Optimising Design Parameters of a Building-Integrated Photovoltaic Double-Skin Facade in Different Climate Zones in Australia

: Energy used in buildings is mainly attributed to provide the desired thermal comfort, which could result in an increase in carbon emission and, in turn, lead to further environmental degradation. A Building-Integrated Photovoltaic Double-Skin Façade (BIPV-DSF) is a promising way to maintain indoor thermal comfort, obtained with low environmental impact and energy consumption. The appropriate design of BIPV-DSFs can maximise indoor thermal comfort and energy efficiency for buildings. This paper presents optimal BIPV-DSF design solutions, which are dedicated to offering comfortable and energy-efficient buildings, through optimisation of the most important design parameters of a BIPV-DSF under three different climate conditions in Australia. The results illustrate how thermal transmittance (U-value) and solar heat gain coefficient (SHGC) of windows of the BIPV-DSF, as the most important design parameters, were optimised for application in the context of different climates, operation modes, and orientations. The paper contributes to the matters concerning the integrated effect of BIPV-DSFs on thermal comfort and energy performance in buildings.


Introduction
The impact of built environment on climate change has become significant [1], which is responsible for 39% of global carbon emissions, far higher than other sectors [2]. Greenhouse gases are the main driver of climate change [3], while carbon dioxide accounts for about 76% of total greenhouse gas emissions [4]. According to the statistics revealed in the 2022 World Economic Forum Annual Meeting [5], buildings as a major component within the built environment contribute to a high 37% of carbon emissions due to energy consumption, while office buildings are one of the substantial sources of energy consumption [6]. As a matter of fact, a large proportion of the energy consumption goes to the maintaining of thermal comfort in buildings [7]. Thus, the control of energy consumption and thermal comfort in buildings is crucial in mitigating climate change [8].
As an important part of a building, façades link the interior and exterior environments, which affects energy consumption and indoor thermal comfort in the building to a large extent [9]. However, conventional facades can lead to an increase in energy consumption and thermal discomfort due to their poor insulation and ventilation performance [10]. In comparison, adaptive façades can adapt to variable climatic conditions and thereby reduce building energy consumption and improve indoor thermal comfort, and these performances have been demonstrated in the last few decades [11][12][13]. Building-Integrated In this paper, the most important design parameters of the BIPV-DSF of an Australian office module, according to the sensitivity analysis we recently presented [31], were optimised by using a specific optimisation method, namely Pareto optimality. Consequently, the optimal design solutions of the BIPV-DSF affecting the indoor thermal comfort and thermal energy consumption of the office module were determined for various contexts.

Design Parameters to Be Optimised
In general, this study was a continuation of our previous studies [26][27][28][29] and was especially based upon the most important design parameters of the BIPV-DSF identified through the previously conducted sensitivity analysis [31]. The parameters can be summarised in Table 1. The best-performing ventilation modes of the BIPV-DSF in the context of three distinctive climate conditions (represented by three Australian cities-Darwin, Sydney, and Canberra) can be summarised in Table 2 as per our previous studies [28,29]. Moreover, the BIPV-DSF facing four different orientations (due north, due south, due east, and due west) were considered in the optimisation.  The proposed optimisation was carried out by perturbing the important design parameters within a range of variations from their original values, and then determining the optimal design parameter values based upon the resultant variations of indoor thermal comfort and thermal energy consumption from the simulation modelling in TRNSYS. Furthermore, the perturbation of thermal parameters of the PV glazing (external window) could not be implemented due to the limitation of the manufacturer's information. Thus, a regular window with a range of thermal parameters, such as SHGC, based on the International Glazing Database in the TRNSYS window library, was chosen to model the external window of the BIPV-DSF, while the PV electric power production was calculated separately. Table 3 presents the variation space (including the original values) for the identified most important design parameters for optimisation, where the values for perturbing the glazingrelated parameters were taken from the International Glazing Database. It should be noted that the values of U in and SHGC out were not varied regularly due to the confined capacity of the database at the time of the study. Although there is a lack of evidence showing the impact of SHGC and U-value on the efficiency of PV glazing, a previous study [42] indicates that a PV glazing with a lower SHGC and U-value may be more efficient as less solar thermal heat will be transmitted than a PV glazing with a higher SHGC and U-value. On the other hand, Chen et al. [43] demonstrated higher PV efficiencies would result in a lower SHGC. It was assumed that there was no interference between PV efficiency and SHGC for the semi-transparent PV glazing in this study, as the efficiency of the selected semi-transparent PV panel was not as high as an opaque crystalline silicon PV panel. In fact, the reduced light absorbance determines semi-transparent PVs have much lower efficiency than opaque ones [44]. As a result, the PV efficiency under the standard test condition (STC) was fixed in this study, and varying U-value of the PV glazing (U out ) was not considered in the proposed optimisation.

Mathematical Model
Basically, the indoor thermal comfort was evaluated by counting discomfort hours using the "analytical comfort zone method" given by ASHRAE 55 [45]. Specifically, the discomfort hours were calculated for the Predicated Mean Vote (PMV) comfort zone, which can be implemented using the following equation in association with TRNSYS simulation [45]: where EH is the exceedance hours or total discomfort hours, and H dis is a discomfort hour.
To estimate thermal energy consumption of the proposed office module, the following equations based on the sensible heat gains (in terms of conduction, convection and radiation) were used in association with TRNSYS simulation [46]: q s,i = q comb,s,i + S s,i + Wallgain where q s,i is the conductive heat flux from the wall at the inside surface, q s,o is the conductive heat flux into the wall at the outside surface, q comb,s,i is the combined convective and radiative heat flux in the space, q comb,s,o is the combined convective and radiative heat flux to the surface, S s,i is both the solar radiation and long-wave radiation generated from internal objects, S s,o is the solar radiation from external surfaces, and Wallgain is a user-defined energy flow to the inside wall or window surfaces. In addition, PV electric power production would influence thermal energy saving for the office module and, therefore, the net thermal energy consumption. The following equations were used in TRNSYS simulation for the calculation of PV-produced electricity [47], which was also considered in the net thermal energy consumption simulation: where P PV is the PV electric power production, A is the PV panel exposed area, τα is the product of the PV panel's transmittance and absorptance, the subscript n is the normal incidence angle of the solar radiation, IAM is the incidence angle modifier, G T is the total incident solar radiation on the PV panel surface, and η PV is the PV power conversion efficiency.

Pareto Optimality Method
Overall, this study looks into two objectives-discomfort hours and energy (net thermal) consumption-for the office module on a yearly basis. Therefore, the optimal values of the most important design parameters could be determined using the method of Pareto optimality [36], which is widely used in the optimisation of multiple objectives for the performance of buildings and building energy systems [37][38][39][40][41]. Fundamentally, Pareto optimality deals with multi-objective functions that are to be either minimised or maximised, while a scenario of two objective functions can be illustrated in Figure 1. of the most important design parameters could be determined using the method of Pareto optimality [36], which is widely used in the optimisation of multiple objectives for the performance of buildings and building energy systems [37][38][39][40][41]. Fundamentally, Pareto optimality deals with multi-objective functions that are to be either minimised or maximised, while a scenario of two objective functions can be illustrated in Figure 1. The proposed study attempted to minimise both discomfort hours (f1) and energy consumption (f2). Given that there were 7 variations (including the original value) for Uin and SHGCout, respectively, so there were 49 solutions for the two contradictory objectives f1 and f2 for each orientation. Figure 1 shows a set of solutions including dominated and non-dominated solutions; the non-dominated solutions lying on the "Pareto front" are the most interesting solutions, where the optimal solution comes from [38]. The shortest distance of the non-dominated solution to the "ideal point" is deemed to be the optimal solution; the ideal point' is unattainable because both objectives cannot be minimised simultaneously due to their conflicting nature [38]. The distance can be determined as [38]: where x is the design variable corresponding to a Uin and SHGCout among the 49 solutions, f1(x) is the objective function 1 (that is, discomfort hours), f2(x) is the objective function 2 (that is, energy consumption), min(f1) is the minimum value of the objective function 1 among the 49 solutions, and min(f2) is the minimum value of the objective function 2 among the 49 solutions.

BIPV-DSF Model
The validated BIPV-DSF model in TRNSYS from our previous research [28,29] was used for the simulation. The model was a single-room office module with a BIPV-DSF based on a real building test bed developed by Peng et al. [20], which could be used in the two desired operation modes for ventilation: Non-Ventilated BIPV-DSF (NoVent-DSF) and Naturally-Ventilated BIPV-DSF (NatVent-DSF). Specifically, the office module had a double-skin façade structure, where an air cavity (0.4 m of depth) was located in between the external and internal layers of the façade, allowing for the operation of the different ventilation modes through the ventilation louvres; a semi-transparent PV panel and a float glass served as the respective external and internal windowpanes. TRNFlow, an external simulation engine of TRNSYS, was used to simulate the natural ventilation through the The proposed study attempted to minimise both discomfort hours (f 1 ) and energy consumption (f 2 ). Given that there were 7 variations (including the original value) for U in and SHGC out , respectively, so there were 49 solutions for the two contradictory objectives f 1 and f 2 for each orientation. Figure 1 shows a set of solutions including dominated and non-dominated solutions; the non-dominated solutions lying on the "Pareto front" are the most interesting solutions, where the optimal solution comes from [38]. The shortest distance of the non-dominated solution to the "ideal point" is deemed to be the optimal solution; the 'ideal point' is unattainable because both objectives cannot be minimised simultaneously due to their conflicting nature [38]. The distance can be determined as [38]: where x is the design variable corresponding to a U in and SHGC out among the 49 solutions, is the objective function 2 (that is, energy consumption), min(f 1 ) is the minimum value of the objective function 1 among the 49 solutions, and min(f 2 ) is the minimum value of the objective function 2 among the 49 solutions.

BIPV-DSF Model
The validated BIPV-DSF model in TRNSYS from our previous research [28,29] was used for the simulation. The model was a single-room office module with a BIPV-DSF based on a real building test bed developed by Peng et al. [20], which could be used in the two desired operation modes for ventilation: Non-Ventilated BIPV-DSF (NoVent-DSF) and Naturally-Ventilated BIPV-DSF (NatVent-DSF). Specifically, the office module had a double-skin façade structure, where an air cavity (0.4 m of depth) was located in between the external and internal layers of the façade, allowing for the operation of the different ventilation modes through the ventilation louvres; a semi-transparent PV panel and a float glass served as the respective external and internal windowpanes. TRNFlow, an external simulation engine of TRNSYS, was used to simulate the natural ventilation through the air cavity. Figures 2 and 3, respectively, illustrate the proposed BIPV-DSF office module with dimensions (the internal and external window dimensions were identical) and the two BIPV-DSF typologies, while their characteristics are further described in Table 4.
Buildings 2023, 13, x FOR PEER REVIEW 6 of 14 air cavity. Figure 2 and Figure 3, respectively, illustrate the proposed BIPV-DSF office module with dimensions (the internal and external window dimensions were identical) and the two BIPV-DSF typologies, while their characteristics are further described in Table 4.   In addition to the important design parameters (variables), other parameters such as occupation information, thermal loads, building fabric other than the DSF, and building air cavity. Figure 2 and Figure 3, respectively, illustrate the proposed BIPV-DSF office module with dimensions (the internal and external window dimensions were identical) and the two BIPV-DSF typologies, while their characteristics are further described in Table 4.   In addition to the important design parameters (variables), other parameters such as occupation information, thermal loads, building fabric other than the DSF, and building  In addition to the important design parameters (variables), other parameters such as occupation information, thermal loads, building fabric other than the DSF, and building services systems for the BIPV-DSF office module were designed with fixed values (constants), as this study was focused solely on the behaviour of the BIPV-DSF. These constant values are specified in Table 5. To simplify the modelling processes, the discomfort hours calculation was based on a whole year of 8760 h rather than the whole year's operating hours (that is, 2400 h). Cooling (reversible heat pump system) SCoP: 2.5 Setpoint temperature: 26 • C Previous research [29] Furthermore, a perovskite solar cell-based external windowpane was used in the optimisation in part due to its high electric power conversion efficiency in comparison with the other types of PV cells demonstrated in our previous studies [28,29]. Although the amorphous silicon solar cell, compared with other solar cell options, was determined as the most appropriate option for the high-humidity summer and warm winter climate (Darwin) in regard to the indoor thermal comfort, the discrepancy in indoor thermal comfort performance among all the PV options investigated was very slight. Overall, the perovskite-based solar cell possessed the best performance in controlling indoor thermal comfort as well as thermal energy consumption for the BIPV-DSF. Table 6 presents both thermal and optical properties of the selected semi-transparent perovskite PV panel.

Results and Discussion
In this study, the design solutions of the BIPV-DSF in relation to indoor thermal comfort and net thermal energy consumption were refined by optimising the most important design parameters. The results of the optimisation are presented and discussed through an integral analysis of both objective functions based on Pareto optimality in the following sections. Figure 4 shows the trade-off between the annual discomfort hours and net thermal energy consumption based on the variations of the most important design parameters (U in and SHGC out ) for the NatVent-DSF under the year-round high-humidity summer and warm winter climate (Darwin), where the four orientations were considered. Fundamentally, the optimal solution was determined using the Equation (7) for the scenarios of different orientations. For example, when the BIPV-DSF faced due north, the optimal solution refers to the non-dominated solution point where the respective values of U in and SHGC out were 5.16 W/m 2 K and 0.81; in this case, the number of discomfort hours was 360, while the energy consumption (net thermal) was about 100.37 kWh/m 2 .

Optimising BIPV-DSF for High-Humidity Summer and Warm Winter Climate (Darwin)
Buildings 2023, 13, x FOR PEER REVIEW 8 of 14 Figure 4 shows the trade-off between the annual discomfort hours and net thermal energy consumption based on the variations of the most important design parameters (Uin and SHGCout) for the NatVent-DSF under the year-round high-humidity summer and warm winter climate (Darwin), where the four orientations were considered. Fundamentally, the optimal solution was determined using the Equation (7) for the scenarios of different orientations. For example, when the BIPV-DSF faced due north, the optimal solution refers to the non-dominated solution point where the respective values of Uin and SHGCout were 5.16 W/m 2 K and 0.81; in this case, the number of discomfort hours was 360, while the energy consumption (net thermal) was about 100.37 kWh/m 2 . In addition, a set of outcomes for the optimal solution among the 49 solutions for the BIPV-DSF (NatVent-DSF) with different orientations is presented in Table 7, which indicates the values of the various parameters of an optimal solution including the two objectives (f1(x) and f2(x)), minimum values of both objectives (min(f1) and min(f2)), the shortest distance of the optimal solution (non-dominated) to the "ideal point" (d(x)min), and the optimal values of the most important design parameters-Uin and SHGCout. Basically, 5.16 W/m 2 K for Uin and 0.81 for SHGCout were optimal values for most orientation scenarios of the BIPV-DSF within the given solution space, except for the east-facing scenario where the optimal Uin was 5.53 W/m 2 K.  In addition, a set of outcomes for the optimal solution among the 49 solutions for the BIPV-DSF (NatVent-DSF) with different orientations is presented in Table 7, which indicates the values of the various parameters of an optimal solution including the two objectives (f 1 (x) and f 2 (x)), minimum values of both objectives (min(f 1 ) and min(f 2 )), the shortest distance of the optimal solution (non-dominated) to the "ideal point" (d(x) min ), and the optimal values of the most important design parameters-U in and SHGC out . Basically, 5.16 W/m 2 K for U in and 0.81 for SHGC out were optimal values for most orientation scenarios of the BIPV-DSF within the given solution space, except for the east-facing scenario where the optimal U in was 5.53 W/m 2 K.

Optimising BIPV-DSF for Warm Temperate Climate (Sydney)
Given that both NatVent-DSF and NoVent-DSF were the most appropriate ventilation modes of the BIPV-DSF for the hot and cold months, respectively, in the warm temperate climate (Sydney), where the hot months fall from September to May while the cold months fall from June to August, the optimisation should take into account the two ventilation modes for the BIPV-DSF, while the optimal U in and SHGC out should be unique because the window components of the BIPV-DSF cannot be substituted in reality. As can be observed in Figure 5, the Pareto front is indicated based on the non-dominated solutions (the yellow dots) within the given solution space for the combined NatVent-DSF and NoVent-DSF operations across the year, which is apparent although both clusters of dominated and non-dominated solutions are not dispersed to each other to a large extent for all of the scenarios of orientation.

Optimising BIPV-DSF for Warm Temperate Climate (Sydney)
Given that both NatVent-DSF and NoVent-DSF were the most appropriate ventilation modes of the BIPV-DSF for the hot and cold months, respectively, in the warm temperate climate (Sydney), where the hot months fall from September to May while the cold months fall from June to August, the optimisation should take into account the two ventilation modes for the BIPV-DSF, while the optimal Uin and SHGCout should be unique because the window components of the BIPV-DSF cannot be substituted in reality. As can be observed in Figure 5, the Pareto front is indicated based on the non-dominated solutions (the yellow dots) within the given solution space for the combined NatVent-DSF and NoVent-DSF operations across the year, which is apparent although both clusters of dominated and non-dominated solutions are not dispersed to each other to a large extent for all of the scenarios of orientation.  Table 8 shows the details of the optimal solutions for the BIPV-DSF for different orientations in Sydney. Apparently, 5.87 W/m 2 K for Uin and 0.81 for SHGCout were optimal values for most orientation scenarios of the BIPV-DSF among the given feasible solutions, except for the south-facing scenario where the optimal Uin was 5.16 W/m 2 K. This was possibly due to the relatively low sun exposure when the orientation of the BIPV-DSF was fixed to due south; in this case, a lower Uin can reduce the heating demand during cold months and therefore reduce the overall thermal energy consumption. By comparison, it did not make a notable difference in thermal performance for the BIPV-DSF facing north or south in Darwin, as it is closer to the equator. Furthermore, a significantly high number of discomfort hours can be noticed for all the scenarios of Sydney, because such a crowded office module can impact greatly on its indoor thermal comfort [49]. However, this issue did not affect the design parameter optimisation within the given solution space.  Table 8 shows the details of the optimal solutions for the BIPV-DSF for different orientations in Sydney. Apparently, 5.87 W/m 2 K for U in and 0.81 for SHGC out were optimal values for most orientation scenarios of the BIPV-DSF among the given feasible solutions, except for the south-facing scenario where the optimal U in was 5.16 W/m 2 K. This was possibly due to the relatively low sun exposure when the orientation of the BIPV-DSF was fixed to due south; in this case, a lower U in can reduce the heating demand during cold months and therefore reduce the overall thermal energy consumption. By comparison, it did not make a notable difference in thermal performance for the BIPV-DSF facing north or south in Darwin, as it is closer to the equator. Furthermore, a significantly high number of discomfort hours can be noticed for all the scenarios of Sydney, because such a crowded office module can impact greatly on its indoor thermal comfort [49]. However, this issue did not affect the design parameter optimisation within the given solution space. Same as in the case of Sydney, both NoVent-DSF and NatVent-DSF were selected for the Canberra case's optimisation and the optimal values of the most important design parameters were unique. Specifically, in this case, the NoVent-DSF mode was applied to the cold months (falling from June to August), while the NatVent-DSF was applied to the hot months (falling from September to May). As shown in Figure 6, the Pareto front for the corresponding BIPV-DSF orientation scenario can be found by indicating the non-dominated solutions through the compact distribution of the feasible solutions.

Optimising BIPV-DSF for Cool Temperate Climate (Canberra)
Same as in the case of Sydney, both NoVent-DSF and NatVent-DSF were selected for the Canberra case's optimisation and the optimal values of the most important design parameters were unique. Specifically, in this case, the NoVent-DSF mode was applied to the cold months (falling from June to August), while the NatVent-DSF was applied to the hot months (falling from September to May). As shown in Figure 6, the Pareto front for the corresponding BIPV-DSF orientation scenario can be found by indicating the nondominated solutions through the compact distribution of the feasible solutions. Furthermore, the details of the optimal solution for the BIPV-DSF for different orientations in Canberra are given in Table 9, which shows the exact same optimal Uin and SHGCout values as that of the Sydney case; that is, Uin of 5.87 W/m 2 K and SHGCout of 0.81 were optimal values for the most orientation scenarios of the BIPV-DSF within the solution space, except for the south-facing scenario where the optimal Uin was 5.16 W/m 2 K due to the low sun exposure. Although a large number of discomfort hours also can be found for Canberra's scenarios because of the small-sized office module, the optimal values of Uin and SHGCout were determined explicitly. In general, the SHGCout was supposed to be higher for the BIPV-DSF under all the three climate zones. Furthermore, a lower Uin of the BIPV-DSF was desired for the hot climate (Darwin), while the BIPV-DSF with a higher Uin was expected for both cool temperate (Canberra) and warm temperate (Sydney) climates. Furthermore, the details of the optimal solution for the BIPV-DSF for different orientations in Canberra are given in Table 9, which shows the exact same optimal U in and SHGC out values as that of the Sydney case; that is, U in of 5.87 W/m 2 K and SHGC out of 0.81 were optimal values for the most orientation scenarios of the BIPV-DSF within the solution space, except for the south-facing scenario where the optimal U in was 5.16 W/m 2 K due to the low sun exposure. Although a large number of discomfort hours also can be found for Canberra's scenarios because of the small-sized office module, the optimal values of U in and SHGC out were determined explicitly. In general, the SHGC out was supposed to be higher for the BIPV-DSF under all the three climate zones. Furthermore, a lower U in of the BIPV-DSF was desired for the hot climate (Darwin), while the BIPV-DSF with a higher U in was expected for both cool temperate (Canberra) and warm temperate (Sydney) climates.

Conclusions
This paper presents the optimisation of a BIPV-DSF applied to an office module for achieving the best performance of thermal energy conservation and indoor thermal comfort for the office in the context of three distinctive Australian climate zones. In terms of two different ventilation modes of the BIPV-DSF, namely naturally-ventilated and nonventilated BIPV-DSFs, the following most important design parameters of the BIPV-DSF in the four cardinal directions (north, south, east, and west) were further optimised using the Pareto optimality method: • Thermal transmittance of internal window of the BIPV-DSF (U in ); • Solar heat gain coefficient of external window of the BIPV-DSF (SHGC out ).
Based on the optimisation results presented for the three climate zones, the respective optimal design solutions of the BIPV-DSF-equipped office module among a set of feasible solutions can be summarised as follows:

•
In the high-humidity summer and warm winter climate zone (Darwin): naturallyventilated BIPV-DSF with a semi-transparent perovskite-based PV glazing either facing north, south or west being utilised throughout the year. In this case, a U in of 5.16 W/m 2 K and a SHGC out of 0.81 are optimum; while the U in and SHGC out should be 5.53 W/m 2 K and 0.81, respectively, when the BIPV-DSF is east-oriented.

•
In the warm temperate climate zone (Sydney): a semi-transparent perovskite-based PV glazed BIPV-DSF facing north, east and west should be non-ventilated and naturallyventilated during the cold and hot months, respectively. In this case, a U in of 5.87 W/m 2 K and SHGC out of 0.81 are optimum. However, the U in and SHGC out should be 5.16 W/m 2 K and 0.81, respectively, when the BIPV-DSF is south-oriented.

•
In the cool temperate climate (Canberra): a semi-transparent perovskite-based PV glazed BIPV-DSF facing north, east and west should be operated as non-ventilated and naturally-ventilated modes, respectively, during the cold and hot months. In this case, a U in of 5.87 W/m 2 K and SHGC out of 0.81 are optimum, while the respective U in and SHGC out should be 5.16 W/m 2 K and 0.81 when the BIPV-DSF is facing south.
However, the optimisation presented in this paper was confined to a given solution space for both U in and SHGC out , which was based on the International Glazing Database in the simulation programme (TRNSYS) used during the course of the study. Future research is needed to investigate a bigger database of the window components for the BIPV-DSF and hence further refine the optimisation. On the other hand, a larger office building may be considered for the future study so as to reduce the excess number of discomfort hours from the crowded office module. In addition, further study on a multi-storey office building will also help understand BIPV-DSF performance in the real world.
Funding: This research received no external funding.

Data Availability Statement:
The authors confirm that the data supporting the findings of this study are available within the article.

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