Design optimisation of perforated solar façades in order to balance daylighting with thermal performance

ARQUITECTURA, PATRIMONIO Y SOSTENIBILIDAD: ACÚSTICA, ILUMINACIÓN, ÓPTICA Y ENERGÍA ARCHITECTURE, HERITAGE AND SUSTAINABILITY: ACOUSTICS, LIGHTING, OPTICS AND ENERGY TEP 130 https://grupo.us.es/grupotep130/es/ Design optimisation of perforated solar façades in order to balance daylighting with thermal performance Doris A. Chi, David Moreno, and Jaime Navarro This is an Accepted Manuscript of an article published by Elsevier: Building and Environment, Volume 125, 2017, Pages 383-400 ISSN 03060-1323 http://dx.doi.org/10.1016/j.buildenv.2017.09.007 Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 2 Authors’ names and affiliations: Doris A. Chi, David Moreno, and Jaime Navarro Instituto Universitario de Arquitectura y Ciencias de la Construcción, Universidad de Sevilla, Spain Corresponding author: Doris A. Chi, Instituto Universitario de Arquitectura y Ciencias de la Construcción, Universidad de Sevilla, Spain Email: abig[email protected]om Abstract On fully-glazed building façades perforated solar screens (PSS) are often used as an outer skin in order to reduce energy consumption and to solve issues such as visual appearance. However, not only must PSS control solar radiation but they must also provide adequate daylight levels, thus requiring a balanced solution. Currently, daylighting simulation software enables us to perform efficient daylight analysis of spaces with PSS. Notwithstanding this, current energy simulation software such as EnergyPlus cannot deal well with such geometry directly, making the thermal evaluation of PSS an infeasible task. This paper presents a methodology for achieving an integrated analysis of daylighting and energy consumption of spaces with PSS during the design stage. Such methodology provides daylight analysis through DIVA, and thermal analysis through EnergyPlus via DIVA/Grasshopper/Archsim. The aim is to optimise the dual performance of a balanced PSS solution through controlling its perforation percentage, matrix and shape, by using the orthogonal arrays (DOA) statistical method. DOA method is efficient in reducing the number of simulations derived from the combination of the aforementioned variables, and in identifying the optimal PSS configuration. In comparison to a non-optimised façade located in Seville, Spain, the predicted optimal PSS achieved a 50% increase in the actual daylit area and a 55% reduction in the total energy demand. Keywords: daylight availability; energy consumption; optimal design; orthogonal arrays; perforated solar screens; simulation tools. 1. Introduction The building envelope plays an important role in controlling and/or admitting the various elements of the external environment. The building envelope can achieve about 80% of an environmental solution, creating an efficient building that interacts with its surrounding environment [1]. Present concerns with energy conservation have induced extensive studies regarding the façade’s performance with the environment. There are numerous examples of buildings which have ignored their climatic conditions by extending the use of highly glazed façades in order for them to be airy, light and transparent. However, as there is a risk of high energy demand in order to maintain indoor thermal comfort [2] their energy efficiency has come into question. Solar shading has, therefore, been an important step in energy saving control for buildings. Shading affects the energy use for lighting, heating and cooling; it also reduces yearly solar gains Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 3 originating from solar radiation, as well as modifying thermal exchanges through the glazed building envelope and, moreover, it influences daylight levels within a building [3]. Perforated solar screens (PSS) are a type of shading device that have gained popularity with the shift from traditional to modern architectural styles [4,5]. Generally, PSS are flat, opaque, perforated panels forming a double skin for fully-glazed building façades. The organisation of their perforations filters out direct incident sunlight, which is prevented from directly penetrating into spaces while still allowing users to view the exterior. The opaque parts of the screen reflect sunlight and act as solar control systems [6,7]. For example, Figure 1 illustrates a façade with a PSS. Figure 1. Rendering of a PSS example. 1.1 The issue of applying the building performance simulation tools Several works have been devoted to the study of the thermal effects of fixed shading systems, such as louvres, overhangs and vertical fins [8,9] using EnergyPlus, TRNSYS and EES software for energy simulations [3]. A few works have reviewed the impact of perforated screens on reducing air conditioning and overheating, but these were developed for desert climates and for studying single design variables such as perforation range [10,11]. The impact of perforated façades on daylighting has, apparently, not been widely studied. There are few detailed studies regarding their effects on indoor illuminances by means of measurements on scale models [6,12,13] and computer simulations with Daysim and DIVA software [1,14,15]. Furthermore, these works addressed single design variables, such as shape [1,16], perforation rate and orientation [14] independently of each other. A limited number of studies have addressed the balance between providing daylight and reducing solar gains derived from using solar control systems. Only a few relevant references exist [17,18]. This lack of studies addressing the integration of the daylighting and energy performances of PSS is due to the fact that such studies are complex tasks since these domains interact at many levels and simulation tools usually specialise in one domain only. The combination, therefore, of daylight and energy performance needs to employ different software packages in order to perform such detailed calculations. Moreover, to obtain accurate results building environmental performance simulation tools require a considerable amount of time and iterations. In addition, PSS usually present complex geometries, making them difficult to model in the current energy performance simulation tools and thus the design process becomes more sophisticated [19]. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 4 EnergyPlus, for example, is a whole building energy simulation program used to model the energy consumption in buildings – for heating, cooling, ventilation, lighting and other loads [20]. This software is well-suited to assessing the energy performance of conventional building systems or whole buildings, yet it is questionable whether such a tool can describe accurately the energy transfer phenomena that occur in complex geometries [21]. Furthermore, EnergyPlus has shown significant shortcomings in predicting the daylight available in a space, especially as the distance from the façade increases [22]. EnergyPlus utilizes the split flux method to model the interior reflections of light by dividing the luminous flux into two components; then, each split component is reflected by an average weighted reflectance of the surfaces above and below the window [20]. This kind of calculation often results in substantial inaccuracies that have direct consequences on electric lighting use intensity [23]. In order to overcome the simulation tools’ limitations, some authors have developed methods using recent advances in software and/or in integrating the use of various software packages. Lagios, Niemasz and Reinhart [24] linked Rhinoceros/Grasshopper to Radiance/Daysim in order to evaluate key design parameters, such as window size and material descriptions. Azadeh [25] proposed a process for utilising daylighting and energy analysis software for optimising the performance of a sun-shading screen. To further understand the available daylight in the test space, a climate-based metric was calculated in DIVA. In order to model the effect of the screen on the energy consumption, the screen's hourly shading coefficient was calculated. An electric lighting schedule for the year was then generated and loaded into Design Builder for thermal simulations. González and Fiorito [26] integrated parametric design with performance simulation tools. They used Galapagos/Grasshopper to define randomly the set of tests and then used DIVA both to calculate daylight metrics and to create an artificial lighting schedule. Finally, they used the DIVA thermal component to calculate the energy consumption and CO2 emissions. Trubiano et al. [27] integrated the use of Grasshopper with Radiance and EnergyPlus through Matlab. Adopting genetic algorithms and a single objective function, they developed an evolutionary optimisation script to demonstrate the possibility of generating the optimal shape of atriums. Lobaccaro et al. [28] applied a similar method for optimising the geometry of a building in order to maximise the envelope’s annual exposure to solar radiation. David et al. [29] applied the combination of daylight and thermal analysis for assessing solar shade efficiency. In order to rate the performance of different typologies of external overhangs, they used Radiance and EnergyPlus to calculate the shading coefficient, cooling energy demand, daylight autonomy, sun patch index and useful daylight illuminance. 1.2 The design optimisation problem The optimisation problem, related to the design of external shadings in an office building, is linked to the time required for performing daylight simulations. This has been demonstrated to be about 35 times longer than that required for performing a full thermal dynamic analysis. Consequently, the feasibility of conducting an optimisation process for large areas or complex geometries is limited, especially when time is a constraint [26]. Furthermore, PSS design requires a wide variety of variables to be taken into consideration, so a comprehensive study of possible variable combinations requires a large amount of different models, simulations and time, something which is difficult to manage. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 5 The Design of Experiments using Orthogonal Arrays (DOA) statistical method can simplify the interrelated study of a large number of variables, reducing the number of experiments/simulations and obtaining the maximum information which may be of use in PSS design [30]. The DOA method has been used efficiently in different fields of science, contributing valid conclusions and optimising processes [31]. It has been used to optimise building shape design in order to achieve energy savings [32] and to reduce construction costs [33]. It has also been used to optimise some window design parameters aimed at improving daylighting and solar control [34] and at maximising energy savings [35]. Chi, et al. [36] propose a methodology for applying orthogonal arrays (OA) to optimise the perforation percentage, shape, matrix and orientation of perforated screens, reducing the number of simulations from 256 to 16 and obtaining the best combination of variables for improving daylighting. 1.3 Aims of current research As the energy demand of a building is greatly influenced by the levels of daylight and solar radiation entering through the perforations, enhancing daylighting and reducing solar gains are important considerations in PSS design. This paper aims to study the simultaneous taking into account of both daylighting and thermal performance of PSS to achieve the annual overall balanced solution. A workflow is proposed to integrate the use of daylighting and energy simulation packages to characterise and quantify the global performance of PSS. As, these studies are often complex and time-consuming due to a large number of simulations, this approach uses the DOA method to predict the optimal design derived from the combination of different PSS design variables such as perforation percentage (PP), matrix (M) and shape (S). The optimised PSS aims to find the right balance between the daylight availability and the reduction of the total energy consumption (lighting plus heating and cooling) for a typical office space in Seville, Spain. 2. Methodology The proposed methodology consists of four main phases. First, the DOA method is applied to study simultaneously the interrelation of the PSS design variables and to reduce the number of study models. The second stage includes the parameters, performance metrics and software used for daylighting evaluation. The next phase includes an energy consumption calculation process by using different computer programs. Finally, a balanced solution, where the daylighting and thermal performance are considered, is identified. The required steps are summarised in Figure 2 and developed in more detail in the case study. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 6 Figure 2. Workflow for daylighting and energy analysis of complex geometries. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 7 2.1 Case study The optimal PSS configuration for an open-plan office space located in Seville, Spain is investigated. A reference model measuring 7 m × 7 m and 3 m in height was modelled by using Rhinoceros software. It is a space that is sidelit through a fully-glazed, south-facing façade. Table 1 summarizes the model characteristics and materials that are set up according to the study domain. Namely, visible reflectances for daylighting calculations [37]; solar reflectances for annual solar radiation calculations [37]; and thermal properties for energy simulations [38]. These values remain fixed in all simulations in order to dismiss their effects on results. Table 1. Characteristics of the internal model surfaces, PSS and glazing. Wall Visible reflectance 50% Solar reflectance 50% Material Adiabatic Floor Visible reflectance 20% Solar reflectance 20% Material adiabatic Ceiling Visible reflectance 80% Solar reflectance 80% Material adiabatic Glazing Visible transmittance 78.1% Solar transmittance 60.4% Solar Heat Gain Coefficient (SHGC) 0.703 Thermal Transmittance (U-value) 2.785 W/m2K PSS Visible reflectance 90% Solar reflectance 90% Material White Paint finish 2.2 PSS design PSS are externally mounted at a distance of 0.05 m from the reference model’s fully-glazed façade (Figure 1). The PSS dimensions are 7 m wide × 3 m high; the thickness is not considered. Characteristics of the PSS material are summarised in Table 1. Three design variables that are usually determined at the conceptual design stage are selected to characterise and evaluate the PSS performance: (1) PP: Ratio of the total surface of the openings to the opaque surface. (2) M: Vertical × horizontal distribution of openings on the screen. The distance between openings for each matrix is of 0.25, 0.33, 0.50 and 1.00 m, respectively, measured from the centre and vertically and horizontally equidistant. (3) S: Four regular shapes are proposed. The different-shaped openings have the same opening area when M and PP are the same. Figure 3 shows the levels for each design variable, together with their nomenclature between Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 8 parentheses which is used to name the PSS derived from the combination of the variables. For example, a PSS with a PP 37.5%, M 9×21 and S circular is named 372CS, where S is referring to the south. The reference model is termed REF100S, where 100 is referring to WWR (window-to-wallratio) 100%. Figure 3. PSS design variables. 2.3 Orthogonal Array All combinations of the four levels of the factors produce 64 PSS configurations, that is to say, 64 computer simulations need testing in different computer programs in order to obtain a simultaneous evaluation of daylighting and solar gains. This implies an increase in the number and time of simulations which can be difficult to handle in practical situations. There is a need, therefore, to propose an effective strategy for addressing multiple performance criteria, finding close-to-optimal solutions in a short period of time and with the minimum number of simulations. To achieve this, the present paper uses the DOA method, validated in a previous study [36], in which some PSS design variables were analysed in terms of daylighting performance. The DOA method selects a representative fraction of all possible combinations of factors with the aim of distributing the experiments uniformly within the test range, accurately representing the overall situation [39]. The advantages of the DOA method are that the number of trials needed to complete the experiment is relatively small and the test results can be analysed through mean analysis (ANOM) and variance analysis (ANOVA). The method is highly efficient for arranging multi-factor experiments with optimal combination levels [40]. In DOA the experiment selection is OA-based, represented by a matrix which is expressed as LN (l)k, where L is OA, N the number of experiments, l the level of factors and k the number of factors or columns [30]. Many standard OAs have been tabulated for using DOA [39]. One of these arrays can be used directly for planning the simulation cases. It consist of three factors with four levels each: L16(43). The factors constitute the PSS design variables and the levels are the values of these variables, as summarised in Table 2. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 9 Table 2. Factors and levels of L16(43). Levels Factors 1 (PP) 2 (M) 3 (S) 1 50% 12x28 Circular 2 37.5% 9x21 Hexagonal 3 25% 6x14 Quadrangular 4 12.5% 3x7 Triangular L16(43) uses only a fraction of the possible 64 combinations of the three factors with four levels each (43=64 runs), reducing to 16 the number of PSS to be tested. Table 3 presents the 16 PSS configurations, which were obtained using a statistical analysis program [41]. Table 3. Simulations required in L16(43). Simulation PSS Factors 1 (PP) 2 (M) 3 (S) 1 501CS 1 (50%) 1 (12x28) 1 (Circular) 2 502HS 1 (50%) 2 (9x21) 2 (Hexagonal) 3 503QS 1 (50%) 3 (6x14) 3 (Quadrangular) 4 504TS 1 (50%) 4 (3x7) 4 (Triangular) 5 371HS 2 (37.5%) 1 (12x28) 2 (Hexagonal) 6 372CS 2 (37.5%) 2 (9x21) 1 (Circular) 7 373TS 2 (37.5%) 3 (6x14) 4 (Triangular) 8 374QS 2 (37.5%) 4 (3x7) 3 (Quadrangular) 9 251QS 3 (25%) 1 (12x28) 3 (Quadrangular) 10 252TS 3 (25%) 2 (9x21) 4 (Triangular) 11 253CS 3 (25%) 3 (6x14) 1 (Circular) 12 254HS 3 (25%) 4 (3x7) 2 (Hexagonal) 13 121TS 4 (12.5%) 1 (12x28) 4 (Triangular) 14 122QS 4 (12.5%) 2 (9x21) 3 (Quadrangular) 15 123HS 4 (12.5%) 3 (6x14) 2 (Hexagonal) 16 124CS 4 (12.5%) 4 (3x7) 1 (Circular) 2.4 Daylighting Simulation The aim of this stage is to investigate the daylighting performance of the PSS. The 16 daylighting simulations are performed with DIVA-for-Grasshopper [42]. DIVA is a highly-optimised daylighting and energy modelling plug-in for Rhinoceros. It comes with an enhanced user interface for Grasshopper, a graphical algorithm editor that enables designers with no formal scripting experience to generate parametric forms [43] rapidly. Grasshopper components [42] provide daylight analysis through Radiance/DAYSIM and thermal analysis through EnergyPlus/Archsim. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 16 Figure 9. Thermal model: a) 3D geometry, and b) Basic thermal behaviour. Table 7. Energy performance indicators SCannual Annual mean value of all SChourly values quantified at each PSS. TSRE Annual transmitted solar radiation energy, normalised by floor area (kWh/m2). Lighting energy consumption Total annual energy used on-site to supply the electric lighting system and normalised by floor area (kWh/m2). Cooling energy consumption Total annual energy used on-site to supply the cooling system and normalised by floor area (kWh/m2). Heating energy consumption Total annual energy used on-site to supply the heating system and normalised by floor area (kWh/m2). Total Energy Consumption Sum of the annual energy consumed for heating, cooling and artificial lighting and normalised by floor area (kWh/m2). 2.6 Balancing daylighting and thermal performance The ratio of the actual daylit area to the SCannual is counted as an index of both daylighting and solar shading in this study [34]. A high value of the actual daylit area corresponds to better daylighting performance. A lower SCannual value corresponds to better annual solar shading performance; thus, high values of this index represent a better integrated performance of solar shading and daylighting. 3. Results Table 8 and Figure 10 present the annual results of the 16 simulations. Figure 10a shows the percentages of the modified Daylight Availability and Figure 10b shows the annual energy used for lighting, cooling and heating, the SCannual and the TSRE. The index appears in both figures a and b to show the interrelation between the daylighting and thermal performance. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 17 Table 8. Annual results of simulations. Simulation PSS Non-daylit area (%) Actual Partially daylit area (%) Actual Daylit area (%) Overlit area (%) Annual Solar Radiation on Façade (kWh/m2) SCannual TSRE (kWh/m2) Lighting energy (kWh/m2) Cooling energy (kWh/m2) Heating energy (kWh/m2) Index - REF100S 0 0 0 100 1147.04 1.00 289.29 9.21 248.62 4.66 0.00 1 501CS 0 0 43 57 726.78 0.70 154.28 13.39 138.71 1.50 0.61 2 502HS 0 0 42 58 646.41 0.59 140.27 21.24 134.11 1.27 0.72 3 503QS 0 0 43 57 707.90 0.68 150.91 21.96 143.11 1.55 0.63 4 504TS 0 0 45 55 669.78 0.60 145.81 13.07 131.98 1.34 0.75 5 371HS 0 0 49 51 596.91 0.60 127.75 23.59 126.25 1.05 0.82 6 372CS 0 0 49 51 515.53 0.48 113.66 24.78 116.67 0.81 1.02 7 373TS 0 0 47 53 532.78 0.51 116.68 16.89 112.62 0.79 0.92 8 374QS 0 0 50 50 471.36 0.42 106.19 14.92 103.81 0.64 1.20 9 251QS 0 36 23 41 381.95 0.37 86.56 26.24 98.85 0.54 0.63 10 252TS 0 34 23 43 392.84 0.39 88.37 25.82 99.85 0.56 0.59 11 253CS 0 35 20 44 338.36 0.31 79.11 26.35 94.00 0.50 0.66 12 254HS 0 31 29 40 333.27 0.31 78.10 26.30 93.24 0.49 0.94 13 121TS 50 15 5 31 154.61 0.13 43.43 27.26 72.69 0.56 0.35 14 122QS 47 23 8 22 191.23 0.19 49.58 27.23 76.35 0.49 0.43 15 123HS 48 24 13 14 190.97 0.19 49.42 27.44 76.45 0.51 0.70 16 124CS 44 16 13 27 171.06 0.16 46.03 27.42 74.40 0.55 0.82 Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 18 Figure 10. Annual Results in L16(43). Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 19 3.1 OA analysis The ANOM and ANOVA of the OA L16(43) are used to predict the optimal design derived from the combination of the three design variables. The optimal levels, therefore, must increase the area lit with useful illuminance for occupants and reduce the area lit with excessive illuminance that can be associated with glare and thermal discomfort. The ‘actual daylit area’ must be maximised and the ‘non-daylit’, ‘actual partially daylit’ and ‘overlit’ areas must be minimised. Furthermore, the optimal levels must maintain electrical energy consumption for lighting, cooling and heating as low as possible. As it represents the best integrated performance of daylighting and solar shading, the index must be maximised. Table 9 summarises the ANOVA results of L16(43), where the statistical significance to 5% is of PP for all indicators and M for the index. The sum of squares (SS) indicates the relative importance of each factor and is ordered as follows: PP>M>S for all indicators (except for the overlit indicator that follows the order PP>S>M). Table 9. ANOVA of L16(43) when α=0.05 Indicator Factor GL SS F p Significance Nondaylit area 1 (PP) 3 6751.44 1467.03 0.00 * 2 (M) 3 4.60 1.00 0.46 3 (S) 3 4.60 1.00 0.46 Residual error 6 9.20 Total 15 6769.85 ‘actual’ partially daylit area 1 (PP) 3 3296.90 144.46 0.00 * 2 (M) 3 27.12 1.19 0.39 3 (S) 3 14.22 0.62 0.63 Residual error 6 45.64 Total 15 3383.88 ‘actual’ Daylit area 1 (PP) 3 3868.34 254.39 0.00 * 2 (M) 3 45.43 2.99 0.12 3 (S) 3 25.78 1.70 0.27 Residual error 6 30.41 Total 15 3969.96 Overlit Area 1 (PP) 3 2559.32 48.43 0.00 * 2 (M) 3 13.76 0.26 0.85 3 (S) 3 54.09 1.02 0.45 Residual error 6 105.70 Total 15 2732.88 TSRE 1 (PP) 3 22480.90 152.38 0.00 * 2 (M) 3 163.30 1.11 0.42 3 (F) 3 1.00 0.01 1.00 Residual error 6 295.10 Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 20 Total 15 22940.20 Lighting energy 1 (PP) 3 274.33 7.54 0.02 * 2 (M) 3 38.61 1.06 0.43 3 (F) 3 30.49 0.84 0.52 Residual error 6 72.72 Total 15 416.15 Cooling energy 1 (PP) 3 8363.61 80.35 0.00 * 2 (M) 3 147.82 1.42 0.33 3 (F) 3 21.27 0.20 0.89 Residual error 6 208.18 Total 15 8740.88 Heating energy 1 (PP) 3 2.12 49.83 0.00 * 2 (M) 3 0.06 1.37 0.34 3 (F) 3 0.00 0.08 0.97 Residual error 6 0.08 Total 15 2.26 Index 1 (PP) 3 0.38 18.86 0.00 * 2 (M) 3 0.23 11.47 0.01 * 3 (F) 3 0.05 2.57 0.15 Residual error 6 0.04 Total 15 0.70 Table 10 presents the results of the L16(43) ANOM. Delta values are used to compare the relative magnitude of effects depending on orthogonal design [41]. It also shows the optimal PSS configuration which obtains the highest index values. Table 10. L16(43) ANOM. Mean values Nondaylit area (%) ‘actual’ Partially daylit area (%) ‘actual’ Daylit area (%) Overlit area (%) TSRE (kWh/m2) Lighting energy (kWh/m2) Cooling energy (kWh/m2) Heating energy (kWh/m2) Index PP T1 (50%) 0 0 43 57 147.82 17.42 136.98 1.41 0.68 T2 (37.5%) 0 0 49 51 116.07 20.04 114.84 0.82 0.99 T3 (25%) 0 34 24 42 83.03 26.18 96.49 0.52 0.70 T4 (12.5%) 47 19 10 23 47.12 27.34 74.97 0.53 0.58 Delta 47 34 39 33 101 10 62 1 0.41 Rank 1 1 1 1 1 1 1 1 1 M 147.82 T1 (12×28) 13 13 30 45 103.00 22.62 109.13 0.91 0.60 T2 (9×21) 12 14 31 43 97.97 24.77 106.75 0.78 0.69 T3 (6×14) 12 15 31 42 99.03 23.16 106.54 0.84 0.73 T4 (3×7) 11 12 34 43 94.03 20.43 100.86 0.75 0.93 Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 21 Delta 1 3 4 2.52 9 4 8 0 0.33 Rank 2.5 2 2 3 2 2 2 2 2 S T1 (C) 11 13 31 45 98.27 22.99 105.95 0.84 0.78 T2 (H) 12 14 33 41 98.89 24.64 107.51 0.83 0.80 T3 (Q) 12 15 31 42 98.31 22.59 105.53 0.80 0.72 T4 (T) 13 12 30 45 98.57 20.76 104.29 0.81 0.65 Delta 1 2 4 5 1 4 3 0 0.15 Rank 2.5 3 3 2 3 3 3 3 3 Optimal PSS 374H Note: the numbers in bold represent optimal levels according to the indicators. Figure 11 presents the L16(43) ANOM. 10a plots the annual modified Daylight Availability where the non-daylit area can be observed to remain at zero in PPs larger than 25% and shows fluctuations that are broadly similar for all levels of M and S. The actual partially daylit area remains at zero for PPs greater than 37.5% and presents close fluctuations between levels M and S. The actual daylit area reaches its highest value at 37.5% PP, followed by 50% PP. It then decreases as PP decreases. This area shows a slight increase at levels 4 (3×7) for M and 2 (H) for S. The overlit area decreases as PP decreases and presents close results in all 4 levels of M and S. Figure 11b plots the annual means of the PSS energy performance indicators. It can be observed that, similar to the overlit area, TSRE decreases as PP decreases; furthermore, it reaches highly similar values in M and S levels. SCannual behaves the same as TRSE in the three design variables. Lighting energy increases slightly as PP decreases and presents fluctuations at levels M and S. Cooling energy decreases as PP decreases; moreover, it is lower in M4 (3×7) and presents fluctuations at S levels. Heating energy remains practically the same over all variables. With regard to the index, PP 37.5%, M 4 (3×7) and S 2 (C) and 1 (H) levels obtain the best simultaneous performances in the two aspects under study. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 22 Figure 11. L16(43) ANOM results. The index is used for the daylighting and thermal characterisation of the PSS and endeavours to find a balance between natural daylight and thermal efficiency. The following design criteria for southfacing, Mediterranean PSS have been derived from their optimal levels:  PP is the determining variable in PSS design since it was statistically significant for all indicators. PP should be limited to 37.5% for the following reasons (See Table 10). In terms of daylighting performance, a PP of 37.5% gives the highest actual daylit area value (49%); Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 23 PPs greater than 37.5% increased the overlit area in more than 50% of workplane (57%), while PPs of less than 37.5% led to a considerable (10-24%) reduction. In terms of thermal performance, a PP of 37.5% gives intermediate values with respect to lighting, heating and cooling energy consumption, achieving annual savings when compared with larger PPs. The highest index value is obtained with PP 37.5% and therefore it is effective when describing simultaneously the PPs’ daylighting and thermal performance.  The second most important factor is the matrix. In order to achieve the best balance between daylight and energy performance, matrices with the smallest number of large perforations are recommended. According to the results in daylighting performance, level 4 (3x7) obtains the highest actual daylit area values, while in terms of the overlit area, all four levels are roughly equal, with levels 3 (6×14) and 4 (3×7) giving the lowest values. In terms of thermal performance, level 4 (3x7) is the most advisable because it achieves the lowest levels of energy consumption for all energy uses, as well as the lowest TSRE levels. With regard to the index, the optimal level is level 4 (3x7) and is therefore effective in characterising both conditions simultaneously. Even M is statistically significant for the index (See Table 9).  Shape is the least relevant variable, allowing for greater design freedom. The results showed no significant differences in any indicator (See Table 9). 3.2 Analysis of the use and non-use of south-facing PSS This section compares the space’s daylighting and thermal conditions with and without PSS, selecting for that purpose configuration 374QS from the simulations that had already been performed. This configuration was chosen because it combines the optimal and statistically significant levels derived from the OA, as well as being the PSS with the highest index (See Figure 10). Figure 12a shows the absolute quantified error in 374QS with respect to REF100S for modified Daylight Availability, as well as the quantified percentual error for both energy consumption and TSRE. The results demonstrate that using optimised south-facing PSS can increase the actual daylit area by 50% and decrease the overlit workplane area by 50% when compared with a fully-glazed façade. Although with PSS artificial lighting consumption rises by 62%, daylighting on the workplane is improved considerably. Furthermore, there is a 63% reduction in TSRE while cooling and heating consumption decrease by 58% and 86%, respectively. This gives a 55% total annual saving in energy consumption. It is, therefore, advisable to use PSS on south-facing glazed façades in line with the abovementioned design criteria. Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 24 Figure 12. Differences between use and non-use of an optimised south facing PSS. Figure 12b compares the daylighting and thermal performance of the optimised PSS with respect to a simple aperture with WWR 37.5%. The absolute error in 374QS with respect to WWR 37.5% for modified Daylight Availability is shown, as is the quantified percentual error in 374QS with respect Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 25 to WWR 37.5% for energy consumption and TSRE. The results show that using a simple aperture can increase the actual daylit area by 63% and reduce the overlit area on a workplane by 63% with respect to the fully-glazed façade. Artificial lighting consumption, however, increases by 62% which is similar when using PSS. Moreover, TSRE decreases by 56% and cooling and heating consumption by 37% and 54%, respectively. There is only a 34% decrease in overall energy consumption; 21% less than when using PSS. On balance, therefore, it is more advisable to use PSS on glazed façades instead of a simple aperture in the wall. 3.3 Characterisation of PSS daylighting and thermal performance Figure 13 shows an overlap of the four areas of the modified daylight availability at each sensor point in 374QS. The white areas represent a sensor with DA300 for at least 75% of the working year that do not reach UDI>3000 during 5% of the occupied hours (in short, the favourable actual daylit area). The clear grey scale shows sensors with DA300 between 50 and 75% of the working year that do not reach UDI>3000 during 5% of the occupied hours (in short, the nominal actual daylit area). In addition, the REF100S results also appear in Figure 13 for in order to present daylight on the workplane without PSS. Not only can the daylighting improvement be observed in the increased actual daylit area but also in the reduction of the overlit area and, furthermore, in the reduction of the annual time percentages with excessive illuminances at each sensor point. Figure 13. Daylight Availability in 374QS and REF100S. In this work, illuminance and TSRE information are shown using annual temporal maps. These temporal maps are produced in MATLAB in order to show, on a single graph, the periods of the year Design optimisation of perforated solar façades in order to balance daylighting with thermal performance TEP 130 32 Fundamentals, I-P Editio, ASHRAE, Inc, Atlanta, 2013. [65] J. Mardaljevic, Spatio-temporal dynamics of solar shading for a parametrically defined roof system, Energy Build. 36 (2004) 815–823. View publication stats