The Study of Architectural Geometry and Shape in the Energy Balance of Glazed Roofs

Abstract

Triggered by the global call for low-carbon design, the idea of “productivity for a building envelope” has permeated the role of building to produce alternative (renewable) energy alongside weather and solar protection, and the authors hypothesized that the geometrical shape and configuration of a roof is a significant contributor to low-carbon design. Bibliometric networks such as VOS Viewer revealed a gap among most research works which have yet to discover “roof geometry” as a design determinant for photovoltaic electricity production. In this study, the authors tested their hypothesis by studying and comparing the balancing of solar energy harvesting and energy consumption and saving due to the uncontrolled admittance of daylight, glare, and solar heat gain of different geometric shapes of roofs in the subtropical climate. Twelve recent signature public buildings in Shenzhen city are studied for the tendency of architectural geometry of roof shapes. These roof shapes are then simplified and classified into three distinct geometries—square, pyramidal, and curvilinear—for comparative study of the best-performing low-carbon architectural geometry. The results of the simulations using the “Daysim” and “Energy-Plus” models show the desirability of an optimized design. The preliminary findings shed light on the preferred use of specific roof shapes for enhanced PV output. The curvilinear geometry has been shown to be the most effective of all. This study targeted the roof potentials by multiple criteria and a parametric evaluative protocol for building design known as the energy balance paradigm. This research paves the way in (1) changing the impression of the roof as a mere weather protector to that of a “productive roof” in response to the global call for carbon neutrality, (2) raising the awareness of architectural geometry (i.e., the building envelope), focusing on the roof form and its shape in response to low-carbon design requirements, and (3) identifying multiple criteria for the low-carbon design of architectural roof geometry.

1. Introduction

1.1. Background

Humans have inspired the instinct to build effective weatherproof enclosures in response to the effects of natural extreme weather conditions since primitive times [1,2]. The quality of dwellings is constantly improving with the ingenuity of human beings, gradually transforming from temporary tent-style shelters into housing structures with walls and roofs [3]. The traditional function of the roof is to use its geometry to protect people and property, reduce the penetration of wind, rain, and snow, and simultaneously meet human expectations for heat insulation and cold resistance [4]. Subsequently, the development of the roof has experienced constant challenges and innovations. By the early 21st century, as rapid urbanization disrupted the ecological balance [5], the impact of building envelope technology on sustainable buildings and urban spaces drew attention. The roof is an important part of the building envelope, accounting for nearly 20–25% of the total urban surface area [6]. Therefore, with the improvement of construction and horticultural technology, green roofs and urban farms are considered nature-based solutions [7,8] to the challenges posed by global warming and increasing greenhouse gas emissions. Later, when it comes to the information era, the “smart cities” constructed by “new media”, “digital technology”, the “Internet of Things” and “virtual space” has become a hot topic in the field of architecture [9,10,11]. Commercial and public building skins have gradually evolved into LED digital public screens and interactive media facades (Figure 1).

At present, the rapid consumption of natural resources and the deep understanding of sustainable development have caused most architects to pay attention to the application of energy-saving technologies in architectural design and also the use of sunlight and shading technologies for building surfaces. Moreover, following the recent global call for carbon peak emission (year 2030) and carbon neutrality (year 2050 or 2060), it is not surprising to find that most nations have prioritized building-integrated renewable energy (BIPV) as a national initiative for building design. For instance, the Ministry of Housing and Urban-Rural Development of China launched a mandatory national standard for offsetting carbon emissions by promoting renewable energy production in building design [14]. The US also launched government policies (e.g., the Clean Energy Standard (CES)) [15] and legislation such as carbon taxes and the “Cap-and-Trade Programs” (i.e., emissions trading) to promote carbon capture and sequestration technologies and renewable energy utilization [16]. Among these strategies, solar photovoltaic (PV) technology has been widely applied to substitute traditional energy. The Fortune report on the solar PV market predicts that the global solar photovoltaic market is expected to grow from USD 199.26 billion in 2021 to USD 1000.92 billion in 2028 at a growth rate of 25.9% [17]. For China, the new policies for climate change and carbon neutrality offset initiatives have led to an estimated growth of PV installed capacity, targeting 403 GW in 2025 [18].

Furthermore, these governmental initiatives coincided with recent developments in PV technology and products, as the world market has seen new products that are increasingly affordable, efficient, and design-friendly. The thermodynamic, optical, and acoustic properties of the applied materials are also considered for new PV products. They can be colored, translucent, and fabricated in flexible, arbitrary shapes [19,20,21]. This enables the integration of photovoltaics with building façades or roofs without compromising the architectural form or aesthetics of the building.

Table 1. New technologies or products of PV.

No.	Technologies or Products	Example	Efficiency
1	Organic PV (OPV)	(Source: left = ARMOR/GerArchitektur [22]; right = Fraunhofer Institute for Solar Energy Systems ISE [23])	15.2% [24]
2	Flexible solar PV (Perovskite)	(Source: Iaremenko, iStock, and Getty Images [22])	21.6% [24]
3	Colorful PV (dye-sensitized solar cell)	(Source: left = Iaremenko, iStock, and Getty Images [22]; right = Solar Energy Research Institute of Singapore (SERIES))	11.9% [24]

shows the new PV technologies and products, such as organic PV (OPV), flexible solar PV, and colorful PV modules.

Studies on photovoltaic technologies and the invention of new products are critical to enhancing solar energy harvesting productivity. A literature review is conducted in Section 1.2, focusing on those precedent studies on photovoltaics and roof geometry.

On the other hand, the authors hypothesize that the geometrical configuration of the roof is the other significant contributor to energy-efficient and low-carbon architecture. Actually, the architectural design paradigms are constantly changing. In the process of urbanization in recent years, the pursuit of cultural creativity has appeared in many developed cities in China [25]. This development trend has coincided with the view that non-residential buildings serve the purpose of being a spearhead in new ventures, such as BIPV applications.

This research focuses on considering the three functions of the building skin: daylighting, energy saving, and power generation, taking the design of the building’s form and shape as a key factor for maximizing solar electricity and building energy efficiency. In this study, the authors hypothesize that the geometrical configuration of the roof is a significant contributor to low-carbon architecture and try to find the ideal roof shape and area ratio of PV panels. The above development trend is expected to generate a new way of thinking about roof design.

1.2. Literature Review

Studying the evolution of high-frequency keywords helped to track research trends as well as identifying potential research gaps [26]. In this paper, the authors conduct a bibliometric analysis of the design optimization of rooftop photovoltaic systems. Using the Web of Science database and the VOSviewer software, the authors produced a co-occurrence network of titles, keywords, and abstracts based on the keyword of “photovoltaic roof”. In total, 1712 articles published in the last decade were identified (Figure 2). According to the analysis of keywords, 414 keywords appeared at least 5 times among the total of 5957. As shown in Figure 2, the larger the font size of the keywords in the figure, the higher the frequency of occurrence. The diameter of each circle reflects how often the keyword exists, and the width of the link line indicates how often the keywords are used together. The color scheme shows the year of publication. In contrast to Figure 2, Figure 3 shows the frequency of keyword usage. Keywords marked in bright yellow and larger fonts refer to higher usage frequencies.

The above keyword co-occurrence network clearly shows the main aspects involved in the field of photovoltaic roofs. The keywords that frequently appear in the literature related to photovoltaic roofs include “performance”, “energy”, “system”, “optimization”, and “design”. The yellow circles (consumption, energy performance, climate change, and rooftop PV) in Figure 3 are those keywords that appeared around year 2019 and can be considered relatively new or hot research fields. This shows that for prior studies, scholars were mainly focusing on improving PV system performance by technical optimization.

In addition, recent photovoltaic studies focused on the integration of solar technologies with typical building components, referred to as building-integrated photovoltaics (BIPV) [27]. Increasingly, BIPV has been promoted as an integral part of the building design process. The multi-functional BIPV element can both improve the energy performance of a building envelope and generate electricity from solar radiation in the urban environment [28]. At the same time, designers acknowledge that the roof is by far the best performer in terms of PV output among all the surfaces of a building [29]. Therefore, the authors continued their search on the Web of Science with “BIPV”, “roof geometry”, and “energy performance” as keywords and a search period of 10 years. A total of nine related works were found, as shown in

Table 2. Comparative study of works on “BIPV”, “roof geometry”, and “energy performance”.

Author(s)	Study Area	Research Focuses	Findings
Ghani, F., Duke, M., and Carson, J. K. (2012)	N.A.	Estimation of BIPV conversion efficiency	In this paper, the authors proposed an artificial neural network that can be used to calculate the power generation of photovoltaic arrays of specified shapes. By simulating the photovoltaic power generation of each scenario, the optimal configuration can be selected [30].
Li, S. et al. (2014)	USA	Performance analysis of BIPV/T systems with corrugated unglazed transpired solar collectors (UTCs)	This study investigated the optimal geometry of UTC with photovoltaic panels. The results of the study found that wavelength and PV panel height had the greatest impact on UTC with PV panels [31,32].
Pacheco-Torres, R. et al.(2015)	Spain	The relationship between building morphology, energy efficiency, and generation capacity of PV panels	This study analyzed three residential building types: single-family detached, semi-detached, and multi-dwelling houses. The results indicated that the single-family detached dwelling model is less energy efficient. For multiple dwellings, the optimal building height can be obtained according to the building area to reduce building energy consumption [33].
Savvides, A. and Vassiliades, C. (2017)	Cyprus	Optimal building geometry with higher solar radiation	The results of the study show that massing configurations in which the south-facing roofs and façades of the community plan contain more building volume and can absorb more solar radiation [34].
Walker, L., Hofer, J., and Schlueter, A. (2019)	Switzerland	BIPV modeling and optimization simulation methods	The results demonstrate that by using genetic algorithms, BIPV layouts and morphologies can be simulated and optimized in urban environments to minimize power losses in BIPV networks with various modules [35].
Arnaout, M. A., Go, Y. I., and Saqaff, A. (2020)	Malaysia	Technical assessment and economic analysis of BIPV	Eight proposed configurations of roof systems for Heriot-Watt University Malaysia were compared from energy and economic perspectives. Results show that systems using CdTe thin film modules provide the highest energy potential [36].
Paydar, M. A. (2020)	Iran	Optimal design of BIPV as movable sunshade device	The results show that the movable BIPV shading system has a significant effect on the reduction of the annual heat load of a building, which can be reduced by up to 20%. However, the change in the tilt angle of the BIPV panel has little effect on the power generation, and the annual power generation of the movable BIPV is only 2% higher than that of the fixed type [37].
Yin, Y. et al. (2020)	N.A.	PV conversion efficiency for ethylene-tetrafluoroethylene (ETFE) cushion roofs	This study presented a 3D numerical model that elucidates the coupling relationship between heat, interior air, and the ETFE roof structure, thereby proposing potential solutions to dissipate excess heat to optimize future designs [38].
Kaplanis, S., Kaplani, E., and Kaldellis, J. K. (2022)	Greece	PV temperature and performance	This study presented a model for predicting PV temperature and performance, including predicting the effects of ambient temperature and dip angle on PV heat transfer coefficient, efficiency, and aging [39].

.

It can be seen that the above studies primarily focused on the shape design of PV modules [31,32], performance optimization [36], and performance prediction methods of BIPV or PV arrays [35,38,39]. In addition, Savvides, A., and Vassiliades, C. focused on community-level planning and examined the relationship between blocks and solar radiation in different combinations of simple building blocks (Figure 4) [34]. Pacheco-Torres, R. et al. conducted studies on building morphology. Still, these studies focused on different building types, such as single-family detached houses, semi-detached houses, and multi-dwelling buildings (Figure 5) [33]. The authors did not find any study on the energy efficiency of different roof morphologies, nor was there a study combined with natural daylighting.

The energy balance of a building consists of making an inventory of all energy flows within the building [40]. Solar irradiation also plays an important role in the building energy balance [41], especially for buildings with fully glazed roofs. The equation of the energy balance of a building is “Total energy gain = Total energy losses”. Previous studies on the energy produced by BIPV in building energy balance found that compared with the standard buildings, the high-performance buildings with BIPV generally require more material and more components of PV. Consequently, it causes more environmental impacts during the operation stage of the building’s life cycle [40,42]. Another experiment on energy balance focused on the integration of PV (i.e., energy generation) and external shading systems (i.e., reducing energy loss) [43]. The PV panels were applied as shading devices, and the size, geometry, and installation positions of the PV panels on the windows were considered the influencing factors on the energy generation, daylighting, and visual comfort. It can be seen that reducing energy consumption and utilizing renewable energy are important ways to resolve the power consumption of buildings [44]. Previous research demonstrates that PV windows and roofs are used in different climate zones, and the total energy consumption of a building changes accordingly [45,46,47,48,49,50,51]. The roof is the most crucial building envelope in a hot environment [52], as its morphology significantly impacts energy consumption and thermal comfort. However, the authors could not find any study on the interrelationship of different roof shapes and renewable energy generation, such as pyramidal and curvilinear roofs.

On the other hand, the previous studies mainly focused on applying BIPV on building facades and windows, with an absence of BIPV for glazed roofs of different architectural forms. It is not surprising to witness the speedy development of architectural design, which has favored glazed roofs and flamboyant architectural forms and shapes.

Combining the conflicting energy consumption of artificial lighting and air conditioning is a significant challenge in a refrigeration-dominated climate to achieve overall energy savings goals when optimizing roof designs concerning the daylight, cooling loads, artificial lighting power, and electricity production of PV panels. Based on the above research gaps, this paper studies the relationship between roof forms, PV panels’ proportions, and energy consumption.

Meanwhile, there is a lack of research on the usability of PV panels and glazed roofs in Shenzhen, a megacity located in South China with a subtropical climate. Therefore, it is necessary to conduct targeted research on different building forms in different climate zones based on regional climate data and provide suggestions for promoting photovoltaic building-integrated design.

1.3. Research Objectives

In this study, the roof is entrusted as a renewable energy producer and an energy-saving device for balanced daylight admittance and thermal heat gain. There are two research objectives of the study. The first is to compare the solar energy harvesting productivity of the three prevailing roof shapes, where computer-aided design tools (i.e., Grasshopper with Radiance, Daysim, and Energy Plus via the plug-ins Honeybee and Ladybug) were applied to simulate the daylighting, energy consumption, and electricity generation of three typical roof geometries (i.e., flat roof, pyramidal roof, and curvilinear roof) of cultural facilities in the coastal city of Shenzhen. The second goal was to quantify the optimal PV panel coverage ratio relating to different roof geometries. The impacts of the ratio of PV panel coverage to indoor natural lighting, lighting energy consumption, cooling energy consumption, and PV panel power generation were analyzed to better understand the trade-off relationship between these different and conflicting performance considerations.

In Section 2, the roofs of up to 12 Shenzhen’s top cultural facilities were classified into three typical geometries for simulation purposes. For the models which assume an identical base (ground area), the three geometries yielded different roof forms and roof surface areas. The percentages of PV panels to the roof area were from 10% to 90%. Other parameters are also defined in Section 2. The simulation results and comprehensive analysis are shown in Section 3.

2. Methodology

2.1. Classification of Typical Design Forms of Roofs

Shenzhen is one of the four largest economic cities in mainland China. It is a fast-growing city in terms of GDP as well as city infrastructure. Nationwide, it is an example for the rest of the nearly 700 Chinese cities. In the recent decade, it has embraced sustainability and won attention as a major national leader in green architecture. It has also invested in building up the cultural and higher education facilities through its Grande Project initiatives. Therefore, the roof geometries of Shenzhen’s 12 selected top cultural facilities were classified into 3 typical forms: flat roof, pyramidal roof, and curvilinear roof (including curve shapes) (

Table A1. Classification of roof geometry of Shenzhen top cultural facilities.

Roof Geometry		Project	Quantity
Flat		The Shenzhen Reform Exhibition Hall Source: Sou Fujimoto Architects	5
		The Guoshen Museum (Tentative Name) Source: Architectural Design Research Institute of SCUT Ltd.
		The Shenzhen Natural History Museum Source: Shenzhen Municipal Public Works Department
		The Shenzhen Art Museum Source: KSP Jürgen Engel Architekten International GmbH
		The Shenzhen Institute of Innovation and Design Source: Shenzhen Municipal Public Works Department
Pyramidal		The Shenzhen Financial and Cultural Center Source: Shenzhen Municipal Public Works Department	1
Curvilinear		The Shenzhen Opera House Source: Ateliers Jean Nouvel	6
		The Shenzhen Science and Technology Museum Source: Zaha Hadid Architects
		The Shenzhen Creative Design Museum Source: MAD and Proloog
		The Shenzhen Ocean Museum Source: SANAA
		The Shenzhen International Performing Arts Center Source: Ennead Architects
		The Shenzhen Conservatory of Music Source: Shenzhen Municipal Public Works Department

) for daylighting and energy performance simulations.

2.2. Modeling

The normalized roof forms were three simple boxes with different roof types representing the three primary roof forms of Shenzhen’s top cultural facilities: a flat roof, pyramidal roof, and curvilinear roof (

Table 3. Case selection and three typical models of roofs.

Representative Case	Normalization Process
The Shenzhen Reform and Opening Up Exhibition Hall (Source: Sou Fujimoto Architects and Donghua Chen Studio)	Flat roof Height: 50 m; roof area: 10,000 m2
The Shenzhen Financial and Cultural Center (Source: China Southwest Architectural Design and Research Institute and Swooding Architects)	Pyramidal roof Height: 50 m (25 + 25); roof Area: 11,180 m2
The Shenzhen Ocean Museum (Source: SANAA)	Curvilinear roof Height: 50 m (25 + 25); roof area: 13,172 m2

). The three case models are non-residential buildings with all-glazed roofs. In particular, in this study, we were concerned about the impact of different roof types and PV percentages of glazed roofs on energy performance and natural lighting, and PV panels are only set on all-glazed roofs. Therefore, for a valid comparison, the authors established three normalized models of different roof shapes with the same base area of 10,000 m² and a height of 50 m.

Table 4. Model parameters.

Roof Type (Front View)	Percentage of PV Panels to Roof Area
	0%	20%	30%	40%	50%	60%	70%	80%	90%
Flat roof
Pyramidal roof
Curvilinear roof

shows the different percentages of PV panels to the roof area, which were set from 0% to 90%, though 10% was omitted and not a typical case in this article. This is because such a low coverage rate of PV panels (i.e., 10%) on the roof cannot help to receive enough solar energy for the power supply. Meanwhile, it will increase the glaring probability. In this study, the monocrystalline silicon panel was used for its high photoelectric conversion efficiency. The same photovoltaic configuration was set for the three roof types. The reference PV cell used for the simulation was LG365N1C-A6 [53], and the relevant characteristics are presented in

Table 5. Characteristics of the PV modules used in this research.

Input	Description/Value
Mount type (configuration)	Close (flush) roof mount (PV array mounted parallel and relatively close to the plane of the roof (between 5 cm))
Width (cm)	4 cm
Module efficiency (%)	20%
Peak power (Pmax)	273 W
Temperature coefficient (percentage/deg. Celsius)	−0.5%/°C
Module active area percent (%)	100%

. The comparisons of daylight illuminance performance and energy performance between the different coverage of PV panels will be conducted in this study.

2.3. Climate Data

The case buildings are located in Shenzhen, China (22.62 N, 114.07 E). The solar energy in Shenzhen is extensive (Figure 6), with annual solar radiation of 1.41 MWh/m² [54]. As one of the first eight low-carbon pilot cities selected by the China National Development and Reform Commission in 2010, Shenzhen has led a number of urban low-carbon transformation initiatives [55]. Under the adverse environmental conditions of a hot summer and warm winter, the majority of the public buildings in Shenzhen are cooled by air conditioners from April to November [56]. Therefore, passive solar energy can be fully utilized in architectural design for energy saving and reduce carbon emissions.

2.4. Daylighting Performance Simulation

Daylight simulations were run through Grasshopper software with Daysim and Radiance via the Ladybug and Honeybee plug-ins. Useful daylight illuminance (UDI) is the most common dynamic indicator used to evaluate the supply of sunlight. According to published papers and reports [57,58,59], solar illuminance between 300 and 3000 lux is generally considered desirable. Illumination below 300 lux is generally regarded as insufficient illuminance, and illumination greater than 3000 lux may cause glare and visual discomfort. In this study, the three interval indicators were set to be less than 300 lux, 300–3000 lux, and more than 3000 lux, corresponding to the three situations of low daylighting, moderate daylighting, and possible glare. For the simulation schedule, the research took into consideration 365 days of the year but only the hours from 8:00 a.m. to 5:00 p.m. on typical working days. For the purpose of this study, the occlusion of surrounding buildings was not considered in the simulation to better evaluate the lighting and energy consumption of the different scenarios.

Table 6. Input details of building model.

Building Parameter	Unit	Value
Roof glazing type	mm	Double glazing (6, 12, and 6 mm)
Roof U-value	W/(m2·K)	1.8
Visible transmittance	-	0.8

shows the input details of the envelopes applied in this research.

2.5. Energy Performance Simulation

Energy performance simulations were run through Grasshopper software with Energy Plus via the Honeybee and Ladybug plug-ins. The model parameters of the energy simulation were set in accordance with the “Design Standard for Energy Efficiency of Public Buildings (GB 50189-2015)”, “Design code for heating ventilation and air conditioning of civil buildings”. and “Technical Standards for Nearly Zero Energy Buildings (GB/T 51350-2019)”:

• The lighting power density of the building was set to 9 W/m². When the indoor natural illuminance was lower than 300 lux, the lighting control system would automatically initiate artificial lighting;
• The COP of the cooling system was specified as 3.5;
• The per capita area of the room was set to 8 m² per person;
• The equipment load per area was set to 8 W/m²;
• The HVAC temperature set point was 26 °C.

3. Results and Discussion

The cultural facilities in Shenzhen are generally open from 9:00 a.m. to 6:00 p.m. Glazed roofs with different PV coverage ratios will change the amount of solar radiation entering the room, affecting daylighting and air conditioning loads. Increasing the PV panel area will reduce the amount of solar radiation entering the building, thereby reducing the cooling energy consumption in summer. Meanwhile, it may also increase the lighting energy consumption of the building. Thus, an energy balance study on buildings with different roof types and PV coverages was conducted in this section, considering the primary energy consumption for lighting and cooling and the power generation from PV panels.

3.1. Useful Daylight Illuminance Performance

Figure 7, Figure 8 and Figure 9 illustrate the relationship between the ratio of PV panels to the glazed roof area and useful daylight illuminance. Based on the simulation results of three different roof types, it can be seen that as the PV coverage ratio increased, the ratio of UDI for more than 3000 lux generally decreased gradually. Compared with the flat roof (Figure 7), the UDI values of the pyramidal roof (Figure 8) and curvilinear roof (Figure 9) were relatively high. This is because the building depths of the pyramidal roof and curvilinear roof are smaller than the flat roof under the same building height, which is more susceptible to glare. Furthermore, compared with the curvilinear roof, the glare range of the pyramidal roof was slightly higher, especially when the PV panels accounted for 40% or more of the roof area. This is related to the location of the PV panels. The PV panels on the pyramidal and flat roofs were evenly distributed, and the PV panels on the curvilinear roof were distributed downward from the center of the top (Table 4).

For UDI values in the range of 300–3000 lux, it can be seen that the value first increased and then decreased, and the changes were uneven. This was because as the PV coverage increased, part of the solar radiation was blocked, thereby affecting the natural lighting of the building. Unlike the flat roof and pyramidal roof, the curvilinear roof had an inflection point at 70% of the PV coverage, which was reduced from 73.6% to 43.9%. The flat roof and pyramidal roof showed an inflection point when the PV coverage reached 80% and then dropped from 75.58% to 40.15% and 70.69% to 62.13%, respectively. Compared with the pyramidal roof and curvilinear roof, the UDI of the flat roof had a relatively high value in 300–3000 lux, indicating that the flat roof had more comfortable daylighting.

For the range of insufficient illuminance (i.e., UDI less than 300 lux), it can be observed that as the PV coverage ratio increased, this ratio first remained stable and then increased sharply. Unlike the flat roof and curvilinear roof, the UDI value had a minor increase in this range for the pyramidal roof. This is because the pyramidal roof can form more diffuse reflections, allowing more soft natural light to enter the room, such as with the Louvre Pyramid designed by I.M. Pei. In particular, for the curvilinear roof, a relatively strong mutation occurred when the PV panel coverage reached 70% and above. This was due to the uneven coverage of PV panels on the curvilinear roof, which blocked a large amount of light from entering the building.

In summary, we infer that only a specific range of PV panel to glazed roof area ratios would provide adequate daylight and avoid glare. For the flat roof and curvilinear roof, when PV panels accounted for 60–80% of the glazed roof area, the illuminance range was more comfortable. For the pyramidal roof, the range was 70–90%. It can be seen that when the roof was made of all glass, the lower proportion of PV panels in the roof area would receive too much sunlight, therefore increasing the chance of uncomfortable glare.

3.2. Year-Round Energy Performance

3.2.1. Lighting Energy Consumption

Figure 10 shows the relationship between the lighting energy consumption and the PV panels’ coverage area ratio of the three different roof types. It can be seen that as the PV coverage ratio increased, the lighting energy consumption of the building was basically unchanged and then sharply increased. This was because that part of the sunlight was blocked from entering the room as the PV coverage area increased. When the UDI was less than 300 lux, artificial lighting would automatically turn on and generate lighting energy consumption. Compared with the flat roof and pyramidal roof (after 80% PV coverage), the lighting energy consumption of the curvilinear roof significantly increased after 70% PV coverage. This was due to the uneven distribution of PV panels on the top of the curvilinear roof, making the northeast part of the building allow less sunlight to enter the room and requiring more artificial lighting. At the same time, compared with the building with a pyramidal roof, the flat roof saw greater lighting energy consumption. This was because for the building with a flat roof, the range and time of UDIs less than 300 lux were higher, and more artificial lighting was required.

3.2.2. Cooling Energy Consumption

Regarding the PV panel area and cooling energy consumption on the glazed roof, the three roof types had a clearly observable negative nonlinear relationship (Figure 11); that is, the index of the latter decreased with the increase in the former, although the speed was different. In particular, a strong negative linear relationship was observed for the flat roof and pyramidal roof. Among them, the cooling energy consumption of the pyramidal roof was reduced from 525 MWh to 352 MWh. More specifically, this value remained constant at first and then decreased at a gradually decreasing rate. The cooling energy consumption of the flat roofs showed a clear downward trend from 546 MWh to 209 MWh. It can be seen that the increase in the percentage of PV panels in the area of the glazed roof had a greater impact on the cooling energy consumption of the flat roof and pyramidal roof. On the contrary, a weak correlation was observed for the building with a curvilinear roof. It can be seen that as the PV coverage ratio increased, the cooling energy consumption of the curvilinear roof changed slightly, and it was maintained at around 20,000 kWh before slowly decreasing. As the percentage of PV panels in the area of the glazed roof increased, the impact on its cooling energy consumption was not apparent. This phenomenon was due to the smaller shape coefficient of the building with a curvilinear roof. Compared with the buildings with flat roofs and pyramidal roofs, the heat dissipation area of the building envelope structure of the curvilinear roof was relatively small, and the energy-saving effect of the building was also better.

In general, when comparing the three types of roof forms, as the proportion of the PV in the glazed roof area increased, the cooling energy consumption decreased in the trend of flat > pyramidal > curvilinear, which was related to the building’s shape coefficient and the coverage ratio of the PV panels on the roofs.

3.2.3. PV Panel Power Generation

In this study, monocrystalline silicon panels were used, and the photoelectric conversion efficiency was set to 20%. Grasshopper and Ladybug plug-ins were used to simulate the solar harvesting potential of the roofs in the three cases in Shenzhen (Figure 12).

As shown in Figure 13, as the PV coverage ratio increased, the power generation of the three roof types gradually increased. Among them, the curvilinear roof with PV panels had the largest power generation, while the flat roof and pyramidal roof were almost the same. This was mainly attributed to the area of the PV panels and the difference in the average global solar radiation of different orientations in Shenzhen. In general, the power generation was proportional to the roof surface area. The curvilinear roof had the largest roof surface area (13,172 m²), absorbing more solar radiation. Hence, more electricity was generated. Meanwhile, the area of the pyramidal roof was 11,180 m², which was larger than the square roof area of 10,000 m², and the amount of power generated was not that different from that of the flat roof. According to the meteorological data and solar radiation simulation results in Shenzhen (Figure 12), the PV panels on the north side of the pyramidal roof received less solar radiation, which affected the total power generation.

However, it is worth noting that although the solar radiation received by the PV panels on the north and south sides of the roof was different, the irradiance changes along the pyramidal and curvilinear roof surfaces were insignificant. The irradiance on the north side of the roof was only about 20% lower than that on the south side. This is because Shenzhen is located in a subtropical low-latitude area, where the diffuse reflection of solar radiation is a large component. To support this, we compared the annual solar radiation and diffuse reflectance of the same building in a low-latitude city (Shenzhen, 22.62 N, 114.07 E) and a high-latitude city (Harbin, 45.45 N, 126.46 E) in China. The simulation results are shown in

Table 7. Radiation comparison between a low-latitude city and a high-latitude city.

Location	Sun Path and Diffuse Horizontal Radiation (21 Mar)	Radiation Analysis (1 Jan–31 Dec)
		Flat Roof	Pyramidal Roof	Curvilinear Roof
Low-latitude city (Shenzhen, 22.62 N, 114.07 E),
High-latitude city (Harbin, 45.45 N, 126.46 E)

. Compared with low-latitude cities, high-latitude regions had lower solar elevation angles, relatively less solar radiation, and diffuse reflection. When the building was located at high latitudes, the difference in solar radiation received on the north and south sides of the roof was greater. This means that the corresponding photovoltaic optimization design should be adopted for roofs in different regions. For low-latitude cities such as Shenzhen, the installation of PV panels was relatively less affected by the orientation of the roof.

In addition, carbon reduction benefits are also increasingly a global concern for combating climate change and checking greenhouse gas emissions. In this research, the carbon reduction was calculated using one of the baseline methodologies proposed by the UN Framework Convention on Climate Change (UNFCCC). As the grid-connected electricity generation from renewable sources (ACM0002) method proposed, the emission factor (EF) can be obtained by first taking the arithmetic mean of the operating margin (OM) and build margin (BM) [60]. Then, the annual equivalent carbon emission reduction can be obtained by multiplying the emission factor by the annual power generation of the PV panels. The formula can be expressed as

Eco₂ = EPV × EF = EPV × (OM × 0.5 + BM × 0.5)

(1)

where Eco₂ is the annual carbon emission reduction, EPV is the photovoltaic power generation, EF is the emissions factor, OM is the operating margin, and BM is the build margin.

Shenzhen belongs to the China Southern Grid. According to Equation (1) and

Table 8. Emissions factors for Chinese regional grids (2019).

Power Grid	EFgrid,OM Simple,y (tCO2/MWh)	EFgrid,BM,y (tCO2/MWh)
North China Grid	0.9419	0.4819
Northeast Grid	1.0826	0.2399
East China Grid	0.7921	0.3870
Central China Grid	0.8587	0.2854
Northwest Grid	0.8922	0.4407
Southern Grid	0.8042	0.2135

Source: Ministry of Ecology and Environment of the People’s Republic of China (2020) [61].

, it can be calculated that the EF of the research case was 0.5086. The carbon emissions reductions of the three study cases are shown in Figure 14.

In general, the carbon emission reductions were proportional to the PV panel area and power generation. These results show that the development of large-scale public building rooftop photovoltaics can effectively contribute to the reduction of carbon emissions and mitigation of global climate change.

3.3. Energy Balance

Energy balance is an important indicator for evaluating the efficiency of photovoltaic systems. It is an accounting of the energy input and output of a building over a period [62,63].

The integrated PV on the building envelope has multiple functions (e.g., energy generation, daylighting, and shading). The practical design of BIPV should not only consider the power generation but balancing the targeted conflicts (i.e., energy generation, energy consumption, glare, and daylighting). Hence, high coverage of BIPV on the roof may not be the best solution for building energy balance and carbon reduction during the entire building life cycle. The coverage of BIPV on the roof must consider the balance between the energy generated by the PV system and the end user’s energy consumption.

In this study, the energy balance was determined by comparing the building’s power generation with the end use energy consumption (Figure 15).

The end use energy includes lighting, air conditioning (only cooling, as there is no heating used in Shenzhen), and equipment energy (166,400 kWh). The simulation results were used for the calculation of the end use energy (Eend-use) according to Equation (2):

E_end-use = E_L + E_C + E_E

(2)

where E_end-use is the end use energy consumption, E_L is the total electrical energy used for lighting, E_C is the total electrical energy used for cooling, and E_E is the total electrical energy used for equipment energy.

Meanwhile, the power storage capacity (E_S) of the PV system is given by Equation (3) and corresponds to the photovoltaic power generation (E_PV) minus the end use energy consumption (E_end-use):

E_S = E_PV − E_end-use

(3)

where E_S is the power storage capacity, E_PV is the photovoltaic power generation, and E_end-use is the end use energy consumption.

The results indicate that the energy consumption of buildings can be very different and dependent on the roof form and PV panel coverage. It can be seen from Figure 14 that when the indoor artificial lighting operated in the automatic control mode, with the increase in the PV coverage ratio, the total energy consumption of a building with a flat roof decreased first and then increased, and the inflection point appeared near 80%. This is because PV panel coverage can bring shading effects to buildings in the summer, reducing the building’s cooling energy consumption. However, at the same time, too high of a PV coverage ratio will affect the indoor natural lighting, and artificial lighting will be turned on to supplement the range of insufficient lighting, thereby increasing the building’s lighting energy consumption. Meanwhile, as the PV ratio increased, power generation, power storage (power generation−power consumption), and carbon emission reductions gradually increased. Different from the flat roof, as the PV ratio increased, the total energy consumption of the building with a pyramidal roof was stable at the beginning and then decreased before increasing until around 80%. In contrast, the total energy consumption of the building with a curvilinear roof first decreased slowly and then increased, and the increase was more obvious.

On the other hand, consistent with the trend of the building with the flat roof, as the PV ratio increased, the power generation and storage power of the buildings with pyramidal and curvilinear roofs gradually increased, although their respective power consumptions changed significantly. This can be attributed to an order of magnitude in the difference between the power generation and energy consumption.

From a comparison of the three types of roof forms, it can be clearly seen that with the increase in the PV coverage ratio, the total energy consumption of each type of roof was affected differently. For example, at a 0% PV coverage ratio, the building with a flat roof consumed the largest energy consumption, followed by the pyramidal roof and curvilinear roof. When the PV coverage ratio was 80%, the building with a pyramidal roof was the largest energy consumer, and the energy consumption for the buildings with flat roofs and curvilinear roofs were almost the same, being much smaller than that for the building with a pyramidal roof. In general, the total energy consumption of the building with a curvilinear roof in this research model was always less than that of the flat roof and pyramidal roof. Moreover, it can also apparently be observed that regardless of the PV coverage ratio, the curvilinear roof had the largest power storage capacity, followed by the pyramidal roof and the flat roof. At the same time, when the proportion of the PV panel coverage in the roof area was 20% for the flat roof and pyramidal roof and about 10% for the curvilinear roof, the balance of supply and demand could be achieved. This shows that the curvilinear roof and related PV configuration shall be more cost-effective in the whole life cycle of the building.

In summary, when considering energy consumption and lighting comfort, for the flat roof and pyramidal roof, the recommended coverage area of PV panels is 80%. For the curvilinear roof, the recommended coverage area ratio of the PV panels is 70%. This is because for the curvilinear roof, the higher coverage area will lead to insufficient lighting and an increase in overall energy consumption. If the study’s buildings achieve the above suggested proportion of rooftop PV to replace the current fossil fuel power generation, then 1448–1553 tons of equivalent carbon emissions will be reduced per year.

3.4. Economic Analysis

The economic analysis included both the electricity subsidy benefits brought by the PV system and the system, operation, and maintenance costs. The net present value (NPV) represents the value of future savings from the PV system. The NPV is a monetary quantity determined by subtracting the initial investment cost from future benefits, which are the feed-in tariff subsidies for electricity generated by the PV systems in this study. The initial cost analysis considered the component costs and the annual operation and maintenance costs. As photovoltaic panels are exposed to the outdoors, components will experience aging and wear, which can affect the photoelectric conversion efficiency. Therefore, the attenuation rate of the photovoltaic modules is also an important factor to be considered. According to the literature research, the attenuation rate of components is generally about 2.5% in the first year and then attenuated by 0.7% per year [64]. The production cost of the PV modules and system equipment investment in China was nearly CNY 2/W and CNY 5/W [65] (USD 1 = CNY 6.89 in 2022, according to The World Bank), respectively. The cost of installing a PV panel on the roof is about CNY 0.4/W [64]. Therefore, the initial cost of rooftop PV in this study was CNY 7.4/W. The photovoltaic products selected in this study had a power of 273 W with module dimensions of 1740 mm × 1042 mm. For the convenience of calculation, the initial cost was converted into the cost per unit area, which was about CNY 1116/m². In addition, according to market research, the operation and maintenance costs are usually 1–3% of the initial cost. Considering that the operation and maintenance costs of the pyramidal roof and curvilinear roof will be higher, this study took 1%, 1.5%, and 2% as the annual operation and maintenance costs of the flat roof, pyramidal roof, and curvilinear roof, respectively, for prediction and calculation.

In this study, the PV equipment life cycle was considered to be 25 years. In 2021, the National Development and Reform Commission, the Ministry of Finance, and the National Energy Administration issued a notice on matters related to photovoltaic power generation. For distributed photovoltaic power generation projects that adopt the mode of “self-generated and self-consumption, and surplus electricity connected to the grid”, the subsidy standard for surplus electricity is CNY 0.32/kWh [66]. The authors assume that the subsidy remained constant over 25 years, and the formula for the NPV is as follows:

$$\mathrm{NPV} = \mathrm{Es} \times {\displaystyle \sum }_{i=1}^n(1-{\displaystyle \sum }_{i=1}^n{\alpha }_i\times \mathrm{P} - \mathrm{A} \times \left(1116\times \left(1+ \mathrm{m}\% \times \mathrm{n}\right)\right)$$

(4)

where E_S is the power storage capacity of the PV system if E_S > 0 (if otherwise, it is 0), P is the government subsidies for a PV project (CNY 0.32/kWh), n is the number of years (n <= 25), $\alpha$ is the attenuation rate of the PV module, A is the PV coverage area, and m is the PV panel maintenance fee for the three roof types (m = 1 for the flat roof, m = 1.5 for pyramidal roof, and m = 2 for curvilinear roof).

Figure 16, Figure 17 and Figure 18 show the NPVs for the three roof types with different PV coverage ratios. As can be seen from the figures, the flat roof with PV panels had the shortest payback period, and the cost could be recovered in the shortest time period of 15 years. For the pyramidal and curvilinear roofs, this value was 18 years. This is due to the lower operation and maintenance costs of the flat roof, and at the same time, the solar radiation received by the flat roof is stronger. Therefore, the PV panels on the flat roof have higher power generation per unit area. In terms of the coverage area of PV panels, the shortest payback period for the flat roof and pyramidal roof appeared at a 90% coverage area, and net profits of CNY 6.91 million and CNY 3.88 million, respectively, could be obtained in the whole life cycle (25th year). However, the shortest payback period of the curvilinear roof appeared at 70% of the coverage area, and the net profit of up to CNY 3.9 million could be obtained in the 25th year. This is due to the high cost of operating enclosures with curvilinear roofs. Meanwhile, for curvilinear roofs, the higher coverage area of PV panels will cause a serious shortage of indoor lighting, resulting in higher energy consumption. At the same time, when the PV coverage area exceeded 40%, 50%, and 30% of the flat roof, pyramidal roof, and curvilinear roof, respectively, the payback could be obtained in the whole life cycle of the PV panels.

In the actual project process, the installation fee, maintenance fee, and policy subsidy of the photovoltaic panels were not fixed, so the specific situation should be considered in combination with actual factors. In general, we should combine the economic profitability of PV panels with building energy savings, lighting comfort, and reductions in greenhouse gas emissions, thereby contributing to the process of urban sustainability.

4. Conclusions

This study investigated the relationship between the three fundamental roof geometries and energy balance design by comparing the different photovoltaic panel area coverage ratios and roof forms in terms of the energy use of the entire building. Three typical roof forms from 12 public building prototypes in Shenzhen were constructed and simulated by Rhino Grasshopper, Honeybee, and Ladybug. The relationship between the design of the combination of photovoltaic panels with different roofs and lighting and energy consumption was thus determined. The roof of the building was constructed in three different forms, and the ratio of the PV panels to the roof area was used as the independent variable of the simulation analysis. The impact of the building roof morphology on energy consumption was evaluated, the energy saving potential of roofs with different PV panel coverage ratios was explored, and the payback period of the PV panels was calculated.

The research result show the following: (1) combining PV panels with the transparent glazed roof will result in low heat transfer and prevent excessive solar radiation penetration and glare. (2) The roof shape has a large impact on carbon emissions and sustainable design. The curvilinear roof design provides the maximum potential for solar power generation when compared with the flat roof and pyramidal roof design patterns. (3) For buildings in Shenzhen, rooftop PV panels also have good energy potential toward the north side of the roof. This is because of the radiative nature of the low-latitude regions, which has a large diffuse component. (4) Supply and demand balance can be achieved when the coverage ratio of the PV panels is about 20% for flat roofs and pyramidal roofs and 10% for curvilinear roofs. Lastly, (5) considering energy consumption and lighting comfort, the recommended PV coverage area for the flat roof and pyramidal roof is 80%, which can obtain benefits of CNY 6.11 million and CNY 3.26 million, respectively, in the entire life cycle. For the curvilinear roof, the recommended coverage rate of photovoltaic panels is 70%, and CNY 3.9 million in income can be obtained throughout the life cycle.

The contributions of this study are as follows: (1) Optimization of the energy consumption and daylighting performance of PV roofs was combined with traditional passive building design factors, and the maximum energy saving potentials of different photovoltaic and building roof designs in Shenzhen area were determined. (2) Taking three roof models of typical public buildings in Shenzhen as an example, we conducted in-depth comparative modeling and simulations to illustrate the impact of the architectural form, urban environment, and PV panel coverage on end use energy consumption and comprehensively considered natural lighting, lighting, air conditioning load, equipment energy consumption, photovoltaic panel power generation, payback period, and other indicators. (3) This study inspires carbon-reducing sustainable designs for roof shapes. The main research results of this study will provide engineers, architects, and researchers with optimal selection suggestions when determining the coverage rate of PV panels for all-glazed roofs and comparing different design schemes, which will help to promote the decision-making process of green buildings and the large-scale promotion and application of photovoltaic roof integration. Finally, (4) the authors brought out a multi-criterion approach for the implementation of low-carbon design for engaging the geometry of roof shapes.