Optimization method for perforated solar screen designto improve daylighting using orthogonal arrays and climate-based daylight modelling

https://grupo.us.es/grupotep130/es/ TEP 130 ARQUITECTURA, PATRIMONIO Y SOSTENIBILIDAD: ACÚSTICA, ILUMINACIÓN, ÓPTICA Y ENERGÍA ARCHITECTURE, HERITAGE AND SUSTAINABILITY: ACOUSTICS, LIGHTIING, OPTICS AND ENERGY Doris A. Chi, David Moreno, Paula M. Esquivias and Jaime Navarro This is an Accepted Manuscript of an article published by Taylor and Francis: Journal of Building Performance Simulation, Volume 10, 2, 2017, Pages 144-160, ISSN 1940-1493 https://doi.org/10.1080/19401493.2016.1197969 TEP 130 1 Authors’ names and affiliations: Doris A. Chi a, David Moreno a, Paula M. Esquivias a, Jaime Navarro a a Instituto Universitario de Arquitectura y Ciencias de la Construcción (IUACC), Universidad de Sevilla, Spain Corresponding Author: Doris A. Chi, Instituto Universitario de Arquitectura y Ciencias de la Construcción (IUACC), Universidad de Sevilla, Spain Email: abig[email protected]om Abstract This paper analyses the influence of different perforated solar screens (PSS) in annual daylight conditions expressed using climate-based daylight metrics. The PSS design require parametric studies that are often complex and time consuming due to a large number of simulations. Hence, a new methodology is proposed to optimize PSS design by applying Design of Experiments using Orthogonal Arrays (DOA). A case study from the DOA perspective has been conducted, which involves an office space in Seville, Spain. The goal is to assess the effect of the following PSS design variables in daylighting performance: perforation percentage, matrix, shape and orientation. DOA results reveal that optimized PSS can increase daylit area by 33% and reduce over lit area by 35%, compared with reference models with no PSS. DOA method reduces the number of simulations from the 256 required to 16, so it could save time during the initial stages of building design. Keywords: perforated solar screens; optimal design; orthogonal arrays; climate-based daylight metrics; daylight availability 1 Introduction The Energy Performance of Buildings Directive (EPBD) highlights the importance of reducing building energy consumption given that this accounts for over 40% of total energy consumption in the European Union (EC 2010). In Mediterranean climates, characterized by many sunny sky days, much of the available daylight is not used to its full potential (Lim, Ahmad, and Ossena 2013). In fact, artificial lighting consumption accounts for over 30% of the total energy consumption in Spanish office buildings (MITC 2007). However, daylighting is a way to reduce lighting energy consumption. Suitable architectural design and consideration of local climate variability can ensure a balanced thermal and visual indoor environment, reducing the use of artificial lighting and active thermal conditioning systems (EC 2010; TEP 130 2 Bodart and De Herde 2002; Galasiu, Atif, and MacDonald 2004). However, solar radiation is also one of the main reasons for overheating and glare, particularly in summer, so it must also be taken into account (Bodart and De Herde 2002). Building envelopes are crucial to daylighting as they act as interfaces for building-urban surroundings (Lai and Hokoi 2015). They offer protection from direct solar radiation, provide daylight and allow visual contact (Zawidiski and Kahn 2014). Fully glazed façades in buildings gained popularity in the 1990s. This popularity coincided with the appearance of new solar control systems on façades to provide solar protection and reduce glare and thermal demand generated by emerging modern architectural trends (Blanco et al. 2014). In this situation, perforated solar screens (PSS) were implemented not only for solar control but also to meet the expectations for the visual image of envelopes (Wang, Rivard, and Zmeureanu 2006; Villalba, Monteoliva, and Pattini 2011). Their design has been governed by aesthetic, morphological and symbolic criteria rather than by parameters relating to their contribution to the improvement of indoor daylighting conditions or the reduction of thermal gains (Villalba, Monteoliva, and Pattini 2011; Goia, Haase, and Perino 2013). PSS are flat opaque perforated panels, relatively thin in relation to their length and width, which form a double skin for building façades. Placed in front of building fully glazed façades, PSS are not merely decorative. The organization of their perforations filters out incident direct sunlight, which is prevented from directly penetrating into spaces while still allowing users to view outside. The opaque parts of the screen reflect sunlight and act as solar control systems (Aljofi 2005; Pattini et al. 2011). In recent years, certain design variables for some perforated solar protections and their influence in daylighting and energy consumption have been studied in order to take them into account from the initial building design stages. Sherif, El-Zafarany, and Arafa (2012) find that perforated solar protections on residential building windows reduce air conditioning consumption by 30%, especially with perforation percentages of 80% to the west and north and 90% to the east and south. Sherif, Sabry, and Rakha (2012) recommend using perforation percentages of 40-90% on windows of residential buildings in desert locations, to obtain 200 lux during 50% of annual occupation hours, over at least 30% of space. Aljofi (2005) determines that the circular shapes openings of solar protection on windows tend to result in lower Daylight Factor (DF) percentages, compared to quadrangular shapes. In addition, the highest daylight contributions are found in the central areas of spaces. Sherif et al. (2011) recommend the use of perforated screens on windows, with a shape ratio (vertical: horizontal) of TEP 130 3 openings of 18:1 to the north and 1:1 to the south, as they obtain 200 lux on at least 70% of the workplane and reduce energy consumption in desert areas. Etman, Tolba, and Ezzeldin (2014) conclude that quadrangular openings used in west-facing façades in office buildings in Cairo (Egypt) improve indoor illuminance distribution of 54-78% with illuminance levels of 300-500 lux, for the 6 simulated hours in the 3 days selected. Sabry et al. (2011) conclude that the mean illuminance in the space is directly proportional to the horizontal axial rotation angle of perforated protections used in residential building windows in desert climates. As seen before, perforated solar screens improve daylighting conditions and reduce energy consumption. Although these studies focus on their application on windows in desert climates, PSS constitute a second façade for buildings and are used in a wide range of climate conditions. In view of the above, PSS design requires the consideration of a wide variety of variables. A comprehensive study of possible variable combinations requires a large amount of different models, which is difficult to manage. As a result, most research concentrates on a single design variable regardless of its relationship with others. Nevertheless, statistic Design of Experiments (DOE) tools can simplify the interrelated study of a large number of variables, reducing the number of experiments or simulations and obtaining maximum information which may be of use in the design of PSS (Park 2007). These tools include Design using Orthogonal Arrays (DOA) which selects a representative fraction of all possible combinations of factors so as to distribute the experiments uniformly within the test range, accurately representing the overall situation. This method is highly efficient in reducing the number of experiments required and in achieving optimal combination levels (Taguchi and Yokoyama 1993). The DOA method has been used efficiently in different fields of science, contributing valid conclusions and optimizing processes (Franek and Jiang 2013). While not specifically applied in the design of PSS, DOA has been applied in the formal design of buildings. Yi, Srinivasan, and Braham (2015) used it to study basic architectural design parameters such as geometry, size and shape of windows, obstructions, orientation, etc. These successfully optimize the design process and reduce construction costs. Chlela et al. (2009) used DOA to study some characteristics of the building envelope: thermal properties of walls, transmissivity and solar absorption of glazing, etc. Simulations were reduced from 1024 to 32, successfully describing the energy consumption model for offices and reducing heating, cooling and lighting demands by 81%, 63% and 45%, respectively. Gong, Akashi, and Sumiyoshi (2012) use it to optimize 7 passive strategies to reduce annual thermal loads and replace HVAC systems in winter. Wang, Zmeureanu, and Rivard (2005, 2006) implement TEP 130 4 it to reduce the environmental impact of the building's lifecycle, optimizing orientation, window size, and the insulation materials and properties of green buildings. Using DOA, Zhu et al. (2013) put the following construction design variables into order of importance: glazing > outer wall > floor > solar protection > ceiling; minimizing carbon emissions, as well as lighting, equipment and climatization consumption. Wei, Zhao, and Chen (2010) implement it to optimize the window design parameters suited to each Chinese location studied, achieving energy savings of 25% for warm climates and 34% for cold climates. Huang and Wu (2014) apply it to establish the order of importance in daylighting and solar control conditions of the parameters of Chinese splayed windows. As can be observed, DOA presents several advantages in the field of design, especially as regards the effectiveness of results and the reduction of the number of experiments and/or computational simulations arising from the combination of diverse design variables. Therefore, this study develops a new methodology based on DOA to optimize PSS design. It aims to study the interrelation of the impact of different PSS design variables on annual indoor daylighting conditions. A case study has been conducted from the perspective of DOA, which involves a typical office space in the Mediterranean Climate of Seville, Spain. For this, the following design variables have been selected: perforation percentage (PP), matrix (M), shape (S) and orientation (O). The results obtained in the case study are presented in three phases. The first one analyses the orthogonal array (OA) proposed for each daylighting metric, describing and classifying the importance of the effects of each design variable. In addition, optimal combinations are obtained to ensure useful illuminances on the workplane. OA results are corroborated in the second phase by carrying out daylighting simulations to verify optimal metric results from DOA. In the third phase the optimized series are contrasted with the reference model in order to assess daylighting conditions with and without PSS. Finally, conclusions are stated and future research is suggested. 2 Methodology for applying orthogonal arrays to optimize PSS design Practical work usually involves three or more variables or factors, which requires multifactor analysis. Multi-factor experiments include full factorial design and fractional factorial design. Full factorial design tests all possible combination of variables. For a full factorial experiment with five factors and four levels, the number of trials is 54=625. The number of full factorial experiment is large and time consuming that it is difficult to be implemented. As an alternative, the DOA method is used. DOA selects representative points from full factorial experiment in a way that the points are distributed uniformly within the test range and thus can represent the overall situation. The advantages of DOA method are that the number of trials needed TEP 130 5 to complete the experiment is relatively small and the test results could be analysed through range analysis and variance analysis. This method is highly efficient for the arrangement of multi-factor experiment with optimal combination levels (Zhu et al. 2013). In DOA, the selection of experiments is based on orthogonal array (OA). This is represented by a matrix which is expressed as LN (l)k, where L is orthogonal array, N the number of experiments, l the level of factors, and k the number of factors or columns (Park 2007). OA follows two properties: on each column the number of occurrences is the same for each factor on different levels; the combination of levels of factors is complete and balanced on every row. These two principles represent the advantages of OA: uniform dispersion and regular comparable. In other words, any factor on any level is compared with all other factors on different levels (Zhu et al. 2013). This study proposes a new methodology which applies DOA in the optimization of PSS design in order to carry out a cross-section comparison of different PSS design variables, evaluating the effect of each of these and reducing the number of computational simulations required to calculate daylighting conditions. Some of the terminology used in DOA is similar as that used in PSS design (Park 2007). Table 1 presents these equivalences. DOA PSS Design Description of the design Factor PSS design variables Characteristics of the PSS which affect indoor daylighting conditions Level Values of design variables Values which each design factor or variable may have Characteristic function Objective function Daylighting conditions expressed in indicators, which can be maximized or minimized Table 1. Terminology in DOA and in PSS design. The methodology proposed consists of seven steps, described in Figure 1. These steps are developed and explained in greater detail in the description of the case study. TEP 130 6 Figure 1. Methodology proposed for the design of PSS applying orthogonal arrays. TEP 130 7 3 Case study for DOA methodology 3.1 Simulation setup Daylight calculations are carried out using Radiance-based software Daysim 3.1e (Ward and Shakespeare 1998; Reinhart 2010). The climate file used is IWEC for the Spanish city of Seville (DOE 2010), at 37°42’N, 5°9’W, with Mediterranean climate. Table 2 shows the set of simulation parameters according to the typical scene 2 used in Radiance (Reinhart 2010). Ambient bounces Ambient division Ambient sampling Ambient accuracy Ambient resolution Direct threshold Direct sampling 7 1500 100 0.1 300 0 0.2 Table 2. Simulation parameters The reference model is a 49 m2 surface from a space measuring 7 m x 7 m x 3 m. This is deep and wide enough to be adapted to different variations of the office typology, such as group offices or combined use (IDAE 2011). The space has one fully glazed façade with a double-clear-glazing with a visual transmittance of 78.1%. The height of the workplane is 0.80 m above ground level, with sensors points placed 0.25m apart and 0.50 m from walls. Reflectances of the model surface are found in Table 3. The reference model is represented in Figure 2. Ceiling 0.80 Floor 0.20 Wall 0.50 PSS (opaque Surface) 0.90 Table 3. Reflectances of model surfaces. Figure 2. Reference model and calculation grid. Floor, cross-section and perspective. TEP 130 8 3.2 PSS design variables Commonly, PSS are flat opaque perforated panels, without thickness in relation to their length and width, which form an outer skin for building fully glazed façades. The perforations configurations filters out incident sunlight and their design is widely varied. Notwithstanding, different parameters can be assessed in order to study the influence of PSS in daylighting indoors. In this work, specific PSS input parameters are as follows: The PSS are externally mounted at a distance of 0.05 m from the fully glazed façade. The PSS dimensions are 7 m in width and 3 m in height (the thickness is not considered). Four design variables that are usually determined at the conceptual design stage and that have critical influence on daylighting performance are selected to characterize PSS. Each design variable takes four levels. The four PSS design variables and their four level values are described below and in Figure 3. (1) Perforation percentage (PP): Ratio of the total surface of the openings to the wall. Four PP are proposed for study: 50%, 37.5%, 25% and 12.5%. (2) Matrix (M): Distribution of openings on the screen achieving the established perforation percentages. Four regular matrixes are established: 12x28, 9x21, 6x14 and 3x7. The distance between openings for each matrix is of 0.25 m, 0.33 m, 0.50 m and 1.00 m, respectively; it is measured from the centre and is vertically and horizontally equidistant. (3) Shape (S): Shape of each individual opening. Four regular shapes are proposed: circular, hexagonal, quadrangular and triangular. The different-shaped openings have the same opening area when M and PP are the same. (4) Orientation (O): The application of the PSS on a façade oriented following the four cardinal points is analysed: North (N), South (S), East (E) and West (W). TEP 130 15 Figure 6. Daylight metrics and objective function. 4 Experiment results 4.1 Analysis of orthogonal array OA analysis aims to calculate the combination of optimal levels of variables and to propose optimal combinations to maximize useful illuminances for at least 50% of the working year and to minimize illuminances exceeding 3000 lux for at least 5% of the working year (actual daylit area). Table 6 shows the results obtained in the 16 computational simulations of array L16(44), for each daylight metric. Additionally, the fully daylit area has been added in order to compare results obtained through the objective function vs those achieved according to code officials. Simulation PSS Space percentage Fully daylit area (%) Non-daylit area (%) ‘actual’ Partially daylit area (%) ‘actual’ Daylit area (%) Over lit area (%) 1 501CN 0 0 89 11 100 2 502HS 0 0 43 57 100 3 503QE 0 0 42 58 100 4 504TW 0 0 47 53 100 5 371HE 0 0 61 39 100 6 372CW 0 0 57 43 100 7 373TN 0 7 91 2 93 TEP 130 16 8 374QS 0 0 47 53 100 9 251QW 0 34 29 37 66 10 252TE 0 34 36 30 66 11 253CS 0 16 41 44 84 12 254HN 0 40 60 0 60 13 121TS 32 31 16 20 37 14 122QN 57 27 16 0 16 15 123HW 47 28 12 13 26 16 124CE 39 25 20 16 36 Table 6. Results of orthogonal array L16(44). Table 7 presents the variance analysis (ANOVA) and statistical significance (p-value) of experimental results when α=0.05. The sum of squares (SS) indicates the relative importance of each factor; the factor with the greatest sum of squares has the greatest impact (Minitab 2000). Accordingly, the ANOVA results show significance to 5% of PP for all metrics, S for the actual and fully daylit areas and O for the actual daylit, fully daylit and over lit areas. About SS results, PP is the most important factor for all metrics, except for the over lit area where O is the most important. The second result is S for the actual partially daylit area, O for the actual and fully daylit areas and PP for the over lit area. In case of the non-daylit area, M, S and O show equal relevance. Metric Factor GL SS F p Significance Non-daylit area 1 (PP) 3 5765.84 69.22 0.00 * 2 (M) 3 83.30 1.00 0.50 3 (S) 3 83.30 1.00 0.50 4 (O) 3 83.30 1.00 0.50 Residual error 3 83.30 Total 15 6099.05 ‘actual’ Partially daylit area 1 (PP) 3 3257.79 26.69 0.01 * 2 (M) 3 34.98 0.29 0.83 3 (S) 3 149.52 1.23 0.44 4 (O) 3 95.49 0.78 0.58 Residual error 3 122.05 Total 15 3659.83 ‘actual’ Daylit area 1 (PP) 3 5190.64 100.20 0.00 * 2 (M) 3 256.52 4.95 0.11 3 (S) 3 710.30 13.71 0.03 * 4 (O) 3 2104.64 40.63 0.01 * Residual error 3 51.80 Total 15 8313.91 Over lit area 1 (PP) 3 2212.88 19.70 0.02 * 2 (M) 3 64.67 0.58 0.67 3 (S) 3 290.34 2.58 0.23 4 (O) 3 3884.58 34.58 0.01 * Residual error 3 112.35 TEP 130 17 Total 15 6564.81 Fully daylit area 1 (PP) 3 13386.60 1130.62 0.00 * 2 (M) 3 68.90 5.82 0.09 3 (F) 3 219.10 18.50 0.02 * 4 (O) 3 353.00 29.82 0.01 * Error residual 3 11.80 Total 15 14039.40 Note: The asterisk denotes 5% significance; characters in bold denote first place, and italics second place, in importance. Table 7. Variance analysis of orthogonal array metrics ( α =0.05). Table 8 presents the results of the mean analysis (ANOM) of array L16(44). Delta value is an index used to compare the relative magnitude of effects depending on ortogonal design (Park 2007). Classification or rank is based on Delta values: 1 for the highest Delta value, 2 for the second highest, and so on. Rank indicates the relative importance of each factor to the results of the different metrics (Minitab 2000). Table 8 also shows the optimal combinations which obtain the highest and the lowest percentages of the daylight metrics according to the objective function. Mean values Total space area (workplane) Fully daylit area (%) Non-daylit area (%) ‘actual’Partially daylit area (%) ‘actual’ Daylit area (%) Over lit area (%) PP T1 (50%) 0 0 55 45 100 T2 (37.5%) 0 2 64 34 98 T3 (25%) 0 31 41 28 69 T4 (12.5%) 44 28 16 12 29 Delta 44 31 48 32 71 Rank 1 1 1 2 1 M T1 (12x28) 8 16 49 27 76 T2 (9x21) 14 15 38 33 71 T3 (6x14) 12 13 47 29 76 T4 (3x7) 10 16 43 30 74 Delta 6 4 11 6 5 Rank 3 4 4 4 4 S T1 (Circular) 10 10 52 28 80 T2 (Hexag.) 12 17 44 27 71 T3(Quadrang) 14 15 34 37 71 T4 (Triang.) 8 18 48 26 74 Delta 6 8 18 11 9 Rank 3 2 3 3 3 O T1 (N) 14 19 64 3 67 T2 (S) 8 12 37 44 80 T3 (E) 10 15 40 36 75 T4 (W) 12 15 36 37 73 Delta 6 7 28 40 13 TEP 130 18 Rank 3 3 2 1 2 Optimal PSS 501TS 503CS 371CN 121TN 503CS Note: Characters in bold indicate the optimal levels for each factor according to the objective function. Combination of these levels results in the optimal PSS. Table 8. Results for means of L16(44). For the non-daylit area, the first place in importance is for PP (44) but the other three variables show equal relevance (6). Figure 7 indicates that the non-daylit area increases as PP decreases, however, it still zero for all PP larger than 25%. M and S show fluctuations with results close to each other although optimal values for achieving the lowest values of the non-daylit area are 12x28 and triangular. The most advisable orientation to reduce the non-daylit area is S and the least suitable is N. Figure 7. Main effects for the non-daylit area means For the actual partially daylit area, the order of effects is PP (31) > S (8) > O (7) > M (4). Figure 8 shows that the actual partially daylit area achieves its maximum value at PP 25%, closely followed by PP 12.5%, and its minimum value at PP 50%. Regarding M and S, the lowest actual partially daylit area is for 6x14 and circular, respectively, while the other three levels show fluctuations with results TEP 130 19 very close to each other. About O, the lowest value is achieved at S and the highest value at N, while similar results are obtained for E and W. Figure 8. Main effects for the ‘actual’ partially daylit area means. For the actual daylit area, the order of effects is PP (48) > O (28) > S (18) > M (11). Figure 9 indicates that the actual daylit area achieves its maximum value at PP 37.5%, followed by PP 50%, and its minimum value at PP 12.5%. M shows fluctuations but it is observed that the highest value is achieved at 12x28, closely followed by 6x14. About S, the highest value is reached in the circular level and the lowest value in the quadrangular one. Regarding O, the highest value is achieved at N and the lowest value is obtained at S. TEP 130 20 Figure 9. Main effects for the ‘actual’ daylit area means. As regards the over lit area, the order of effects is O (40) > PP (32) > S (11) > M (6). Figure 10 shows that the over lit area decreases as PP decreases. M shows fluctuations although it is observed that M 12x28 slightly achieves the lowest values. For S, the quadrangular level gets the highest values while the other three levels achieves lower values and very close to each other. About O, level N is by far the best option because it provides a considerably lower over lit area (3%) in comparison with the other cardinal points that achieves more than 35%. Besides, S is the least favourable orientation because it increases this area, almost over the half of the workplane. TEP 130 21 Figure 10. Main effects for the over lit area means. For the fully daylit area, the order of effects is PP (71) > O (13) > S (9) > M (5). Figure 11 indicates that the fully daylit area decreases as PP decreases. M shows fluctuations with results very close to each other but it can be observed that the highest value is achieved at 6x24, closely followed by 12x28. About S, it also shows fluctuations but the highest value is reached in the circular level while the other three levels show results very close to each other. Regarding O, the highest value is achieved at S and the lowest value is obtained at N. TEP 130 22 Figure 11. Main effects for the fully daylit area means. It is important to mention here that the fully daylit area is reported in this paper in order to compare the percentage of workplane that is considered ‘fully daylit’ according to code officials and green rating systems, against the percentage of workplane that is assessed as ‘actual daylit’ in this work. About this, Figure 12 shows the comparison between the cited daylit areas and also indicates with the two red dashed lines the nominally acceptable and favorably/preferred percentages of the workplane (55 and 75%, respectively) that are required in LM-83 and LEED V.4. From this, the results of the fully daylit area indicate that only PP 12.5% do not achieve the nominally area. Moreover PP 50 and 37.5%, M 6x14 and 12x28, S circular and O south and east exceed the favorably area while the rest of levels are within the nominally and favorably areas. With these results, it could be concluded that all levels, except PP 12.5%, are a good alternative for designing PSS according to code officials and green rating systems; however, this assumption is not certainly valid. For example, from Figure 10 it can be observed that PP 50% and south orientation also get the highest levels of the over lit area which result in a contradictory proposal (the best levels of PP and O for maximizing DA300,50% are 50% and south, but the most recommendable for minimizing UDI>3000,5% are 37.5% and north). Thereby, the fully daylit area by itself do not allow identifying TEP 130 23 clearly the optimal levels to design PSS. This is because the fully daylit area also maximize excessive illuminances as there is no upper limit in DA300,50%. In contrast, from Figure 12 it can be observed that the results of the actual daylit area do not necessarily reach the nominally acceptable or favorably/preferred spaces. About this, only PP 37.5 and 50%, and O north meet at least 55% of the workplane, so just these levels can be considered nominally acceptable according to LM-83 and LEED V.4. Notwithstanding, from Figure 10 it can be observed that PP 37.5% achieves lower values of the over lit area (34%) than PP 50% (45%). Furthermore, N orientation obtains the lowest values of the over lit area (3%) while S achieves the highest percentages (44%). These are two proposals properly showed in Figure 12, since the actual daylit area in PP 37.5% is higher than in PP 50% and since the north is the best orientation for maximizing the actual daylit area and simultaneously minimizing the over lit area. From the combination of these two variables results, it can be concluded that PP 37.5 and 50% at north are the optimal levels. Consequently, these results of PP and O indicate that the best levels predicted by the actual daylit area are the optimal instead of those predicted by the fully daylit area. Figure 12. Main effects for the fully and actual daylit areas means. TEP 130 24 Regarding M and S, the results of the four levels show larger differences for the actual daylit area than for the fully daylit area. Hence, it can be observed an increase of the actual daylit area in M 12x28 and S circular, and a noticeable decrease in M 9x21 and S quadrangular. Once again, the optimal levels are identified in a clearer way through the actual daylit area instead of the fully daylit area because the first integrates simultaneously the values of the daylit and over lit areas. Table 9 shows a comparison between optimal PSS derived from code officials and those obtained through the actual daylit area. LM-83 indicates that the fully daylit area must meet at least 55 and 75% of working area for a space nominally acceptable and favorably/preferred, respectively; therefore, LEED V.4 provides two and three credit points, respectively. On the other hand, this paper proposes that the highest values of the actual daylit area indicate the best levels for each variable, so the combination of these best levels can origin the optimal PSS. Fully daylit area ranked by LM-83 and LEED V.4 Actual daylit area guidelines PP 50 % Favorably/Preferred (100) 37.5% (64) 50% (55) 37.5% Favorably/Preferred (98) 25% Nominally acceptable (69) M 6x14 Favorably/Preferred (76) 12x28 (49) 12x28 Favorably/Preferred (76) 3x7 Nominally acceptable (74) 9x21 Nominally acceptable (71) S Circular Favorably/Preferred (80) C (52) Triangular Favorably/Preferred (74) Hexagonal Nominally acceptable (71) Quadrangular Nominally acceptable (71) O S Favorably/Preferred (80) N (64) E Favorably/Preferred (75) W Nominally acceptable (73) N Nominally acceptable (67) Note: Numbers in parentheses are the results for means of L16(44), specifically of the fully and actual daylit areas. Table 9. Comparison of recommendations for daylit areas. 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