associated with a decrease in primary energy consumption, and the global costs consequently increased due to the higher investment costs for insulation. In Turin, this trend varied over the groups of solutions characterised by different

window types and insulation materials. As has already been observed, PCM2 was seldom selected. Moreover, PCM was never chosen for the solutions characterised by the minimum global cost. Therefore, the use of PCM was found not to be cost-optimal. The Pareto fronts were characterised by an increasing

Fig. 7. Mapping of the variables on the Pareto fronts for the two-objective analyses in Palermo, the RTe and RTi cases.

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Fig. 8. Mapping of the variables on the Pareto fronts for the two-objective analyses in Turin, the RTe and RTi cases.

increase with the PCM thickness, according to the following relationship (except for the solutions with aerogel): Tp,1 = 35.8 t10.15 (R2 = 0.814) ; however, only a narrow range of temperatures at around 19.7 °C was selected. It could be argued that a relationship between the melting temperature and EP should rather be identified; however, the goodness of fit was significantly lower. This result is in line with the findings of

thickness of PCM1 in order to decrease the primary energy consumption (which resulted in a increase in the global costs), except for the RTe case in Turin, where high thicknesses were mostly chosen. The relationship between PCM thickness and primary energy consumption (as well as the global costs) was found to be linear. Moreover, in the RTe case in Palermo, the peak melting temperature of PCM1 was found to

Fig. 9. Mapping of the variables on the Pareto fronts for the three-objective analyses in Palermo, the RTe cases.

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was characterised by the highest cooling energy needs, while window type 3 (90% Ar-filled DGU with selective coating) was chosen when the cooling energy needs were reduced, and window type 2 (air-filled DGU with a low-e coating on face 2) characterised solutions with an intermediate energy performance. Although individuals with window type 1 were characterised by a better winter performance, the difference, compared to window type 3, can be considered negligible. In Turin, window type 4 (90% Ar-filled DGU with a low-e coating on face 3) was only used by a small group of solutions, which were characterised by the lowest investment costs and highest cooling energy needs. Window type 5 (90% Ar-filled DGU with a low-e coating on face 2), which had previously almost never been selected, was used in the cluster characterised by the lowest cooling energy needs and therefore highest heating energy needs, and vice versa for window type 7 (90% Ar-filled TGU with a low-e coating on faces 3 and 5). As far as the insulation material is concerned, aerogel was selected in the RTe cases when minimising the heating energy needs, especially in Turin. Because of its low thermal conductivity, low U-values could be obtained with a limited thickness. This has an important implication on shading; the lower the added thickness, the higher the available solar gains [74]. The colder the climate, the more preventing excessive shading resulted to be important. As for the internal lining material (RTi cases), the use of thermoplaster in Palermo was associated to a reduction of the cooling energy needs, whereas it was mostly selected in Turin for the solutions with both PCMs. In the RTe case, the U-value in Palermo presented a clear trend within each cluster; high values corresponded to low cooling energy needs, and vice versa for low U-values. The Turin case was very different. High U-values within each cluster were mainly associated with high heating energy needs. However, both high and low U-values could lead to low cooling energy needs. In the RTi case, high U-values were associated with high heating energy needs in Palermo, but there seemed to be almost no effect on the cooling energy needs. Low U-values in Turin were instead selected for most of the solutions, and especially for the trade-off solutions that minimised both heating and cooling energy

Zhu et al. [36], who found that the thickness and melting temperature influenced each other when the minimum annual energy demand or the lowest peak load for heating and cooling were being searched for. On the other hand, no such relationship was found in Turin, as the solutions to the RTe case shared an almost constant peak melting temperature of PCM1 (16.9 °C on average), and its thickness tended towards the upper bound. In the RTi cases, the peak melting temperature of PCM1 varied over a small range (around 20 °C in Palermo and 18.5 °C in Turin) and the thermal conductivity assumed medium/high values. Moreover, a very high latent heat of fusion and a medium/low melting temperature range were selected in both the RTi and RTe cases. An almost constant peak melting temperature was observed for the few solutions with PCM2 (RTi cases only), that is 24.6 °C in Palermo and 24.3 °C in Turin, together with a medium melting temperature range, medium/low latent heat of fusion and low thermal conductivity. When the PCM cannot melt and freeze completely, the latent heat of fusion does not need to be increased [79]. Moreover, the maximisation of the latent heat of fusion can be considered as an indicator of how effectively a PCM undergoes melting and solidification cycles. However, as suggested in [80], it is possible that a latent heat of fusion of 230 kJ/kg would have been optimal even when searching over a greater range of variation. 4.3.2. Three-objective analyses The variable mappings on the Pareto fronts for the three-objective investigations are reported in Figs. 9 and 10 for the RTe and RTi case studies in Palermo, and in Figs. 11 and 12 for the RTe and RTi case studies in Turin. For the sake of conciseness, only the projection of the Pareto fronts on the (QH ,nd,QC ,nd ) plane is reported. In the three-objective case studies, the Pareto fronts resulted to be clustered according to the window type, which is in agreement with the results of [23]. Unlike the two-objective analyses, all the window types were selected. In the same way, all the insulation and internal lining materials were used. In Palermo, window type 0 (air-filled DGU) was only chosen for the solutions in the E group. The group of solutions that mounted window type 1 (air-filled DGU with a low-e coating on face 3)

Fig. 10. Mapping of the variables on the Pareto fronts for the three-objective analyses in Palermo, the RTi cases.

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Fig. 11. Mapping of the variables on the Pareto fronts for the three-objective analyses in Turin, the RTe cases.

need, many solutions were also characterised by the simultaneous presence of both PCMs. In Turin, unlike in the two-objective optimisations, solutions characterised by PCM2 or both PCMs were selected more often than solutions with only PCM1. Even though the Pareto front spanned a greater variation of heating energy needs, solutions with both PCMs tended to be selected to simultaneously minimise both

needs. As far as the PCM selection is concerned, PCM1 was generally preferred in Palermo over PCM2. Even though the Pareto front spanned a greater variation of cooling energy needs, the adoption of PCM, compared to the solutions without PCM, mainly resulted in reducing the heating energy needs. However, when reducing the cooling energy

Fig. 12. Mapping of the variables on the Pareto fronts for the three-objective analyses in Turin, the RTi cases.

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selected for both PCMs, and PCM2 was positioned closer to the internal environment. Only 1.0 cm was selected for PCM2 in Turin, and the position of the two PCMs was inverted. Different internal lining materials were also chosen (clay plaster in Palermo and thermo-plaster in Turin). Solution B (minimum global cost) was characterised by EPS insulation (i.e. the cheapest material), lime and gypsum plaster (RTi case) and no PCM. A U-value equal to the upper bound (i.e. the maximum value, according to the national standard) was selected for the RTe cases, whereas a U-value equal to the lower bound was chosen for the RTi cases. Solution C (minimum heating energy needs) in the RTe case in Palermo was characterised by window type 1, a U-value of 0.15 W/ (m2 K), aerogel insulation and a great thickness of both PCM1 and PCM2. In Turin, the main differences were the selection of window type 7, the absence of PCM2 and a lower peak melting temperature for PCM1; this solution was almost identical to the corresponding solution A. In the RTi cases, solution C was characterised by the lowest U-value, aerogel insulation and 4.0 cm of only PCM1. However, different internal lining materials, peak melting temperatures of PCM1 and window types were selected in Palermo and Turin. Solution D (minimum cooling energy needs) was characterised by the window type with the lowest g-value for each location and a great thickness of both PCMs. In the RTe cases, it was also characterised by the highest U-value allowed for the wall, and PCM2 was placed in the outermost position with respect to PCM1. In the RTi cases, the highest U-value was still selected in Palermo, whereas the lowest U-value was chosen in Turin. Thermo-plaster was selected as internal lining material in both locations, and PCM1 was placed in the outermost position with respect to PCM2. Solution E (minimum investment cost) was characterised by the cheapest materials; the cheapest window type, the maximum allowed U-value, EPS insulation, lime and gypsum plaster (RTi cases) and no PCM. This solution was identical to solution B (minimum global cost) in the RTe case in Turin, whereas a different window type was selected in Palermo and in the RTi case in Turin. However, in the latter case, there was no difference, in terms of price, between the window types selected for solutions B and E. It should be mentioned that, due to the stochastic nature of genetic algorithms, it cannot be guaranteed that the true extreme solutions are found. However, the information obtained from the analyses of the Pareto front could allow the properties of the real extreme solutions to

the heating and cooling energy needs. The Pareto front for Palermo was characterised by an increasing PCM1 thickness in order to decrease the heating and cooling energy needs. In Turin, a large thickness of both PCMs was instead selected mainly in the RTe case, especially for the solutions placed in the nondominated set between heating and cooling energy needs, whereas an increasing thickness of PCM2 was observed in the RTi case in order to decrease the cooling energy needs. However, the investment costs drastically increased as the PCM thickness increased. With the hypothesised PCM price, these results suggest that PCM application is not feasible from an economic point of view for the analysed case studies. In a similar way to the two-objective analyses, the peak melting temperature of PCM1 in Palermo exhibited a tendency to increase as the layer’s thickness increased, especially in the RTe case. However, no clear relationship could be identified. The solutions with PCM2 were instead mostly characterised by a peak melting temperature at around 24.5 °C. The peak melting temperature of PCM1 in Turin did not show any clear trend, and varied more than in Palermo. Like Palermo, a uniform peak melting temperature of PCM2 of around 25 °C was found. Low values of the melting temperature range (around 1–1.5 °C) were prevalently selected for PCM1 in Palermo, especially for the RTi case. Higher values were selected for PCM2, and they spanned over a greater range of variation for the RTe case. Melting temperature ranges prevalently around 3–4 °C were selected for PCM1 in Turin, although a greater variability was observed than in Palermo. Lower values, mostly around 2.5 °C, tended to be selected for PCM2. High values of latent heat of fusion were selected for PCM1 in Palermo and for both PCMs in Turin, even though in the latter case the interquartile ranges were not very narrow. No clear trends were observed for the thermal conductivity, which appeared to vary quite randomly. The reason for this lack of a clear choice is investigated in Section 5.2.

4.4. Description of the extreme solutions The characteristics of the extreme solutions, in terms of search space, are reported in Fig. 13 and Table 10. Solution A (minimum primary energy consumption), in the RTe cases, was characterised by aerogel insulation and 4.0 cm of PCM1, with a melting temperature of 20.5 °C in Palermo and 16.0 °C in Turin, a low melting temperature range, a high latent heat of fusion and a high thermal conductivity. In the RTi cases, solution A was characterised by a U-value of 0.15 W/(m2 K) and EPS insulation. In Palermo, 4.0 cm was

Fig. 13. Extreme solutions.

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Table 10 Characteristics of the extreme solutions. Sol.

Window type

Insulation type

Plaster type

U-value

PCM1 properties

[W/(m2 K) ]

PCM2 properties

t1 [cm ]

Tp,1

ΔT1

L1

k1

[°C ]

[°C ]

⎡ kJ ⎤ ⎣ kg ⎦

W ⎡m K⎤ ⎣ ⎦

t2 [cm ]

Tp,2

ΔT2

L2

k2

[°C ]

[°C ]

⎡ kJ ⎤ ⎣ kg ⎦

⎡m K⎤ ⎣ ⎦

W

Palermo, RTe A DGU air, low-e(2) B DGU air, low-e(2) C DGU air, low-e(3) D DGU 90% Ar, sel. (2) E DGU air

Aerogel mats EPS Aerogel mats Aerogel mats EPS

N/A N/A N/A N/A N/A

0.21 0.45 0.15 0.43 0.45

4.0

20.5

1.5

200

0.75

4.0 4.0

22.5 22.5

1.0 1.0

220 220

0.80 0.85

3.0 3.0

24.0 24.0

6.5 2.5

180 190

0.45 0.35

Palermo, RTi A DGU B DGU C DGU D DGU E DGU

EPS EPS Aerogel mats Sheep wool EPS

Clay Lime and gypsum Clay Thermo-plaster Lime and gypsum

0.15 0.15 0.17 0.43 0.45

4.0

21.5

1.0

230

0.30

4.0

24.5

5.0

150

0.35

4.0 3.0

20.5 23.0

3.5 0.5

220 210

0.50 0.75

3.5

24.0

5.3

220

0.50

4.0

16.0

0.5

190

0.90

3.5 4.0

17.0 23.0

2.0 2.5

230 210

0.85 0.90

4.0

26.0

3.5

190

0.35

4.0

18.5

1.5

230

0.60

1.0

25.0

3.0

170

0.25

4.0 4.0

15.5 22.5

4.7 5.3

230 220

0.55 0.90

4.0

25.0

2.0

230

0.5

air, low-e(2) air, low-e(2) air, low-e(3) 90% Ar, sel. (2) air

Turin, A B C D E

RTe TGU 90% Ar, low-e(3,5) DGU 90% Ar, low-e(3) TGU 90% Ar, low-e(3,5) DGU 90% Ar, low-e(2) DGU 90% Ar, low-e(3)

Aerogel mats EPS Aerogel mats Rock wool EPS

N/A N/A N/A N/A N/A

0.15 0.30 0.15 0.29 0.30

Turin, A B C D E

RTi TGU 90% Ar, low-e(3,5) DGU 90% Ar, low-e(3) TGU 90% Ar, low-e(3,5) DGU 90% Ar, low-e(2) DGU 90% Ar, low-e(2)

EPS EPS Aerogel mats Rock wool EPS

Thermo-plaster Lime and gypsum Thermo-plaster Thermo-plaster Lime and gypsum

0.15 0.15 0.16 0.16 0.30

be derived (e.g. selecting a latent heat of fusion for PCM1 equal to the upper bound would allow the results to be improved slightly). Finally, with an added thickness for all the RTi solutions of up to 35 cm, a constraint on the overall wall thickness or floor surface reduction resulted to be desirable to avoid an excessively high added thickness; generally, the smaller the net floor area is, the lower the commercial value of the building. 5. Discussion In order to investigate the reasons for some of the choices—or lack of choices—of the optimisation algorithm, additional analyses were conducted. First, the temperature profiles of the buildings during representative weeks were plotted in order to provide a better understanding of the behaviour of the various solutions and of the reason behind the PCM choice. Subsequently, since it had not been possible to clearly determine the effects of thermal conductivity in the previous analyses, the mutual influence of the thermo-physical properties of PCM was also investigated. The selection of the objective functions and the influence of the efficiency of heating and cooling systems were also discussed, and some design guidelines for PCM selection and application were provided. 5.1. Temperature profiles of the extreme solutions In order to provide a better understanding of the behaviour of the various solutions and of the reasons behind the choice of the lowtemperature PCM in the Palermo climate, the internal air temperature profiles of significant weeks for the extreme solutions of the RTi cases are reported in Fig. 14 and compared with those of the pre-retrofit building (Tai,Ref ). During winter (week A), a significant increase in the night temperatures (when the heating system was turned off) was observed for all the retrofitted solutions, in comparison to the baseline. The highest temperature was reasonably found for solution C (min QH ,nd ). In this

Fig. 14. Temperature profiles of the extreme solutions for significant weeks in Palermo (RTi cases).

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temperature. The optimum primary energy consumption was a trade-off between the heating and cooling energy need results. However, the optimal thermal conductivity was closer to the optimum value for the heating energy needs, due to the higher primary energy share. From these analyses, it can be inferred that finding the optimal thermal conductivity is not a trivial task, due to both the complex non-linear shape of the objective space and to the need for a trade-off between heating and cooling. The mutual influence of the peak melting temperature and melting temperature range on building energy performance is shown in Fig. 16. Similar trends were observed for the RTe and RTi cases. Moreover, the results did not change beyond a melting temperature range of 5 °C. This can explain why the optimisation algorithm almost never selected solutions with melting temperature ranges close to the upper bound. As far as the energy need for heating is concerned, the minimum energy consumption resulted to be ensured with the lowest melting temperature range for peak melting temperatures in the optimal or sub-optimal range. However, as the peak melting temperature moved away from the optimal region, the melting temperature range corresponding to the minimum heating energy needs started to increase towards the upper bound. These results are in agreement with the findings of El Mankibi et al. [44]. Therefore, given the simultaneous optimality of the peak melting temperature, the best melting temperature range is the lowest possible. However, the lack of a clear trend towards the minimisation of ΔT among the GA solutions could be explained by considering that the variations in energy performance for different melting temperature ranges in most of the objective space was limited. As has already been seen in Fig. 15 (but which is more evident in Fig. 16), the objective space resulted to be divided into two separate regions which show different trends. A local minimum can be observed for peak melting temperatures of around 18.5 °C. This is in line with the literature, for which the optimal peak melting temperature should approximately be one or two degrees lower than the internal set-point

way, the smallest amount of energy was needed to bring the indoor air temperature back to the set-point, and less energy was required to maintain it, compared to the other solutions. During spring (week B), cooling energy was already needed. When the HVAC system was switched off at night (at 6:00 PM), the internal air temperature of solutions A (min EP ) and D (min QC ,nd ) dropped, whereas all the others rose. When night ventilation was activated (at 11:00 PM), all the considered cases dropped to the night ventilation set-point temperature, i.e. 24 °C. After two days of free running over the weekend, the solution characterised by the lowest QC ,nd showed an advantage, in terms of cooling, as it remained the lowest curve, and this was followed by the solution characterised by the lowest EP . During summer (week C), when the HVAC system was switched off at night, the internal air temperatures rose dramatically. Night ventilation allowed the temperature to be reduced, but the external conditions were such that its efficiency was severely reduced. Except for the night ventilation, the profiles were similar to those of the pre-retrofit building. This implies that the PCM was always liquid, and there was practically no difference between the solutions. During autumn (week D), when the pre-retrofit building would have started to need heating, all the solutions clearly showed higher temperatures and therefore no or low heating energy needs. However, there was a clear difference between the two solutions with lowest investment and global costs (solutions E and B, respectively), which had no PCM, and all the other solutions, whose temperature was approximately 1–1.5 °C higher. If the solution characterised by the lowest primary energy consumption is compared with those resulting from the three-objective optimisation analyses, it is evident that it provided the best compromise between summer and winter performances, as can also be inferred from the results in Table 9. 5.2. Mutual influence of the thermo-physical properties of the PCMs In order to investigate the effect of thermal conductivity on the optimality of the results in more detail, and to analyse the mutual influence between the thermal conductivity, the peak melting temperature and melting temperature range, a few parametric analyses were performed. The solutions belonging to the C group in Turin were used as a reference (Table 10). The abovementioned thermo-physical properties of PCM1 (the only PCM used in those solutions) were varied in pairs, while all the other properties were kept constant. The resulting values of the building energy needs for heating and cooling were plotted, and the points corresponding to the minimum energy value for each case were highlighted (red dots). The variation in primary energy consumption, considering the system efficiencies reported in Section 2.3.2, is also reported. No information on the influence of the thermophysical properties of PCM on the electricity demand was provided as it was practically negligible in these analyses. The mutual influence of the peak melting temperature and thermal conductivity on building energy performance is shown in Fig. 15. As far as the energy needs for heating is concerned, the thermal conductivity that ensured the minimum energy consumption was found over the exploration range in both the RTe and RTi cases. The optimal thermal conductivity resulted to be dependent on the peak melting temperature. Thermal conductivities equal to the lower bound ensured a slightly better performance outside the optimal ranges for the peak melting temperature. However, since the variation in QH ,nd for such temperatures was very limited, a randomness in the GA solutions can be expected, unless the optimal peak melting temperature is found. As for the energy needs for cooling, the optimal peak melting temperature was the highest over the investigated range (i.e. 23 °C). The best thermal conductivity corresponding to the optimal peak melting temperature did not match the best value for heating for either the RTe or RTi cases. Moreover, no region was observed where the influence of thermal conductivity was significant with respect to that of the peak melting

Fig. 15. Building energy requirements as a function of the peak melting temperature and thermal conductivity of PCM (Turin).

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5.3. Influence of the efficiency of heating and cooling systems Performing a direct optimisation search on the primary energy consumption implies setting the efficiency of the systems. Therefore, different system efficiencies would result in different Pareto fronts, each with its own set of design solutions. If an optimisation search is performed by simultaneously minimising each energy term, the performance of such Pareto solutions could be investigated for various combinations of system efficiencies. In the same way, if the investment costs are also minimised, the global costs could subsequently be estimated. It should be noted that, although a combined optimisation of the envelope and HVAC systems would be preferable to a sequential approach, the improvement was found to be small in consideration of the considerable increase in the computational run time [82]. Such a sequential search process was tested, and the primary energy consumption values associated with the Pareto fronts of the three-objective optimisation analyses were parametrically evaluated. Seasonal efficiencies, ranging from 0.75 to 0.95 for the heating system and from 2.5 to 4.5 for the cooling system, were considered. The minimum primary energy consumption was obviously obtained when the system efficiencies for both heating and cooling were maximised simultaneously. However, interesting considerations can be drawn regarding the identification of the bestperforming solutions on the Pareto fronts. The projections of the Pareto fronts on the (QH ,nd,QC ,nd ) plane are reported in the first row in Fig. 18 for Palermo and Turin, and the overall electricity consumption (due to artificial lighting, equipment and fan operation of the mechanical ventilation system) corresponding to each point is reported in a colour-coded scale. The circled points indicate those individuals that were found to provide the lowest primary energy consumption. The EP values are plotted in the second row as a function of the seasonal efficiencies of the heating and cooling systems for the best performing individuals (the circled ones). A single solution (solution 1 for both RTe and RTi cases) was found

Fig. 16. Building energy requirements as a function of the peak melting temperature and melting temperature range of PCM (Turin).

temperature [81,44]. However, the global minimum was found within another region, characterised by lower peak melting temperatures. The reason for the presence of these two regions can be explained considering that the system only operates during daytime. As the internal air temperatures drop at night, a PCM melting temperature that reduces the difference between air and the set-point temperatures when the heating system is activated in the morning allows more significant energy savings to be made than a melting temperature tuned for diurnal energy savings. From this result, it could be inferred that, for the investigated case studies, two “low temperature” PCMs, characterised by an optimal (global minimum) and a sub-optimal (local minimum) peak melting temperature, could act together in the same season, thereby increasing the number of PCMs that could simultaneously be useful. However, the location of these PCM layers within the walls would influence their optimal peak melting temperature as well as their efficiency. Therefore, the exploitation of the latent heat of fusion of additional PCM layers could be limited, with the result that their choice might not be optimal in economic terms. The mutual influence of the thermal conductivity and melting temperature range on the building energy performance is shown in Fig. 17. A low thermal conductivity was found to lead to higher heating energy needs for a melting temperature range of up to 4 °C. Very low melting temperature ranges were again found to ensure the best energy performance, whereas the thermal conductivity was contrasted among the energy targets. To conclude, the peak melting temperature, the melting temperature range and thermal conductivity resulted to be closely interconnected. Finding the optimal thermal conductivity has proven to be particularly difficult when two energy objectives are simultaneously minimised. As can be confirmed from the box plots of the two-objective optimisation analyses (Fig. 6), convergence towards an optimal range is easier when primary energy consumption is addressed on its own.

Fig. 17. Building energy requirements as a function of the melting temperature range and thermal conductivity of PCM (Turin).

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Fig. 18. Selection of the best performing individuals, in terms of EP , from the three-objective optimisations.

5.4. Design guidelines

to guarantee the lowest value of EP in Turin for each combination of system efficiencies (region 1, corresponding to the whole system efficiency space). The lowest EP for the RTe case was found for the solution characterised by the lowest heating energy needs. The best performance for the RTi case could instead be guaranteed by a trade-off solution between the heating and cooling energy needs. For the analysed case studies, electricity use was the main contributor to the primary energy consumption in both Turin and, to an even greater extent, in Palermo. Since the electricity demand in the RTe case was quite homogeneous, the selection of the best performing individual was driven by the heating energy needs. However, in the RTi case, the best individual, in terms of EP , was characterised by the lowest electricity demand among the group of solutions with the lowest heating energy needs. In the case of Palermo, two solutions were identified as the best performing individuals for the RTe retrofitting option, on the basis of the trade-off between system efficiencies. A solution with moderately low cooling (and heating) energy needs and the lowest electricity demand in the nearby region was found to ensure the lowest primary energy consumption for low SEER values (solution 2 in the objective space and the corresponding region 2 in the system efficiency space). The solution which guaranteed the lowest heating energy needs, together with a low electricity demand, was found to perform better for improved system efficiencies (solution 1 in the objective space and the corresponding region 1 in the system efficiency space). Some additional comments on the shares of the electricity demand are provided. The greatest amount was due to the equipment, but this was a constant value. The energy needs for artificial lighting were a function of the visible transmission coefficient of the selected windows. This explains why only window types 1 and 2 were selected in Palermo for the two-objective optimisation analyses; those windows were characterised by the best trade-off between a high visible transmission coefficient and good thermal properties. As for the electricity use for the night ventilation fans, only a small variability was found over the Pareto fronts, especially in Turin. Understandably, no contrast was observed with the cooling energy needs (i.e. a high electricity use for night ventilation fans was associated with high cooling energy needs, and vice versa).

Considering the results of the optimisation analyses and the subsequent investigations, it is possible to offer a few design guidelines for the application of PCMs to the energy retrofitting of office buildings. However, unless the PCM prices are significantly reduced, their application to the cases under investigation would not be cost-effective. Nevertheless, sub-optimal solutions (from an economic point of view) with a limited amount of PCM were found.

• Regardless of whether the retrofitting is performed on the internal •

•

• •

948

or external side of the walls, the PCM should be placed at the closest position to the internal environment. However, the innermost position is preferable (in agreement with the findings of several authors [83,84,34,79,44]). In cooling-dominated climates with mild winters (such as Palermo), PCM can be effective in improving the heating performance of the building. In heating-dominated climates with mild summers (such as Turin), PCM can be effective in improving the cooling performance of the building. However, in the investigated cases, a peak melting temperature suitable for winter application was found to be the best option for reducing the overall primary energy consumption, regardless of the climate. It should be recalled that this result was found under the hypotheses of the investigated problems (e.g. building systems and their operation). When searching for commercial PCMs with thermo-physical properties close to the optimised (ideal) values, priority should be given to the peak melting temperature and latent heat of fusion, as these properties have resulted be the most significant in deciding whether a solution belongs to the Pareto front or not (as they generally assumed constant or almost constant values). Whenever the application of PCM can be truly effective in reducing the building energy consumption, a high latent heat of fusion is highly advisable. When operation of the system does not imply a constant set-point temperature, the peak melting temperature and thermal conductivity should be optimised simultaneously. In other cases, selecting an appropriate peak melting temperature from among the PCM thermo-physical properties has the greatest implications on the

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achievable energy savings.

• When a PCM with an optimal or sub-optimal peak melting temperature is chosen, a low melting temperature range is preferable. • Increasing the thickness of PCM with optimised properties over the

•

investigated range of variation can often (in consideration of the location and retrofit type) imply a linear reduction of the primary energy consumption.

•

These strategies for PCM selection and application should be coupled with additional energy-saving measures. A low U-value was found to be particularly important in both locations for the case of a retrofitting intervention on the internal side in order to minimise both the primary energy consumption and the global costs. The selection of the windows should also be performed accurately considering the trade-off between the energy needs for space heating and cooling, as well as the electricity demand for daylighting. The use of aerogel insulation, in the case of retrofitting on the external side, was found to reduce the primary energy consumption as a result of a reduced shading in winter, but higher investment costs—and therefore a higher global costs—would be induced by such a choice. Therefore, changing the position of the original windows while adopting cheaper insulation materials should be taken into consideration to reduce both the heating energy needs and costs.

•

6. Conclusions The application of phase change materials for the energy retrofitting of office buildings has been investigated in the present paper by means of multi-objective optimisation analyses. An archetype office building, built in Italy during the 1946–1970 period and located in the climates of Palermo and Turin, was chosen as a case study. Two retrofitting options on the opaque envelope components were considered; intervention on either the external or internal side of the walls (RTe and RTi, respectively). The optimal layer position was investigated, and a maximum of two PCM materials were adopted in the retrofitted solutions. The optimisation problem was addressed by selecting two different sets of objective functions. First, the primary energy consumption and global costs were minimised. Secondly, the optimisations were run to minimise the building energy needs for heating and cooling and the investment cost. The analyses were carried out by coupling a Python implementation of the NSGA-II algorithm with a building energy model that had been developed in EnergyPlus. Since multi-objective optimisations do not generally have a single solution, but result in a series of trade-off solutions, special attention was paid to the post-optimisation analyses of the results. Rather than emphasising the objective values that could be reached by means of the optimisation procedure, the study focused on the variable values that led to the optimal solutions. In this way, the multi-objective optimisation was used as a tool to gain knowledge on specific problems. This process of knowledge extraction was carried out by means of statistical and visualisation tools. Then, to better investigate the reason behind the outcomes of the search processes, the internal air temperature profiles of interesting solutions during representative weeks were also investigated, and the mutual influence of the thermo-physical properties of PCM was explored. Finally, the selection of the objective functions and the influence of the efficiency of the heating and cooling systems were discussed, and some design guidelines for PCM selection and application were provided. The main findings can be summarised as follows:

•

• •

•

•

• In all the investigated cases, retrofitting on the internal side of the •

external walls (RTi) allowed the best energy performance to be achieved with the lowest costs. However, a constraint on the overall wall thickness or on the floor surface reduction resulted to be desirable to avoid an excessively high added thickness. All the solutions of the two-objective investigations in the case of

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retrofitting on the internal side were characterised by a constant Uvalue equal to the lower bound, i.e. 0.15 W/(m2 K). Regardless of the type and number of PCM layers, the PCM in the RTe cases tended to be placed between the existing wall and the external insulation, whereas it was placed close to the internal environment in the RTi cases. In the two-objective investigations, PCM1 (lower peak melting temperature than 23 °C) was preferred over PCM2 (greater peak melting temperature than 23 °C) for both climates. In Palermo, which has a cooling-dominated climate, PCM1 was found to have a stabilising effect on the internal temperature for a longer period of time, because the climatic conditions in winter, and especially during the mid-seasons, are mild. Moreover, the high temperatures in summer tended to be too extreme, even for PCM2 to work effectively. On the other hand, PCM2 was prevalently selected in the heating-dominated climate of Turin in the three-objective investigations, as it could work more effectively there than in Palermo as a result of the milder summer conditions. In the two-objective analyses, the Pareto front was characterised by an increasing PCM thickness in order to decrease the primary energy consumption (hence increasing the global costs). However, the variation in primary energy consumption between the best and worst solution for each Pareto front was very small, ranging from 2 kWh/(m2 y) to 5 kWh/(m2 y). The difference, in terms of global costs, was much more significant. Moreover, PCM was never selected for the solutions that were characterised by the minimum global costs. For the analysed case studies and with the hypothesised PCM price, these results suggest that the PCMs are not feasible from an economic point of view. In Palermo, in the three-objective analyses, the peak melting temperature of PCM1 was found to increase as the PCM thickness increased. In the two-objective analyses, in case of retrofit on the external side, this behaviour was found to be described by a specific relationship (Tp,1 = 35.8 t10.15), whereas no clear dependency was observed in the RTi case. When PCM2 was used, its peak melting temperature varied over a very small range among the non-dominated solutions, which ranged from 24 °C to 25 °C. A very high latent heat of fusion of PCM1 was selected in all the cases, whereas that of PCM2 tended to be maximised only in the three-objective analyses for Turin, where PCM2 resulted to be more effective. In general, the latent heat of fusion had a relevant influence on the results, and its maximisation could be considered as an indicator of the PCM efficiency. In the case of retrofitting on the external side, aerogel was selected when the heating energy needs were minimised, especially in Turin. Owing to its low thermal conductivity, low U-values could be obtained with a limited thickness. This has an important implication on shading; the lower the added thickness, the higher the available solar gains. When the mutual influence of the thermo-physical properties of the PCM was analysed, the objective space resulted to be divided into two separate regions which showed different trends: this could be explained by considering that the system only operated during daytime. As the internal air temperatures dropped at night, a PCM melting temperature that reduced the difference between the air and set-point temperatures when the heating system was turned on in the morning allowed more significant energy savings to be obtained than for a melting temperature tuned to diurnal energy savings. Therefore, an optimisation procedure that searches for the optimal thermo-physical properties of PCMs could be particularly useful when the operation of the system implies a non-trivial solution. Considering an optimal peak melting temperature, the optimal melting temperature range was found to be the lowest possible. Moreover, beyond a melting temperature range of 5 °C, the energy needs for heating and cooling were found to remain unchanged.

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• The thermal conductivity that ensured the minimum energy needs •

•

optimisation criteria, such as thermal and visual comfort or environmental impact, would also be of interest when a multi-objective optimisation is performed as a means of knowledge extraction. However, the greater the number of optimisation objectives, the longer the computational time, and the more difficult the convergence to the true Pareto front and the analysis of the results are. On the other hand, when there is a need to minimise or maximise one or more functions, because the main interest is on the results in terms of objective space, selecting the lowest number of fitness functions allows the optimisation algorithm to be more efficient. As future work, the proposed methodology will be further tested to investigate optimal design/retrofit choices involving both opaque and transparent responsive envelope components. Moreover, investigations on additional optimisation objectives, such as the environmental impact, would be of interest to obtain information on the overall energy use, which is a critical aspect in the application of PCMs. Finally, the post-optimisation process will be investigated in more depth by using data mining techniques to explore the associations among variables, to extract decision rules, to group solutions according to interesting features and to build estimation/prediction models.

for heating was found within the exploration range (0.15–0.9 W/ (m K)). However, the thermal conductivity values that ensured the minimum energy needs for heating and cooling were not the same for the same peak melting temperature. Overall, the peak melting temperature, melting temperature range and thermal conductivity resulted to be closely interconnected. Finding the optimal thermal conductivity proved to be particularly difficult when two energy objectives were minimised simultaneously. Convergence towards an optimal range was easier when only primary energy consumption was addressed. When evaluating the primary energy consumption associated with the Pareto solutions of the three-objective optimisation analyses through a sequential search process, a single individual was identified for each case as the best solution in Turin, regardless of the combination of system efficiencies. Two solutions were instead identified as the best performing individuals, in terms of primary energy consumption, for the RTe retrofit option in Palermo, on the basis of the trade-off between system efficiencies.

Overall, a robust methodology that can help designers make an informed choice of the final retrofitting solutions has been provided. As valuable and non-trivial information can be obtained through postoptimisation analyses, exploring the properties of the non-dominated solutions resulting from a multi-objective search process has in fact proved to be a promising approach that can be applied to a wide variety of applications. Moreover, additional functions to investigate other

Acknowledgements The authors are grateful to Tomás Méndez Echenagucia for having granted the permission to use his implementation of the NSGA-II optimisation algorithm.

Appendix A. PCM modelling The specific heat-temperature curve of the PCM was described by two half-Gaussian curves, according to Eq. (A.1) [85]. Since the shape of the enthalpy-temperature curve was found to influence the optimum phase change temperature [84], a non-linear function with a phase change that occurs over a temperature range was chosen, due to its higher representativeness of practical PCMs. 2

Tp− T ⎞ ⎧ −⎛ ⎪ cs + (cm−cs )·e ⎝ ws ⎠ if T ⩽ Tp c (T ) = Tp− T 2 ⎨ ⎞ −⎛ ⎪ cl + (cm−cl )·e ⎝ wl ⎠ if T > Tp ⎩

(A.1)

In order to fully describe the curve in Eq. (A.1) and which is represented in Fig. 19, the following variables are needed: peak melting temperature, Tp ; specific heat in solid state, cs ; specific heat in liquid state, cl ; specific heat at the peak melting temperature, cm ; curve width in solid state, ws ; and curve width in liquid state, wl . However, in order to reduce the number of variables, the problem was simplified by searching for the peak melting temperature, Tp , the melting temperature range, ΔT , and the latent heat of fusion, L. Moreover, the PCM was modelled considering constant thermal conductivity, k. In order to find the relationship between the optimisation variables and the original parameters of Eq. (A.1), the following simplification was considered: cs = cl (later referred to as c). The latent heat of fusion can easily be evaluated with this assumption. The latent heat of fusion of a PCM is represented by the area beneath the peak of the c (T ) curve (grey area in Fig. 19) and can be calculated by referring to the Gaussian integral, which can be generalised as +∞

∫−∞

2

e−αx dx =

π . α

Therefore, it is possible to write

Fig. 19. Specific heat-temperature curve.

950

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Fig. 20. Constraint on the melting temperature range.

L=

T 2

0

∫−∞ (cm−cs )e−( w ) dx + ∫0

∞

s

T 2

(cm−cl ) e−( wl ) dx ,

which results in

L=

π (cm−c )(ws + wl ). 2

(A.2)

However, considering the exact solution of the latent heat, the melting temperature range is (−∞,+∞) . To be able to identify a finite melting temperature range, the intersection between the c (T ) curve and a constant can be considered. The distance between cs (or cl ) and this arbitrary value was defined as Δc (Fig. 19). In this way, the lower bound of the melting temperature range is obtained as

T1 = Tp−ws ln

cm−cs . Δc

(A.3)

Similarly, the upper bound of the melting temperature range is

T2 = Tp + wl ln

cm−cl . Δc

(A.4)

The melting temperature range is obtained by summing Eqs. (A.3) and (A.4). As ΔT2 = T2−Tp , and r = ΔT2/ΔT , ws and wl can be defined as

wl =

r·ΔT c −c ln mΔc

and ws =

(1−r )·ΔT ln

cm − c Δc

.

which are expressed as functions of cm . Solving Eq. (A.2) for cm , we obtain

cm = c +

2L , π (ws + wl )

whose solution can be obtained iteratively. With this formulation, r should be regarded as a new variable. However, since r can be expected to have less influence on the optimisation results than the other PCM variables, a fixed r of 0.25 was chosen as a reasonable value [84]. The specific heats in solid and liquid states were assumed fixed at 2000 J/(kg K). These variables were not included among the search variables because the optimisation algorithm could be expected to converge to the upper bound. Moreover, finding a PCM that respected all the six optimised parameters might be impossible. Finally, a Δc equal to 0.1 kJ/(kg K) was considered. A.1. Constraints Small melting temperature ranges occur in pure materials, whose latent heat of fusion is higher than non-pure PCMs. Therefore, not all the combinations of melting temperature range and latent heat of fusion may be feasible within their domains. The relation between melting temperature range and latent heat of fusion was analysed for commercial PCMs [86]. The following linear constraint was added on the basis of Fig. 20:

ΔT ⩽ (300−L)/15.

(A.5)

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