Photovoltaic Integrated Shading Devices in the Retrofitting of Existing Buildings on Chinese Campuses Within a Regional Context

Abstract

Retrofitting existing buildings to be more energy-efficient is a tremendous contribution to the sustainability of society. The application of photovoltaic integrated shading devices (PVSDs) accords with this ambition by blocking out unwanted radiant heat gain and generating clean electricity. The deployment of PVSDs needs sensible design strategies to optimize the production of renewable energy while retaining the aesthetic quality of the built-up environment, especially in historic campuses. The concept was tested in a case study of buildings in South China University of Technology (SCUT) using Ladybug 1.4.0 and PVsyst 7.2, utilizing the existing “Xia’s shading” design method in historical environments and optimizing the design from the perspective of photovoltaic performance. Firstly, the photovoltaic (PV) panels were integrated as architectural components, and the parameters were incorporated into a mathematical equation based on “Xia’s shading” design method. This was followed by the assessment of the solar energy harvesting potential based on simulated annual solar irradiation values. Lastly, the PV panels’ solar irradiation potential under these different parameters was shown in figures to identify the optimum parameters combination for PVSD applications. The proposed methodology could evolve as a design tool and thus further assist in promoting the large-scale adoption of PVSDs in retrofit projects.

1. Introduction

One of the most significant challenges in improving sustainability at the global level is the management of climate change and the reduction of greenhouse gas emissions [1,2]. In most developed economies around the world, the energy consumed by buildings accounts for more than 40% of the total energy, and in many developing and emerging economies, this proportion is still rising [3]. In 2020, the total energy consumption of the entire process of construction in China was 2.27 billion tons of standard coal, accounting for 45.5% of the total energy consumption in the country [4]. Following the “Paris Agreement”, China subsequently set a target to peak its carbon emissions by 2030 and achieve national carbon neutrality by 2060 [5]. The building sector plays a critical role in this decarbonization ambition [6].

Energy retrofitting of existing buildings is a huge contribution to the sustainability of society, since building energy consumption takes more than one-fourth of the total energy consumption [3]. As a typical developing country, China has a large number of aged buildings with high green retrofit potential [7]. In China’s “14th Five-Year Plan”, there are plans to retrofit more than 350 million square meters of existing buildings during the 14th five-year period by 2025 [8], and the ‘Work Plan for Accelerating Energy Conservation and Carbon Reduction in the Building Sector’ was released in 2024, aiming to expedite the energy retrofitting of existing buildings [9]. Within the educational sector in China, existing buildings on campuses (hereafter referred to as campus buildings) have a large stock and growth space and consume about 8% of the national energy consumption [10,11]. The total building area of ordinary and vocational higher education institutions is 1.13 billion square meters [12], and there is a rapid development in higher education institutions that has caused an abrupt increase in energy use accompanied by low levels of campus facility operations [13]. However, to reach the climate goals and achieve carbon neutrality, China has strong regulations and enforcement on building energy consumption [14]. Since 2006, China has incorporated energy conservation and emission reduction into an important part of the government’s overall work plan [15]. Accelerating the energy retrofit for large campus buildings is one of the major challenges that China is facing.

Campus buildings have a higher potential for energy savings despite the campus’s low building density and their shortened operating hours during the summer, which falls during the seasons of highest energy use [13]. As educational venues, these campus buildings serve as crucial sites for the practice and promotion of sustainability. Firstly, the environment of these buildings and the processes required for their construction can encourage students to understand the significance of sustainable development concepts for the environment. Simultaneously, the reduction and control of the operational costs of these buildings, particularly energy and maintenance costs, are highly attractive, especially for public university campuses often characterized by challenging annual budgets and constantly rising energy costs [1].

The search for sustainable and renewable energy sources, especially from solar energy, stands out in the building sector to contribute solutions for climate change and the energy crisis [16,17]. Solar energy is one of the most reliable, environmentally friendly, and promising technologies [18]. PV systems, a form of renewable energy technology, harness the power of the sun to fulfill electrical needs. The potential of solar PV lies in its ability to generate dependable, eco-friendly, and steady energy solutions for the future [19] (Clean Energy, SDG 11: Sustainable Cities and Communities, SDG 13: Climate Action). The integration of PV systems in buildings is a strategy for harvesting solar irradiation that is compatible with the worldwide sustainability criteria and the renewable energy use policy, which is on a quest for improved energy efficiency [17,20,21].

External building structures are seen to be a viable option for installing solar PV systems, which have the potential to provide a sizable amount of electricity [3]. When a PV system is installed in the building’s skin, it can enhance the area allocated for energy generation, reduce the need for additional land, and lessen its environmental impact [22]. As the components of buildings, the benefits of PVSDs also include the advantages of typical shading devices, such as boosting the indoor daylight environment, decreasing glare, improving visual comfort [22,23], cutting down the cooling load caused by external radiation, and providing a comfortable indoor thermal, which could reduce the energy consumption of air conditioning and lighting. An adequate design approach should strike a balance between the geometry of the building and its energy generation needs. It must always make an effort to capture as much solar irradiation as possible by aligning PV surfaces at the ideal tilt angle and preventing shadowing [24,25]. Achieving energy efficiency in existing buildings by retrofitting with PVSDs demands integrating them respectfully in the environment and considering the local climatology and the natural resources available [26]. In this context, roofs and facades are critical. Numerous intricate features are present in them, including natural lighting and ventilation; protection from humidity, wind, and heat stress; physical and visual safety; and sound barrier functions. Moreover, in a campus environment, building envelopes shape public areas, define campus features, and are intrinsically connected to the way of living for students.

A recent review [22] revealed that PVSDs require a customized design in each climate and environmental condition between the tilt angle, the blind spacing, and the width to maximize the benefits between energy production and energy savings. Shi et al. [27] investigated the energy performance of PVSDs in five climate zones of China and pointed out that PVSDs could be applicable in hot and cold climates and shading effects could lead to a notable difference in the optimal PVSD style. Sun et al. [28,29] carried out a case study in Hong Kong about PV panels’ power generation and thermal performance as shading devices at different tilt angles and orientations. At the same time, the study showed optimal design solutions for different scenarios of PVSD use. Huang et al. [3] described a methodology for external overhang shading on a university campus in Hong Kong and discussed the applicability of external shading systems in different climatic and the value of this conclusion to the local construction industry. Mandalaki et al. [30] proposed a method for the potential energy savings from using various PVSDs in Chania and Athens using a combination of simulation and measurement (1/10 scale physical model). The study explored a range of PVSD design parameters, including various total solar panel areas used for PVSDs. Li et al. [31] identified an optimal design solution based on the tilt angle and width of the PV panels to minimize energy loss in multi-story buildings caused by shading effects from upper PVSDs. Ref. [32] considered a multi-objective optimization for six design variables based on the geometry and position of PVSDs and built simulation models through EnergyPlus to simulate the energy cost optimization. Zhang et al. [33] discussed the energy performance of employing PV systems for shading designs and power generation in X HOUSE (a positive energy building) and provided a reference and methodology for the design of PV systems and sustainable development. Ref. [34] carried out a case study on building integrated PV projects in three different contexts (residential, office, and historical buildings) and pointed out that it was important to examine retrofit solutions from an architectural perspective, since they were done on existing architectural objects, especially historical buildings sensitive to any changes.

Previous research mainly focused on one of the key parameters of PVSD (the tilt angle, number, spacing, and panel width) to maximize the benefits of energy production, and each parameter is discussed separately. There is limited research on the combination of these parameters for the spatial design of PV panels and their subsequent compatibility with the environment, particularly in the context of historic campus buildings. This study focuses on the impact of parameter combinations on design effectiveness in the retrofitting of campus buildings, their influence on solar irradiation, and the harmonization of PVSDs with the surrounding environment. The research delves into the intricate interplay between these elements, aiming to provide insights into optimizing the design and integration of solar energy solutions in the context of architectural transformations on educational campuses. In this paper, several mathematical relationships between these parameters are described and evaluated based on the amount of solar irradiation, with the goal of maximizing the benefits.

2. Materials and Methods Facade

A specific case study was described to display the impact of mathematical relationships on the PVSDs retrofitting project involving two existing buildings on the campus of SCUT. The research, including 3D modeling, solar irradiation availability, and shading analysis, was done using Rhinoceros application software and plugins Grasshopper and Ladybug tools 1.4.0. Apply PVsyst 7.2 software to simulate the PV yield and analyze the loss. Different facades and the roof were designed and calculated separately to obtain accurate selection guidance and design recommendations.

Different climatic and environmental conditions are suitable for specific PVSDs, so it is necessary to customize the design between the tilt angle, the panel spacing, and the width to maximize the advantages of the PVSDs in different positions [22,35]. The power generation of PV blinds is affected by facade orientation and panel arrangement [36]. The architectural component is an influential aspect in the design of solar shading, which not only enhances the aesthetic and cultural values of the building facade but also directly affects the design of other components [37].

Therefore, the focus would be on discussing the important parameters that affected the aesthetic of the PV shading panel and the PV panels’ solar irradiation potential under these different parameters. The research framework is shown in Figure 1. In the first layer, the PV panels were considered as the architectural component and the construction element of the building facades, integrated with the “Xia’s Shading” design method, which was one of the distinctive features of the campus architecture. In the second layer, considering energy generation, the solar energy harvesting potential of the PVSDs was measured using the simulated annual solar irradiation. Select the cases with the higher solar radiation results, then analyze and compare the shading loss due to the PV panels over others. Based on the above simulation results and analysis, design recommendations were provided.

2.1. “Xia’s Shading” Design Method and Features of Campus Buildings

The campus environment has the characteristics of local Lingnan architectural culture (Lingnan refers to the southern regions of China, including Guangdong, Guangxi, Hong Kong, and Macau, where the local architecture exhibits distinctive features rooted in Lingnan culture). Figure 1 illustrated distinctive features of the campus architecture incorporating the “Xia’s Shading” method applied from past to present [38]. It was observed that these structures exhibited distinct horizontal and vertical components, which not only provided shading but also enhanced the environmental character of the campus. The integration of PVSDs, from a formal perspective, aligns with the overall campus environment, while, from a functional perspective, it meets the shading targets. These buildings incorporate “Xia’s Shading” elements into their facade components. The study suggests that the retrofitting of campus buildings should align with the overall campus environment; therefore, the design of PVSDs should adapt to the built environment. The “Xia’s Shading” design method with regional characteristics was constructed by Mr. Xia Changshi, a Chinese architect and professor at the School of Architecture at SCUT who had studied architecture design in Germany. From 1950 to 1958, Mr. Xia conducted a series of architectural practices for the unique climatic characteristics of Lingnan. Xia researched the related issues of heat prevention in Lingnan’s buildings and put the research results of roof insulation and window shading into practice. He thought that such a shading design was aesthetically pleasing while achieving its function: The setting of the shading panels was made into the first surface that defended against excessive sunlight on the walls and windows. It did not cover the facade of the building but instead produced a distinct shadow contrast and enhanced the three-dimensionality of the building, which could create a new architectural form [39].

“Xia’s Shading” is a method that proposes targeted shading designs for door and window openings using panel components based on the geographical context, climatic characteristics, and solar trajectory. This method aims to achieve shading targets by incorporating both overhang and flank shading. The choice of either option, or a combination of both, depends on the orientation of the facade. The shading effect of Xia’s shading was demonstrated by the quantitative evaluation. In the Physiology and Biochemistry Building shown in Figure 2, the shading effect met expectations, which can block up to 80% of the solar radiation on average, and satisfied the different requirements for solar radiation in the summer and winter. Although it had a certain impact on the indoor lighting situation, reducing the average illuminance value on the working surface by 21.6%, the overall lighting illuminance attained the requirements of the specifications, and the corresponding illuminance uniformity was improved [40]. Considering that the design aimed to block intense sunlight in the hot summer and warm winter zone, and taking into account the characteristics of the Lingnan campus environment, the PVSDs based on “Xia’s Shading” had certain limitations in their applicability.

Xia’s shading design method is suitable for PVSDs from the perspectives of shading requirements, the power generation target, and architectural aesthetics. The main constituent elements of Xia’s shading are the panels to form linear elements on the facade [41], which matches the shape of the PV panels. At the same time, the main target of Xia’s shading design is during the season and time when the solar radiation is strongest [39], which also matches the power generation target of PV systems. Xia’s shading design and PVSDs have a common target in considerations for the optimal tilt angle, PV surface direction, and sun exposure. Therefore, in the context of retrofitting campus buildings, Xia’s shading design method is a good reference for PVSDs to achieve the retrofitting aim of utilizing renewable energy and integrating PV into the local campus environment. Using this method, this research discussed the tilt angle, orientation, number, spacing, and width of PV panels in the mathematical relationship.

This research selected campus buildings that have different facade orientations to serve as examples for retrofitting cases. Two existing buildings in SCUT, Guangzhou, China, were selected to receive PVSD systems to their roofs and facade envelopes, as shown in Figure 3. Building A, built in the 1980s, has been the teaching building of the School of Architecture since its establishment. Constrained by the economic and technological conditions during the construction period, the construction standard was not high and lacked energy-efficient structures, which has become a big problem in upgrading and a heavy burden for subsequent maintenance. The facades of Building A are oriented north–south, composed of vertical lines, and 7 stories high. Building B, Materials Engineering Building, has a different facade orientation with a southwest facade (azimuth 192.5°) and southeast (azimuth 132.5°) and is 6 stories high with overhang shading. These two buildings both have a rectangular plan, regular and flat rectangle facades with square windows, and are not surrounded by other tall buildings, which provides favorable conditions for PV.

2.2. Outdoor Environment and Shading Target

Reasonable sunshade design requires accurately deriving the solar positions that need to be blocked. Xia’s shading method focuses on blocking intense sunlight during the months with higher average temperatures. First, by analyzing meteorological data from the building’s location, the time period during which sunlight should be blocked is determined. The sunshade design mainly targets summer solar radiation, as sunlight is more intense during this season, which can lead to excessive indoor temperatures and increased air conditioning energy consumption. Then, using the solar path diagram of the building’s location, the range of solar altitude and azimuth angles during this time period can be determined. Finally, based on the range of angles and the orientation of the facade, the correct sunshade design is derived.

Guangzhou (23.2° N, 113.5° E) is based on the hot summer and warm winter climate zone [42] in China. Figure 4a shows the average temperature is higher from May to September, so the main shading and heat insulation months can be determined, according to the meteorological data of Guangzhou. Figure 4b identifies the time periods during a summer day when each facade should be shaded. Different building surfaces obtain solar irradiance at different levels on a summer sunny day, as shown. Roofs have the highest irradiance level peaking at 12:00 a.m. The east and west facades take the second-place peaking at 8:00 a.m. and 4:00 p.m. separately. The south facade comes latest, with peaking at 12:00 a.m., and the sun path diagram in Figure 4c is used to determine the solar positions within this time range, including the range of altitude and azimuth angles, as well as the maximum and minimum values. In the following, these maximum and minimum values are brought into the equations for sunshade design.

2.3. PVSDs in Facades

The west facade needed to be shielded from direct sunshine from May to September, and the main shading moment is 4:00 p.m. because of the peak solar radiance. Flank shading should be used for this facade shading because of the low solar altitude angle in the afternoon. It should also be noted that the front of the PV panels should face northwest to block the sunlight. From the geometrical relationship between sunlight and the PV panels shown in Figure 5, when the PV could shade the sunlight at the minimum azimuth angle, the sunlight from other azimuth angles could also be shaded. The minimum azimuth value of 252.07° could be obtained in the range of azimuth from May to September from the sun path diagram of Guangzhou. Then, the installation method of PV panels was expressed as

$$L=D\times \cos \omega +D\times \sin \omega \times \tan \alpha ,\alpha =A_s-A_w.$$

(1)

where $L$ is the shadow length provided by one PV panel, as well as the spacing between PV modules. $D$ is the width of the PV panels. $\omega$ is the tilt angle between PV panels and the west facade surface. $\alpha$ is the difference between $A_s$ and $A_w$. $A_s$ is the solar azimuth. $A_w$ is the azimuth of the exterior normal of the facade. The east facade had a similar design basis and method as the west facade. The PVSDs in the east facade can be based on the same method of operation.

In the retrofitting facades of campus buildings with PVSDs, the shadow of the PV panels should cover the window openings, and the modulus of the external frame in the retrofitting of existing buildings should also be considered. Make the span of the PV structure match the structure of the existing building’s facades with the same column network for normal conditions,

$$l_w\le n\times L\le l_f.$$

(2)

where $l_w$ is the length of the window openings. $l_f$ is the column span length of the existing building’s facade. $n$ is the number of PV panels.

The south facade needs to be shielded from direct sunshine from May to September, and the main shading moment is 12:00 a.m. because of the peak solar irradiance. Overhang shading should be used for this facade shading because of the high solar altitude angle. From the geometrical relationship between sunlight and PV panels shown in Figure 6, when the PV could shade the sunlight at the minimum altitude angle, the sunlight from other altitude angles could also be shaded. The minimum altitude value is 63.67° at 12:00 a.m. on September 30th, and the azimuth is 170.56° at this moment from the sun path diagram of Guangzhou. Then, the installation method of the PV panels was expressed as

$$H_0=D\times \sin \phi +D\times \cos \phi \times tan\theta \times \sec \alpha ,\alpha =A_s-A_w.$$

(3)

where $H_0$ is the shadow length provided by one PV panel. $\theta$ is the minimum altitude. $\phi$ is the tilt angle between PV panels and the horizontal plane.

The shadow length provided by several PV panels can be expressed as Equation (4) when several PV panels combined in the horizontal direction and Equation (5) in the vertical direction shown in Figure 7.

$$\left\{\begin{array}{c}H=D\times \sin \phi +D_{-}\times \tan \theta \ast \sec \alpha \\ D_{-}=\left(n-1\right)\times L+D\times \cos \phi \\ \alpha =A_s-A_w\\ L\le D\times \cos \phi \end{array}\right.,$$

(4)

$$H=\left(n-1\right)\ast L+H_0,L\le H_0.$$

(5)

where $H$ is the shadow length provided by the PV panels. $D$ is the length of PV panels in the horizontal direction. There are certain constraints on the spacing of PV panels to ensure continuous shading effects.

2.4. PVSDs on Roofs

Shading designs for flat roofs can be categorized into two types: one is to block the high solar radiation months of the year and regulate the flux of sunlight, as shown in Figure 8. This type of roof is accessible, with PV panels elevated above the roof, which can provide light and shadow effects for roof activities and natural lighting. Another one is full coverage shading PV panels without lighting for accessible roofs.

Under the first scenario, roofs need to be shielded from direct solar radiation from May to September, and the main shading moment is 12:00 a.m. because of the peak of solar radiance. The range of altitude from May to September can be found from the sun path diagram of Guangzhou, and the minimum altitude angle can be determined at 12:00 a.m. on September 30th. Then, the altitude value 63.67° can be obtained from Ladybug. The front of the PV panels on the roof can optionally be arranged facing south or north. Two PV panels need to be set at different heights as a group to provide space for sunlight penetration when arranged in a southward direction. The sunshine passes through the intervals between the panels when arranged in a northward direction. It should be ensured that light can pass through even when the sun’s altitude angle is at its lowest at noon on the winter solstice. That is, the tilt angle of the PV panels should be no greater than the angle of the sun’s altitude at noon on the winter solstice. From the geometrical relationship between sunlight and PV panels in Figure 9, the installation method of PV panels is expressed as

$$L^{\prime }=2\times D\times \cos \phi -h\times \sec \gamma \times \cot \theta ,\gamma =A_s-A_{pv},$$

(6)

$$L=D\times \cos \phi -D\sin \phi \times \cos \gamma \times \cot \theta ,\gamma =A_s-A_{pv}.$$

(7)

where Equation (6) is for southward PV panels. Equation (7) is for northward PV panels. $L^{\prime }$ is the total length of the group containing two PV panels set at different heights. $h$ is the height difference for sunlight to pass through. $\alpha$ is the difference between $A_s$ and $A_{pv}$. $A_{pv}$ is the azimuth of PV panels’ normal exterior face.

In another scenario, roofs are covered with PV panels for inaccessible roofs in a southward direction, as shown in Figure 10, and the geometrical relationship is expressed as

$$L=D\times cos\phi .$$

(8)

Retrofitting roofs with PV panels should consider the physical structure of the existing building, considering whether the structure of the existing building has excess loads to carry the additional weight of the PV structure. Make the span of the PV structure match the structure of the existing building’s roof with the same column network for normal conditions. The weight can fall directly on the existing building’s columns to reduce the burden of proof slabs. Then, the number of PV panels that can be installed in each span can be expressed as

$$n=\left[{\displaystyle \frac{l_r}{L}}\right],$$

(9)

where $l_r$ is the structural unit width of PV frames on the roof.

2.5. Ladybug and PVsyst

Simulations are the most used systematic analysis methods, especially for external PV blinds, including PV panels [22]. The availability of solar resources was simulated using the Grasshopper and Ladybug plugins. Grasshopper is a graphical algorithm editor integrated with Rhino’s 3D modeling tools [45]. Ladybug is a plug-in used for energy simulation that relies on several EnergyPlus validated models [46] and is capable of performing simulations based on the geometry generated in Rhinoceros, Grasshopper, and the climate file EnergyPlus Weather File (EPW) of the target location. The outputs were the quantity of radiation in kWh/m².year that reached the testing geometry, which was depicted by a colored mesh, and the total annual radiation in kWh for each surface [17]. The simulation results showed a high availability of solar irradiation in Building A and B in Figure 11. The colored mesh experimental results assisted in adjusting the positional relationship between PV panels to optimize the PV performance. The simulated annual solar radiation was used to measure the solar energy harvesting potential of the different PVSD alternatives.

PVsyst is considered as one of the standard simulation software that is in use. It carries out a detailed and explicit study on numerous parameters that influence the efficiency of a system, including shading loss due to PV devices over others. PVsyst offers a high level of accuracy, closely matching actual values [47], and provides a “Loss Diagram” to predict weaknesses in the system design [48]. The “Near Shadings: Irradiance Loss” and “Shadings: Electrical Loss” shown in the “Loss Diagram” are relevant to this study, as the former corresponds to the deficit of irradiance on the PV cells, while the latter results from the mismatch of the electrical response of modules in series and strings in parallel [49]. Figure 12 and

Table 1. Electrical specifications of the PV panels in PVsyst.

Facade	Type	Maximum Power (W)	Maximum Voltage (V)	Maximum Current (A)	Open Circuit Voltage (V)	Open Circuit Current (A)	Dimensions (mm)
West	Si-mono	360	59.1	6.90	70.60	6.500	2008 × 1002 × 40
South	Si-mono	360	36.2	9.940	43.61	10.540	1775 × 997 × 35
Southwest	Si-mono	290	32.00	9.070	39.00	9.730	1600 × 1002 × 30
	Si-mono	162	17.00	9.530	20.20	10.610	1048 × 830 × 60

show simulation models and the electrical specifications of the PV panels used in PVsyst.

3. Results and Discussion

3.1. PVSDs in the West and South Facade of Building A

The main functions of the room on the west facade (azimuth 270°) of Building A are the seminar rooms and bathrooms without sun shading elements. PVSDs could improve the environmental quality of indoor use and provide clean energy for the rooms during the western sun exposure period. The column span on the west side of Building A is 3.6 m, and the height of the window openings is 2 m, so the length of the PV panel was set at 2 m. An external frame corresponding to the column span was laid on the surface of the west facade and constrained by Equation (2). The relationship between the tilt angle, number, and width is shown in Figure 13 based on Equation (1), when the tilt angle started from 10° with a gradient of 10°. It showed that the number of PV panels required for the facade was too large after a tilt angle of over 30°, which was not economical and not conducive to renovation construction. Therefore, three angles of 10°, 20°, and 30° were selected for the subsequent simulation experiments shown in Figure 14. In Figure 15, it could be found that the efficiency of the PV panel per unit area decreased as the angle increased. Although increasing the angle could arrange more PV panels on the facade, the total benefits were also not significantly improved. Under the conditions of the same width and number ($D$ = 0.8 m $n$ = 5, $D$ = 0.9 m $n$ = 5, and $D$ = 1.0 m $n$ = 4), a smaller angle had a better benefit in solar irradiation, both in total and per unit area. Therefore, the small-angle design could be considered first to increase the energy efficiency. The same trend was also validated by PVsyst (

Table 2. Power generation and main losses on the west facade.

$\mathit{\omega }$(°)	Power Generation (MWh)	Irradiance Loss (%)	Electrical Loss (%)
10	24.371	15.6	16.3
20	23.464	19.5	11.5
30	21.834	22.9	8.9

Detailed data can be found in Appendix A.

). With a small tilt angle (10° and 20°), the increase in width hardly affected the amount of solar irradiation per unit area, while, in the case of $\omega$ = 30°, the average irradiation decreased due to the self-shading of PV panels. At the same time, a small angle could reduce the prominence of the PV plane volume, which could minimize the impact of PVs on the campus building environment. Under the joint action of angle and width, the degree of space utilization within each column span was different, which had an impact on the total efficiency. For example, when the tilt angle $\omega$ = 20°, the number of panels was the same as $D$ = 0.8 m and 0.9 m, and the total irradiation of $D$ = 0.9 m was higher than 0.8 m. When the width $D$ = 0.8, the overall irradiation of $\omega$ = 10° was the highest, although the number of planes was not the largest. Different widths and angles can be used to meet different retrofitting goals, providing a reference for flexible responses to PVSDs.

The south side of the building is drawing classrooms, and the south facade has regular rectangle windows (width 3.6 m, height 2.0 m) without shading construction. The PV panel was set to be 3.6 m long and 1 m wide. The best angle for receiving solar radiation in Guangzhou is 23° [50], so the angle of the PV panels was set uniformly to 23°. It could be inferred from Equation (3) that the shadow length provided by one overhang PV panel was 2.3 m larger than the height of the window. The solar irradiation in the total and per unit area was 318,681.97 kWh and 1053.84 kWh/m² from the Ladybug simulation when one PV panel was set for each window. Under the premise of meeting the shading requirements, the spacing between the panels was the main parameter influencing solar irradiation when the PV panels were arranged as overhang shading.

In the simulation experiment consisting of two overhanging panels arranged horizontally and vertically, respectively, shown in Figure 16, the influence of spacing on solar irradiance was discussed. From the solar irradiation of PVSDs in the horizontal and vertical directions (Figure 17), it was observed that the irradiation of horizontally positioned PVSDs gradually increased with the spacing, while the vertically positioned ones showed a significant improvement at 0.7 m and stabilized at 0.9 m. Therefore, we selected the minimum, median, and maximum spacing cases (0.3, 0.7, 0.9, and 1.5) to PVsyst in order to obtain the power generation and identify the main factors causing losses (shown in

Table 3. Power generation and main losses on the south facade.

Direction	Spacing (m)	Power Generation (MWh)	Irradiance Loss (%)	Electrical Loss (%)
Horizontal	0.3	46.061	61.7	8.5
	0.7	54.770	52.1	13.3
	0.9	57.497	47.8	16.6
	1.5	69.839	38.6	13.5
Vertical	0.3	44.295	59.1	18
	0.7	49.618	50.6	23.9
	0.9	53.662	47.4	22.7
	1.5	65.973	41.0	14.9

Detailed data can be found in Appendix A.

).

It was found that, when the spacing was too small, due to the self-shading caused by the outer panel in the horizontal group and the upper panel in the vertical group, the total irradiation showed no effective growth. The irradiation received by the inner panel and lower panel was so small that these panels could not be effectively utilized. Increasing the distance within an appropriate range weakened the self-shading, and the irradiation improvement was significant. As the spacing increased, the self-shading effect reduced, and the general trend of solar irradiation tended towards stability, although there was a slight decrease caused by the shading from panels installed at higher elevations in some cases. It was found that irradiation would show effective growth after the spacing reached an appropriate value. Meanwhile, the horizontal group was more sensitive to the change in spacing compared to the vertical group and reached stability more rapidly with smaller spacing. In the simulation results from Ladybug (Figure 17), the horizontal arrangement reached its peak at a spacing of 0.7 m. A similar trend was observed in the results from PVsyst (Table 3), where the peak required a spacing of 1.5 m. This illustrates the subtle differences between Ladybug and PVsyst. Ladybug highlights the potential for photovoltaic utilization through solar radiation, while PVsyst offers more precise calculations of power generation, as it takes into account the entire operational system of photovoltaic generation. In the vertical arrangement, the interference of sight lines and day lighting should be considered when determining the spacing of PV panels. Under the same spacing, a horizontal arrangement could have better energy efficiency performance than a vertical arrangement. However, the volume protrusion and additional structure were more obvious. However, we could not overlook the interference caused by the protruding volume resulting from the spacing of horizontally placed PV panels on the surrounding environment. In light of the goal of better integrating the retrofit design into the built environment, vertical arrangements should be prioritized.

3.2. PVSDs in the Southwest Facade of Building B

Building B has two deflective parts, with a southwest facade (azimuth 192.5°) and a southeast facade (azimuth 132.5°). On the southwest part shown in Figure 18, the arrangement and size of the windows on floors 1 to 4 are consistent, which was used for this experiment. The window height is 2.1 m, and the width is 3.25 m. Two facades are needed to consider not only the overhang shading to prevent sunlight penetration from the south but also the flank shading to block the sunlight from the side of the window, due to the facades orienting towards the west and east. Under the same shading target, a combination design was carried out.

The overhang shading blocked the direct solar radiation at 12 o’clock from May to September, the minimum angle in this range was 63.67° at 12 o’clock on September 30th with an azimuth 170.56°. The angle α was −21.94° as the southwest facade azimuth was 192.5°. The length of the overhang shading was set to 3.25 m, matching the window width. It could be known from Equation (3) that, when $\phi$ = 0°, $\theta$ = 63.67°, and $D$ = 1 m, the shading length provided by the overhang shading was $H_0$ = 2.2 m, which was more than the window height and met the shading requirement. Through the Ladybug simulation, the annual solar irradiation obtained solely by the overhang PV panels on the southwest facade was 103.3 MWh. The flank shading blocked the direct sunshine at 4:00 p.m. from May to September, the minimum azimuth was 252.07° on September 30th, and the angle α was 59.57° for southwest facade azimuth at 192.5°. The shading length provided by PV panels could be known from Equation (1). The flank shading board height was set to 2.1 m, same as the window height. Then $n$ could be obtained from Equation (2), as the window width was known to be 3.25 m. Experiments were conducted by configuring values of 0.4, 0.6, and 0.8 for the width to discuss the relationship between the tilt angle, the number, and solar irradiation. By simulating the flank shading separately, it could be found that the number decreases with the increase of the tilt angle from Figure 19. However, it was noteworthy that, when the title angle became too large, the required number exhibited a slight increase. Small angles consistently yielded better irradiation gains, both in total and per unit area. In groups with the same number of panels, the same trend held, so small angles were prioritized in power production. It also needed to consider the obstruction of the natural light when the angle setting was too small. Different parameter combinations could achieve very similar irradiation results. Under the settings of $\omega$ = 20° $D$ = 0.4 m $n$ = 6, $\omega$ = 25° $D$ = 0.6 m $n$ = 4, and $\omega$ = 55° $D$ = 1 m $n$ = 3, a solar irradiation level of approximately 190 MWh was achievable, and the ultimate selection could be determined by specific retrofitting objectives based on both aesthetic and lighting requirements. Then, the overhang shading and flank shading were set together for the Ladybug simulation. The numerical sum of the irradiation amounts of the two separate settings of overhang and flank was taken and compared to the irradiation amount obtained from the combined setting simulation in Figure 20. The simulation results from PVsyst (

Table 4. Power generation and main losses on the southwest facade.

Part	$\mathit{\omega }$(°)	Power Generation (MWh)	Irradiance Loss (%)	Electrical Loss (%)
Overhang	-	15.232	38.9	5.2
Flank	10	16.621	37.0	23.6
	20	14.429	34.5	15.5
	40	9.325	36.9	14.7
	85	5.705	62.4	29.4

Detailed data can be found in Appendix A.

) also demonstrated that the power generation of the overhang panels was excellent, while flank panels at smaller angles maintained some efficiency. However, the losses at larger angles were too significant. It was found that the composite design would increase the total solar irradiation, while there was some discrepancy between the simulated results and the sum of the numerical values. When the angle setting of the PV panels was small, the solar irradiation received by the combined setting had a larger loss. This portion of the loss stemmed from the shading of the upper half of the flank panels by the overhang shading PV panels. However, the combined setting could obtain more solar irradiation than the separate setting in general, which was beneficial for obtaining more sustainable energy.

3.3. PVSDs on the Roof of Building A

The two types of roof shading mentioned before could be selected for Building A, according to the functional needs of the roof shown in Figure 21. Building A has a flat roof, with a column span of 8.2 m × 3.6 m. Set 8.2 m × 3.6 m as the PV panel installation unit span. Since the roofs on the north and south sides were identical, the following example only illustrated the roof located on the south side. The PVSDs for partial shading were discussed first.

When the PV panel was facing south (azimuth 180°), the adjacent two PV panels needed to have a certain height difference for sunlight to pass through. The height interval $h=0.2\mathrm{m}$ was set between the two panels. Set the PV panel width $D=1\mathrm{m}$, within a PV panel unit $l_r=3.6\mathrm{m}$. The tilt angle started from 0° with a gradient of 1°. The number of PV panels was obtained from Equations (6) and (9), and the simulation results are shown in Figure 21. The results showed that, with the same installed number, the total solar irradiation decreased as the angle increased. Increasing the angle could accommodate a greater number of panels, but the total irradiation did not show a significant increase. The irradiation per unit area showed a steady downward trend as the tilt angle grew. Meanwhile, it should be noted that the PV panels arranged to the south had a significant volume protrusion in the vertical direction, and with the angle increasing, the volume in terms of height became more pronounced. Therefore, the configuration with a small tilt angle required fewer PV panels, occupied less space, and could achieve similar solar irradiation effects, which was more suitable for use in retrofitting projects.

When the PV panels were facing north (azimuth 0°) for partial shading, the other parameters were consistent, as in the previous. By adjusting the tilt angle, multiple design options could be generated, and the number of PV panels installed in one shading unit could be obtained with Equations (7) and (9). Figure 22 showed that, in the same number group, as the angle increased, the irradiation decreased. When the angle was less than 20°, the number of panels increased, and the total irradiation value showed a noticeable growth, although the irradiation per unit experienced a slight decrease with the increasing angles. However, after an angle greater than 20°, both the total and per unit area irradiation exhibited a pronounced downward trend. Therefore, when the installed number was determined, the smallest angle could be chosen to improve solar irradiation. Since the PV panels were set to the north, it could not fully receive direct sunshine when the angle was too large. Although the number of PV panels that could be arranged increased, the total solar irradiation received was greatly lost.

In the case of full shading facing south, the best angle for receiving solar radiation is 23° [50], so the tilt angle was set to 23°. The relationship between the installed capacity and solar irradiation was discussed using Equations (8) and (9) and shown in Figure 23. It could be found that, with the structural span for accommodating PV panels predetermined, space utilization was crucial for irradiation gains. In groups with the same number of panels, adjusting the width of the PV panels allowed for better space utilization, thus resulting in improved irradiation gains. Therefore, choosing an appropriate panel width to fully utilize the existing building’s column span was worth emphasizing. At the same time, both small panels with a large number and large panels with a small number could achieve favorable space utilization and similar irradiation gains, such as $n$ = 11 $D$ = 0.8 m and $n$ = 4 $D$ = 2.2 m. This provided more combination options, enabling retrofitting designs to flexibly adapt to retrofitting conditions.

3.4. Lessons Learned to PVSDs in Campus Buildings

The assessment indicated that the campus buildings at SCUT held promising prospects for the application of PVSDs. Based on the results and discussion above, and considering both power generation and the built environment, the west and south facades of Building A were assigned values of 24.371 MWh ($\omega$ = 10°) and 49.618 MWh (vertical spacing = 0.7), respectively, while Building B adopted 15.232 MWh (overhang PV) and 16.621 MWh (flank PV $\omega$ = 10°). The total annual power generation capacity across the three facades is 105.842 MWh, resulting in a savings of 325 tons of standard coal over the 25-year life cycle of the PV system.

It is worth noting that the campus environment presents favorable conditions for retrofitting PVSDs. Benefiting from the low-density environment, the shading effects from nearby structures are relatively minimal. The surfaces suitable for PVSD application on these campus buildings exhibit favorable solar irradiation gains to support PV power generation. The solar irradiation per unit area on the roof approaches the optimal value for this region. Although solar irradiation on the south facade has decreased slightly, it still benefits from irradiation levels comparable to those of the roof. Consequently, the roof and south facade were prioritized in the retrofitting process. Favorable conditions were maximized in the design of these two areas to enhance the energy efficiency. Power production could shift from a system with a small tilt angle and large width to one with a large tilt angle and small width. Selecting the appropriate combination of tilt angle and width can optimize space utilization to achieve better irradiation benefits, with smaller angles prioritized for PVSDs.

The retrofitting was also constrained by the inherent conditions of the existing buildings, such as structural load-bearing capacity and the preexisting dimensions of facades. These factors limited the spatial range available for PVSD placement. On the roof, it was necessary to integrate the PV panel structure directly onto the existing columns to address structural load concerns. On facades, the existing divisions typically served as the basis for the placement of PV structures, ensuring that the retrofitting was seamlessly integrated into the contextual facade of the existing building. Given these constraints, achieving optimal irradiative gains within the limited space required careful balancing of the angle, width, and quantity to fully utilize the available area. These conditions were incorporated into mathematical relationships as constraints on parameters in mathematical equations. This approach made the design of PVSDs more adaptable to various existing building conditions. Simultaneously, it provided multiple design alternatives with similar irradiative gains but distinct aesthetic effects, optimizing spatial utilization under constrained conditions to enhance radiative gains and catering to diverse retrofitting objectives. For instance, in the previously mentioned southwest facade of Building B, three different design schemes achieving equivalent irradiative gains were proposed. On the roof of Building A, adjusting the width of the PV panels allowed for better space utilization, resulting in improved irradiation gains.

4. Conclusions

The primary contribution of this study lies in its ability to incorporate the effects of various design parameters into mathematical equations for PVSDs in the retrofitting of campus buildings with regional characteristics. The results illustrate the feasibility of implementing PVSDs in a campus environment and emphasize the substantial positive impact of optimizing the design parameters in relation to the total energy efficiency. Historical features, structural loads, and the original design of building envelopes are all critical influencing factors that affect the implementation of PVSDs in the retrofitting projects of campus buildings. The mathematical approach in this study is based on “Xia’s shading” design method in response to the historical context of the campus, supports the flexible setting of different parameters in accordance with existing conditions, and provides the comprehensive parameter configuration of PVSDs. The study underscores the optimization of PVSDs and extends beyond the singular emphasis on a certain parameter; rather, the performance of PVSDs relies on a comprehensive evaluation of multiple parameters, their interdependencies, existing conditions, and their harmonization with environmental factors. The main findings are as follows:

(1)

Both the facades and roof of the building possess power generation potential. The power generation capacity of PVSDs varies according to their design, including factors such as angle, spacing, number, and dimensions. An appropriate design can significantly enhance electricity generation. The power generation of the south facade can increase from 44.295 MWh (vertical spacing 0.3) to 69.839 MWh (horizontal spacing 1.5 m), representing an increase of 57.7%.

(2)

Recommendations for PVSD design on different façades indicate that flank shading provides greater power generation benefits at smaller angles, ranging from 16.621 MWh (10°) to 5.705 MWh (85°) on the southwest facade. The key influencing factor for overhang shading is the spacing. Under identical spacing conditions, overhang shading performs better in the horizontal direction than in the vertical direction. However, considering the need for integration with the built environment, vertical arrangements should still be prioritized.

(3)

Design parameters were incorporated into a mathematical equation based on the “Xia’s shading” design method, serving as a comprehensive design tool for the modeling of PVSDs.

There are some limitations in this study. First, the model used to simulate sun irradiation was created based on simplified blocks and did not include vegetation, which might not accurately reflect the real environment. Second, the campus buildings selected in this study had a regular shape and façade in the hot summer and warm winer zone, with consistent shape and size windows evenly distributed, and served only as a basic representative of the campus buildings. The types and location of retrofitting buildings might vary. Third, the target of establishing these equations was to shade the strongest solar radiation at several specific points in time, indicating that the shading effect might have limitations. The equations are under the condition that the PV panels are close to the building envelope surface.

This design approach may be improved in further work by modeling with a more comprehensive contextual setting for solar irradiation simulation. In addition, use shading simulation methods to find the shortcomings in this research and make up for them. Last, but not least, to promote the energy efficiency and shading effect of PVSDs in building retrofitting, more case studies should be conducted.

This work identified a methodological design pathway for the PVSD system early design in campus buildings, which is worthy of use by professionals and students of architecture alike. The equations proposed and discussed in this paper contribute to further research on the design methods of deploying PVSDs in building retrofitting and issues related to solar power generation.