Multi-Objective Optimization of Bifacial Photovoltaic Sunshade: Towards Better Optical, Electrical and Economical Performance

Abstract

Bifacial photovoltaic sunshade (BiPVS) is an innovative building-integrated photovoltaic (BIPV) technology. Vertically mounted BiPVS is capable of converting part of the incident solar radiation into electricity, regulating the indoor heat gain from solar penetration and improving daylighting. An excellent BiPVS design should comprehensively consider its impact on building performance and economic viability. This study aims to address this issue by proposing a parametric design-based multi-objective optimization (MOO) framework to maximize indoor useful daylight illuminance, minimize air-conditioning energy consumption, and shorten the payback period by optimizing BiPVS design parameters. The framework utilizes the Ladybug, Honeybee, and Wallacei plugins on the Rhino-Grasshopper simulation platform. It validates the optimization potential of BiPVS in a typical office located in a hot summer and warm winter zone. The results indicate that BiPVS has significant energy-saving and daylighting potential. Compared to the baseline model without BiPVS, useful daylight illuminance is increased by 39.44%, air-conditioning energy consumption is reduced by 12.61%, and the economically satisfactory payback period is 4.80 years. This study provides a practical solution for the competing objectives of daylighting and energy saving in buildings with significant renewable energy utilization. The developed framework is highly efficient and versatile and can be applied to other BIPV designs, which benefits the realization of carbon-neutral goals in the building sector.

1. Introduction

Energy consumption in the building sector accounts for around 20% of total energy consumption in China [1]. Building energy saving is of great significance to cope with the issues of energy shortages and environmental pollution [2]. Solar building integration, or BIPV (building-integrated photovoltaic) technology, has shown great potential for realizing carbon neutrality [3]. Photovoltaic modules were applied on the roof and envelops of various buildings and can be utilized as sunshade structures to block excessive solar radiation. Numerous investigations have demonstrated the advantages of renewable energy exploration, building cooling load reduction, comprehensive energy saving, as well as carbon dioxide emission mitigation [4,5]. BIPV has been recognized as an important measure to decarbonize the power system towards sustainable development.

Recently, the application of bifacial photovoltaic technology in the building sector was brought forward with the rapid development of bifacial PV technology [6,7,8]. The bifacial photovoltaic module is composed of double glass sheets with sandwiched bifacial photovoltaic cells and can convert incident solar energy on both front and rear sides into electricity [9,10]. Bifacial photovoltaic technology is already mature, with commercially available products’ comprehensive solar-to-electricity conversion efficiency exceeding 24.0%. For example, Baumann et al. utilized vertically mounted bifacial PV modules in combination with green roofs in Switzerland [6]. Vertically installed photovoltaic modules can effectively avoid the adverse effects of dust and snow on the photoelectric conversion efficiency and help save valuable space in urban environments. Experimental results have shown that a vertically mounted bifacial PV module occupied the least amount of space yet generated a similar amount of electricity to that of traditional inclined installed PV modules.

Due to the limited roof area in high-rise buildings, it is more realistic and efficient to utilize bifacial PV technology on vertical facades or windows. In 2015, Soria et al. utilized bifacial photovoltaic modules integrated with double-skin vertical facades [7]. The front side of the PV module faces the exterior, blocks the incident solar radiation, and generates electricity. The rear side faces the wall and turns part of the reflected solar radiation into electricity. The results showed that the annual power generation of the bifacial photovoltaic curtain wall increased by 25% compared with the ordinary mono-facial photovoltaic curtain wall. However, the reflecting mirror may cause light pollution issues in the urban environment, and the back side of the photovoltaic module may not be able to dissipate heat. The comprehensive electrical efficiency might be decreased with increasing cell temperature. In addition, the lifespan of photovoltaic modules might be influenced due to the long-term high temperature.

There are other studies directly utilizing bifacial PV modules as building facades and windows. Chen et al. tested the performance of customized semi-transparent bifacial PV modules as the roof and two vertical facades in a prefabricated building [8]. The front side of the modules converted part of the incident solar energy into electricity directly. Part of the transmitted solar radiation through the roof module incident on the rare side of the vertical facade module and enhances the power output. The testing results showed peak electricity generations of 135 W (roof), 103 W (southeast facade), and 80 W (southwest facade) per module with an area of 1.645 m² in August under the climate of Guanghan, China. Though replacing traditional building facades with bifacial PV modules helps reduce energy and material consumption, there were also drawbacks, such as lower thermal resistance and higher indoor heat gain/loss in cooling/heating seasons. Ko [11] proposed a dielectric/metal/dielectric structure with a selective solar reflector to enhance the solar-to-power conversion rate of bifacial photovoltaic modules. The views were not completely blocked, as the facade was semi-transparent. The testing results demonstrated a 13.2% increase in power output by utilizing the solar reflector.

On the contrary, the thermal insulation issue was taken into consideration in the study of Assoa et al. [12], in which the performance of a building-integrated bifacial photovoltaic ventilated facade was experimentally studied. The facade generated 63.8 kWh/m² electricity annually, with year-round electricity generation efficiency of 6.3%. The facade helped to reduce the indoor heat gain in summer and heat loss in winter, mainly due to the additional insulation layer. Further, Tina et al. compared the thermal performance of BIbPV (ventilated building integrated bifacial photovoltaic with a reflection surface on the internal wall) and BIPV (non-ventilated building integrated photovoltaic) [13]. The electricity production of the BIbPV facade was 7.4% higher than the BIPV facade. Meanwhile, an increase in heat loss during winter was observed, which caused additional energy consumption for room heating. Although incident solar radiation and electricity production by the rear side of the BIbPV are important for the bifacial photovoltaic modules, they were not analyzed in previous studies [14,15]. As the price of bifacial photovoltaic modules is commonly higher than mono-facial photovoltaic modules, the payback period is extended if the rear side of the module only generates little electricity with limited incident solar radiation.

One possible method for enabling incident solar radiation on both sides is to mount the bifacial photovoltaic modules vertically to the building facades. This is brought forward as bifacial PV sunshade (BiPVS) [16]. The PV modules directly receive solar radiation from both the front and rear sides while reducing the indoor cooling load from solar penetration. Accordingly, the power output can be enhanced compared with the aforementioned design without compromising the thermal insulation of the facade. This PV sunshade is mostly suitable for buildings with strong solar radiation and high cooling demand.

Table 1. Comparison of bifacial PV modules applications in buildings.

Application Form	Schematic Diagram	Characteristics
Curtain window		The power generation ability of the rear side was not fully explored.
Roof and facade		The thermal insulation was reduced, and cooling load would increase.
Vertically mounted sunshade (BiPVS under investigation)		The incident solar radiation from both front and rear sides were fully explored, without compromising thermal insulation of the envelop.

lists the comparison of different application measures of bifacial PV modules in building envelopes. However, the energy-saving potential was not fully explored as only one fixed set of parameters was applied in [16]. Therefore, the BiPVS was not tailored for the optimized combination of optical–electrical–thermal properties. As a matter of fact, daylighting and photovoltaic power generation are competing objectives and need to be carefully balanced.

Multi-objective optimization (MOO) is widely employed to address conflicting objectives in various fields. Common optimization algorithms include Harmony Search Algorithms, Ant Colony Optimization, Simulated Annealing, and many others [17,18]. Among these, multi-objective genetic algorithms have been extensively used and researched in building-related applications [19]. For instance, Samarasinghalage et al. [20] developed a multi-objective optimization framework using NSGA-II to optimize the design of building-integrated photovoltaic (BIPV) facades, balancing energy performance and cost. Similarly, Yi et al. [21] utilized a MOO approach with the NSGA-II to optimize the structural integrity, daylighting, and material cost of skylight roofing systems. In another study, Fan et al. [22] employed the SPEA-2 to optimize the facade shading ratio of a gymnasium during summer operating hours, aiming to reduce indoor radiation and glare index. These examples highlight the widespread application of MOO methods in architectural design and building performance analysis to achieve optimal trade-offs among multiple objectives, such as energy consumption, daylighting, power generation, and cost. The NSGA-II, incorporating elitism to ensure solution diversity and employing fast non-dominated sorting and crowding distance calculation for computational efficiency, effectively enhances convergence towards the Pareto front [23,24].

Despite current research showcasing the potential of bifacial photovoltaics, a critical gap exists in optimizing the design of BiPVS to fully unlock its capabilities. In order to fully explore the potential of BiPVS, a multi-objective optimization (MOO) framework was developed in this study. The purpose was to balance the competing objectives of daylighting, building energy saving, and payback period through proper BiPVS design. The methodology was practiced in a typical office in Shenzhen, with a hot summer and warm winter climate. This study leverages the Wallacei plugin (v2.7), based on the NSGA-II algorithm, for multi-objective optimization. This plugin seamlessly integrates with other analysis plugins within the Rhino platform (v7.18), enabling a comprehensive workflow encompassing parametric design, performance simulation, and multi-objective optimization. This approach eliminates the need for multiple platforms, offering a user-friendly experience for architects and designers. The proposed BiPVS and optimization method can be applied to different buildings and can fulfill unique building functions and occupant preferences. The rest of this paper is organized as follows: The BiPVS and MOO methodology and the optimization framework are introduced in Section 2. The case study office in Shenzhen is illustrated in Section 3, and the optimization results are presented in Section 4. The main findings and limitations of this work are discussed in Section 5, with the main conclusions presented in Section 6.

2. Methodology

2.1. Multi-Objective Optimization (MOO)

MOO is particularly useful in providing solutions for problems with competing objectives. The major advantage is that MOO helps to save time compared to the traditional one-parameter-at-a-time-sensitive analysis [25]. There are mainly two MOO approaches [26]: One approach utilizes mathematical principles to convert multiple objectives into one index by providing a series of weights for each objective. In this approach, the overall performance of each solution is evaluated by the weighted sum of every objective. The other one is the non-traditional approach, which uses stochastic rules to find a set of Pareto frontier solutions. Pareto frontier solution sets include the non-dominated solutions within the entire feasible variable combinations. The latter approach is increasingly preferred by architects and engineers because it not only enables the consideration of multiple objectives, but also outputs a set of outstanding solutions for designers to choose from based on esthetic considerations and occupant preferences.

In recent years, MOO has been widely applied in architecture design and investigations, covering building layout design [27], envelope design [20,28], and window and skylight system design [21,29]. Multiple objectives are taken into consideration in existing studies applying MOO to improve building fenestration design, as well as building-integrated photovoltaic designs, as listed in

Table 2. MOO applied in building facade designs.

Reference No.	Research Object	Multiple Objectives
[17]	Design energy-efficient shading devices	Reduction in energy consumption Enhancing the comfort level of inhabitants
[20]	Building-integrated PV Envelope design	Maximizing life cycle energy consumption Minimizing life cycle cost
[21]	A skylight roof system	Maximizing the daylight into the indoor space Maximizing the structure strength Minimizing the overall material cost
[22]	Gymnasium facade shading	Hourly average illuminance Hourly average solar radiation accumulation Glare during the opening hours in summer
[29]	Envelope design Facade photovoltaic-integrated surfaces The cooling setpoint	Minimizing energy demand, Maximizing energy generation from PV panels Maximizing adaptive thermal comfort levels for an annual period
[28]	Climate-adaptive building envelope design in a hot and humid climate	d. Minimizing cooling load e. Maximizing daylighting performance during summer
[30]	PV integrated shading devices	Minimizing the total annual net energy electricity use Maximizing the amount of energy converted into electricity by the PV cells Maximizing the daylighting level in the zone measured as the continuous daylight autonomy
[31]	A typical high-rise residential building	Lowest total air conditioning and heating load Highest photovoltaic power generation Lowest investment cost

.

In this study, multi-objective optimization is accomplished using the Wallacei plugin integrated with the Grasshopper parametric design and simulation platform [32]. Wallacei employs the NSGA-II genetic algorithms, which is used to find a set of non-dominated solutions [33]. The principle of genetic algorithms is similar to the evolutionary process in nature and is suitable for providing solutions to problems with competing objectives. A random initial population of solutions (individuals) is created and the fitness (degree of fitting to the optimization objectives) of each solution (individual) is evaluated. Following this, the fittest solutions are selected from the population, which undergoes genetic recombination and mutation to produce a new set of solutions. This process is iterated in a cycle until a predetermined end criterion is reached.

2.2. BiPVS MOO Framework

The multi-objective optimization design of BiPVS consists of three steps: developing the building model and setting the value ranges of the parametric design parameters; setting appropriate optimization objectives and performance simulation; and obtaining the optimized design parameters with evolutionary algorithm. Figure 1 is the MOO process flowchart.

In this study, three competing objectives were applied: to maximize the period of useful daylight illuminance (UDI_500–2000, hour) [34], to minimize the annual building energy consumption for air conditioning (EC, kWh/m²), and to minimize the payback period of the BiPVS (PB, year). The multi-objective optimization problem [35] and its objective function can be described as follows:

$$F\left(y\right)=\underset{x\in {\mathsf{ℝ}}^n}{min}\left[f_1\left(y\right),f_2\left(y\right),f_3\left(y\right)\right]$$

(1)

$$y=g\left(x\right)$$

(2)

$$f_1\left(y\right)=-UD{I}_{max}\left(x\right)$$

(3)

$$f_2\left(y\right)=E{C}_{min}\left(x\right)$$

(4)

$$f_3\left(y\right)=P{B}_{min}\left(x\right)$$

(5)

Subject to the following:

$$k_i\left(x\right)\le 0,i=1,2,\dots ,I$$

(6)

$$h_j\left(x\right)=0,j=1,2,\dots ,J$$

(7)

where x represents a candidate solution in the decision space ${ℝ}^n$. The objective function f₁(y) corresponds to the maximizing of the period of useful daylight illuminance. Due to the MOO goal being minimization, f₁(y) was converted to a negative value. The f₂(y) is minimization of the annual building energy consumption for air conditioning and the f₃(y) is minimization the payback period of the BiPVS. k_i(x) and h_j(x) represent the inequality constraints and equality constraints respectively, while I and J denote the corresponding numbers of each type of constraint.

(1)

The objective of better daylighting (UDI_500–2000)

According to the Standard for daylighting design of Buildings (GB 50033-2013) [36], the threshold for effective daylighting is 500~2000 lux to meet the general office operation requirement. In the national Assessment standard for green building (GB/T50378-2019) [37], the main indoor space should have at least 60% area to meet the lighting requirements within over 4 h per day. Therefore, UDI_500–2000 was adopted as an index representing the objective of better daylighting. The Radiance-based plugin Ladybug (v1.8.0) [38] was utilized to simulate the solar irradiance and daylighting condition. Radiance is a software capable of predicting the illuminance levels from windows and skylights based on the backward ray tracing algorithm [39].

(2)

The objective of less building energy consumption (EC)

In this study, the annual air conditioning system energy consumption was taken as the index representing the objective of less building energy consumption. The EnergyPlus-based plugin Honeybee (v1.8.0) [40] was used to simulate the energy consumption. EnergyPlus is a comprehensive building performance simulation tool that can model the radiative and convective heat transfer between building surfaces and indoor and outdoor environments, as well as the conductive heat transfer through walls, roofs, floors, and other building envelope components. These capabilities ensure accurate simulation of the building environment and energy consumption [41]. Some studies have used comparisons with standard test cases to demonstrate the reliable performance simulation capability of Honeybee based on EnergyPlus [42,43]. Li et al. conducted experimental validation of the annual energy performance for five different tested film-and-glazing combinations, showing good agreement between EnergyPlus simulation results and measured data, with a maximum deviation within 3.0 °C [44]. Similarly, the accuracy of daylighting tools has also been validated through comparisons with standard test cases and experimental measurements in multiple studies [45,46,47]. The reliability of the simulation software itself, combined with the reasonableness of the input parameters, ensures the accuracy of the simulation results.

(3)

The objective of a shorter payback period (PB)

The emphasis on the payback period coincides with reality consideration, since a shorter payback period tends to attract more building owners to adopt BIPV technologies. Payback period (PB) refers to the time required to recoup the initial investment cost. Factors influencing PB are inherently time-dependent [48]. Taking a conventional mono-PV system as an example, its initial investment, project management costs, and PV cell degradation rates are all dynamic processes. Fluctuating financial aspects, such as time-of-use electricity pricing policies and government subsidies, are also crucial [49,50]. Evaluating the payback period of PV systems is a complex topic due to the multistage lifecycle of energy systems [51].

This study simplifies this complex process by focusing on two primary aspects: the system’s initial cost and the total revenue generated from electricity production. Assuming a self-consumption scenario for the BiPVS, the total cost is determined by the initial installation cost and ancillary costs (including system accessories and operating expenses, which are assumed to be a fixed value). The revenue is calculated based on the annual electricity generation of the BiPVS and a fixed electricity price. The PB is then determined by the ratio of total cost to revenue, and this ratio is incorporated into the multi-objective optimization process. This process is shown in Equation (8). The photovoltaic power generations are calculated with the Renewables plugin.

$$PB=\frac{\left(C_i+C_r\right)\times S}{Q\times T}$$

(8)

In which

• PB is the static payback period, y;
• S is the total installed area of the vertical bifacial PV sunshade modules, m²;
• Q is the total annual power generation of the vertical double-sided PV sunshade system, kWh;
• C_i is the cost of PV modules per unit area, CNY/m²;
• C_r is the cost of PV system accessory facilities per unit area, CNY/m²;
• T is the electricity price of power grid, CNY/kWh.

Figure 2 shows the MOO workflow developed on the Rhino-Grasshopper platform. The Wallacei plugin initiates a population of random solutions as the 1st generation, i.e., the combination of designing variables. Then, the daylighting, energy, and economic performance of these solutions are simulated. Once the simulation of the 1st generation solutions is completed, the competing objectives are analyzed based on the preset indexes. Accordingly, the 2nd generation solutions are determined based on genetic operator principles, including crossover and mutation rates. The evolution proceeds spontaneously towards better daylighting, energy, and economic performance. Then, the competing objectives were simulated and analyzed for the 2nd generation solutions. This process goes on until the preset generation number is reached.

3. Case Study

In this study, BiPVS was applied to a typical office in Shenzhen, China. Offices, as high-frequency occupancy spaces, have fixed building codes to follow at the design level, making them representative. The settings of the baseline model in this study are all based on national standards to ensure the broad applicability of the research results. The design parameters were optimized with the proposed MOO framework described in Section 2. Figure 3 shows the structure of the BiPV module and schematic diagram of BiPVS application. A typical BiPV module comprises bifacial PV cells sandwiched between double glazing layers. The PV cells coverage rate can be altered by controlling the total cells area. Multiple BiPV modules are vertically mounted to the wall. Both front and rear surfaces of the BiPV modules can receive beam radiation depending on the solar position. This allows for better exploitation of the advantages of bifacial PV technology over mono-facial PV technology, compared to previous studies on the application of bifacial photovoltaic technology in building envelopes. Moreover, both surfaces continuously generate power from the diffused solar radiation. Therefore, the BiPVS has the potential to generate more electricity than mono-facial PV sunshade of the same surface area throughout the year.

The office is south-oriented with dimensions of 13.20 × 8.40 × 3.90 m. The window is on the south wall with BiPVS. The window-to-wall ratio is 0.6. The other walls, floor, and ceiling are adjacent to other rooms with a similar indoor temperature and are treated as adiabatic. The office is equipped with a central air-conditioning system, and the room temperature is preset to be 26.0 °C in cooling season and 18.0 °C in heating season. The system COP is 3.5 for cooling and 4.5 for heating. The internal loads and operation schedules were set according to the national standard General code for energy efficiency and renewable energy application in buildings (GB 55015-2021) [52]. Other parameters are described in

Table 3. Description of the building simulation parameter.

Parameter	Unit	Value
Window glazing transmittance	-	0.89
HVAC system	-	Ideal loads air
Internal load lighting	W/m2	8
Internal load equipment	W/m2	15
U-value window	W/(m2-K)	2.5
Solar heat gain coefficient	-	0.35

.

In total, seven parameters were adopted to realize the optimized design, including the number of PV modules, width of the modules, height of the modules, distance of the modules edge from the wall, PV cell coverage within the modules, angle between the front of the module and the mounting wall, and solar transmittance of the window glazing. The influences of these parameters on the daylighting, energy, and economic performance of the BiPVS are different and often conflicting. By installing BiPVS with larger module areas and cells coverage rate, more electricity can be generated. However, daylighting and indoor heat gain from solar radiation in the heating season may be sacrificed. Therefore, the area and coverage ratio of the PV cells need to be carefully designed to balance the PV power generation and building energy consumption. The value ranges of these design parameters for BiPVS optimization are listed in

Table 4. Value ranges of the design parameters for BiPVS optimization.

Design Parameter	Unit	Value Ranges
BiPVS module numbers	-	2~17, with an interval of 1
Width of the modules	m	0.3~1.0, with an interval of 0.1
Height of the modules	m	2.4~3.0, with an interval of 0.1
Distance of the modules edge from the wall	m	0.0~0.3, with an interval of 0.1
Angle between the front side of the modules and the wall	°	60~120, with an interval of 5
PV cells coverage rate	%	50~100, with an interval of 1
Window glazing transmittance	-	0.10~0.90, with an interval of 0.01

.

The typical meteorological data of Shenzhen, China, were used [53]. Shenzhen is located in Southeast China, at longitude 114.1 °E and latitude 22.55 °N. Figure 4 shows the monthly averaged ambient temperature and accumulated global solar radiation. The ambient temperature ranges from 4.0 °C to 38.0 °C, and the average temperature is 22.9 °C. The accumulated global solar radiation reaches up to 1509.1 kWh/m² throughout the year. The cooling season lasts over six months in Shenzhen. With fast economic growth and increasing living standards, more and more buildings have installed air-conditioning systems, leading to tremendous energy consumption. This situation presents a significant opportunity for energy savings in the building sector. Moreover, the Shenzhen government has issued supportive policies for building photovoltaics development, encouraging the distributed photovoltaic applications on the principle of “build as much BIPV as possible” according to local conditions.

In recent years, the price of PV cells and modules has dropped significantly thanks to the technology being upgraded. Based on market investigation, the value of C_i was set to be 340 CNY/m². The value of C_r was largely dependent on the specific structure and material types, and it was set to be 30% of C_i in this study. In practical application, the value of C_i should be smaller in systems with large photovoltaic installed capacity and needs to be decided according to the detailed system design and equipment selection. The value of T was set as 0.54 CNY/kWh according to the pricing strategy of the Southern Power Grid. The solar power generation efficiency was set to be 19.0% for the front side of the bifacial PV modules, whereas the electrical efficiency of the rear side was assumed to be 70% of the front side. The temperature coefficient was set to be −0.37%/°C. In the optimization process, the iteration would stop after 20 generations of 40 solutions. The specific parameters are described in

Table 5. Description of the parameters for the optimization.

Name	Value
Generation Size	40
Generation Count	20
Crossover Probability	0.9
Mutation Probability	1/7

.

4. Optimization Result

The simulations were performed on a computer equipped with an Intel^® Core^TM i7-6700HQ CPU (@ 2.60 GHz, 4 cores) and 16.0 GB RAM. Total run time was approximately 29 h.

Figure 5 shows the distribution of the optimization objective index values of 800 individuals in 20 generations. The Pareto frontier solution set contains 68 solutions, i.e., 68 BiPVS design parameter combinations. The X, Y, and Z axes correspond to the three optimization objectives, i.e., minimization of building air conditioning energy consumption EC, maximization of effective daylighting hours UDI_500–2000, and minimization of static investment payback period PB, respectively. The blue dots represent all individuals, that is, the design parameter combinations of semi-transparent photovoltaic sunshade, and the red dots represent the Pareto frontier solutions of the last generation.

The parameter distributions in the Pareto frontier solution set are shown in Figure 6. Among the seven parameters, the module number of BiPVS ranged from 5 to 17, the module width ranged from 0.3 m to 1.0 m, and the module height ranged from 2.6 m to 3.0 m. The total installation area ranged from 4.5 m² to 51.0 m², providing architectural designers with a wealth of choices. Meanwhile, the distances between the PV module edge and the wall were 0 m (installed adjacent to the wall), 0.1 m, and 0.2 m, whereas the candidate value of 0.3 m did not appear. The angle between the front of the component and the wall ranged from 65° to 120°, and the median of the optimization solution set was 110°. The cell coverage ratio ranged from 66% to 100%, with a median value of 98%, and the coverage ratio within the 94% to 100% range dominated the alternative solutions. The window glazing transmittance varied between 0.36 and 0.89, with a median value of 0.60.

The baseline model did not install any sunshade, therefore, there was no cost to install BIPVS. The annual building energy use intensity of the baseline model was 125.72 kWh/m², of which the air-conditioning energy consumption was 48.76 kWh/m², and the effective daylighting duration was 6.90 h. Figure 7 shows the total multi-objective optimization results of the Pareto frontier solution set. The parallel coordinate plot (PCP) ranks all solutions based on their fitness values, with fine lines colored from red to blue representing solutions from the last to the first individual. The Y-axis numbers indicate the specific results of all schemes, with values closer to the lower end of the Y-axis indicating proximity to the optimization objectives. Compared to all solutions, the Pareto front solutions show effective daylight hours ranging from 8.26 to 9.81 h. Air conditioning energy consumption ranges from 42.61 kWh/m² to 47.18 kWh/m², and total building energy consumption ranges from 120.63 kWh/m² to 124.89 kWh/m². Annual PV generation varies from 927.55 kWh to 8697.89 kWh, primarily depending on the total area of PV modules. Correspondingly, the payback period ranges from 3.87 years to 7.20 years. Compared with the baseline model, BiPVS had a significant impact on building performance.

Among the Pareto frontier solutions, solutions G9I3, G17I2, and G19I0 were capable of achieving the maximum daylighting hours, minimum air conditioning energy consumption, and minimum investment payback period, respectively. They can be taken as the single-optimal solutions in this office case study. The optimization results with these solutions are shown in

Table 6. Optimization results of the three single-optimal solutions.

Optimization Objectives	Unit	Solution G9I3	Solution G17I2	Solution G19I0
UDI500–2000	hour	9.81	9.62	9.80
Energy consumption of air conditioning system	kWh/m2	45.54	42.61	47.18
Payback period	year	6.90	4.80	3.87
Annual PV power generation	kWh	2562.74	8697.89	950.83

. Compared with the baseline model without any sunshade, the three optimized solutions improved the natural daylighting hours by 19.68~42.21%. The building air conditioning energy consumption was reduced by 3.25~12.61%, reflecting good energy-saving effects and environmental benefits. Considering that the life span of photovoltaic components is generally over 20 years, all solutions had considerable net income throughout the life cycle.

The optimized solution set did not contain any solution absolutely superior to other solutions. Since no weights were involved, the average fitness values of all Pareto-optimal solutions were ranked to select the optimization result. The study chose solution G17I2, which ranked first, as the final outcome. This solution performed well across the three objectives, exhibiting high photovoltaic generation capabilities and an economical payback period for the photovoltaic system. The corresponding optimization parameters are shown in

Table 7. Design parameters of solution G17I2.

Design Parameter	Unit	Value
Range of BiPVS module numbers	-	17
Width of the modules	m	1
Height of the modules	m	3
Distance of the modules edge from the wall	m	0
Angle between the front side of the modules and the wall	°	115
PV cells coverage rate	%	98
Window glazing transmittance	-	0.89

.

The number of photovoltaic modules was 17, and the width and height of the modules were 1.0 m and 3.0 m, respectively. The component height was higher than the window height and could block more direct solar radiation. Meanwhile, this means that the renewable solar energy could be utilized to a larger extent. Therefore, the major advantage of solution G17I2 was the high PV power generation without large damage to the daylighting performance. As a matter of fact, the UDI_500–2000 value increased from 6.90 h of the baseline case without any sunshade to 9.62 h. Solution G17I2 was also the one with the least building energy consumption and the most annual photovoltaic power generation. Compared with the baseline case, solution G17I2 reduced air conditioning energy consumption by 12.61%, and increased effective daylighting time by 39.44%, with a payback period of the total investment of 4.80 years. Figure 8 shows the simulation results of the UDI_500–2000 distribution, building energy consumption, and photovoltaic power generation simulation with solution G17I2. It should be noted that heating energy consumption in January is negligible, at approximately 0.03 kWh/m².

5. Discussion and Limitation

This study proposes a MOO framework to improve the daylighting, energy, and economic performance of BiPVS. This framework is efficient, versatile, and applicable to other BIPV technologies, contributing to achieving carbon neutrality targets in the building sector. The variable distribution patterns of the Pareto solutions provide insights for general BiPVS design guidelines in Shenzhen. As shown in Figure 6, the median number of PV modules among the 68 Pareto front solutions is 12, which is higher than the median value of 10 in the initial range of 2–17. 75% in the solutions opted for heights greater than 2.7 m. Meanwhile, the numerical distribution of PV module widths is skewed to the right, indicating a preference for wider dimensions. For the distance of PV module edges to the wall, 75% of the solutions chose values less than or equal to 0.1 m, with 69% opting for 0. This suggests that in vertical installations, spacing between the module and the mounting surface for ventilation and cooling is practically unnecessary. Overall, these findings are likely related to Shenzhen’s climate, where cooling loads dominate air conditioning operation. Larger, more numerous BiPVS units positioned closer to windows can block more incident solar radiation, benefiting the building’s energy efficiency.

As analyzed in Section 4, solution G17I2 was chosen as the optimal solution because of the highest building energy saving. Meanwhile, the payback period was a short 4.8 years, under 5 years, which is economically acceptable. This payback period is only one year longer compared to solution G19I0, which has the shortest payback period. It is also shorter than the payback period of 5.31 years in [16], where BiPVS design parameters were not optimized. Notably, after recovering the PV system investment, the PV power generation would bring financial benefits to the building owner. From a practical point of view, solution G17I2 may attract more building owners, considering that the lifespan of buildings (usually over 50 years) and PV modules (generally 20 years) are much longer than the payback period of less than 5 years. Table 6 shows that the annual PV power generation is 8697.89 kWh, which can be converted to savings of 4696.86 CNY on electricity bills with the current electricity price for this single office.

However, this study has limitations that need to be addressed in future investigations. Daylight utilization and landscape view are crucial when designing building fenestration and shading devices. This study only considers the spatial and temporal ratio of suitable daylighting availability. The landscape view may be negatively affected by photovoltaic modules, especially when the modules and the window have extremely small angles. The non-visual impact of sunlight, particularly on the occupants’ circadian rhythm, is not included in this study. This study applies the MOO of BiPVS to a typical office in a hot summer and warm winter climate. However, BiPVS cannot block high-angle incident radiation, and its ability to reduce indoor cooling loads around noon is likely to decrease significantly. Future research should comprehensively consider different climates and building types, as well as the potential of applying BiPVS on facades with different orientations. Additionally, future studies should conduct experimental research on BiPVS to fully analyze its non-visual impacts on building occupants and influences on the landscape. The building operation schedules and occupants’ preferences will also significantly influence the optimization results.

6. Conclusions

BiPVS is an innovative BIPV technology that employs bifacial PV modules as building sunshade. It aids in appropriate daylighting, generates renewable energy, and brings economic benefits after the investment payback period. BiPVS can transform incident solar radiation into electricity on both front and rear sides, producing a larger amount of electricity compared with traditional BIPV applications. The effective design of BiPVS can enhance the overall performance and encourage building owners to adopt this new technology by shortening the payback period.

To optimize BiPVS design and balance potentially conflicting performance objectives, this study developed a multi-objective optimization (MOO) framework. This framework was applied to a typical office building in Shenzhen, China, considering seven design parameters: the number, width, and height of PV modules; distance from the wall; angle between the front surface of the modules and the wall, the PV cell coverage rate; and window glazing solar transmittance.

The MOO process yielded 68 Pareto-optimal solutions, demonstrating significant improvements over a baseline model without sunshades. Effective daylighting hours increased from 6.90 to over 8.20, while air conditioning energy consumption decreased from 48.76 kWh/m² to less than 47.20 kWh/m². Payback periods for these solutions ranged from 3.87 to 7.20 years. Out of the 68 Pareto frontier solutions, solution G17I2 was chosen as the optimized BiPVS design with a large scale of PV application and improved performances. It can reduce 12.61% air conditioning energy consumption, and the effective daylighting time can be improved by 39.44%, with an economically satisfactory payback period of 4.80 years.

Future research will explore BiPVS applications in diverse building types and climates, incorporating experimental validation. Additionally, future work will address the potential impact of BiPVS on views and incorporate subjective perceptions of daylighting and views as optimization objectives.